%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW233+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n006.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 18:18:55 EDT 2024

% Result   : Theorem 1.45s 1.65s
% Output   : Proof 1.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21  % Problem    : SWW233+1 : TPTP v8.2.0. Released v5.2.0.
% 0.12/0.22  % Command    : do_cvc5 %s %d
% 0.21/0.43  % Computer : n006.cluster.edu
% 0.21/0.43  % Model    : x86_64 x86_64
% 0.21/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.43  % Memory   : 8042.1875MB
% 0.21/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.21/0.43  % CPULimit   : 300
% 0.21/0.43  % WCLimit    : 300
% 0.21/0.43  % DateTime   : Sun May 26 06:06:39 EDT 2024
% 0.21/0.43  % CPUTime    : 
% 0.51/0.81  %----Proving TF0_NAR, FOF, or CNF
% 1.45/1.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.45/1.65  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.LgoljnD4e3/cvc5---1.0.5_20042.smt2
% 1.45/1.65  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.LgoljnD4e3/cvc5---1.0.5_20042.smt2
% 1.45/1.65  (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 1.45/1.65  (assume a1 (not (= tptp.v_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))
% 1.45/1.65  (assume a2 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))))
% 1.45/1.65  (assume a3 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)))
% 1.45/1.65  (assume a4 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)))
% 1.45/1.65  (assume a5 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))))
% 1.45/1.65  (assume a6 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))))
% 1.45/1.65  (assume a7 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z) (= V_z V_w)))))
% 1.45/1.65  (assume a8 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))))
% 1.45/1.65  (assume a9 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 1.45/1.65  (assume a10 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))
% 1.45/1.65  (assume a11 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 1.45/1.65  (assume a12 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (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))))))
% 1.45/1.65  (assume a13 (not (= tptp.v_cs____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))
% 1.45/1.65  (assume a14 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))))
% 1.45/1.65  (assume a15 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 1.45/1.65  (assume a16 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))))
% 1.45/1.65  (assume a17 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))))
% 1.45/1.65  (assume a18 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))))
% 1.45/1.65  (assume a19 (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__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))))
% 1.45/1.65  (assume a20 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))))
% 1.45/1.65  (assume a21 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 1.45/1.65  (assume a22 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 1.45/1.65  (assume a23 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 1.45/1.65  (assume a24 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 1.45/1.65  (assume a25 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 1.45/1.65  (assume a26 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 1.45/1.65  (assume a27 (forall ((T_a $$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)))))
% 1.45/1.65  (assume a28 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (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))))))
% 1.45/1.65  (assume a29 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 1.45/1.65  (assume a30 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 1.45/1.65  (assume a31 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a32 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 1.45/1.65  (assume a33 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (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))))))
% 1.45/1.65  (assume a34 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a35 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ab_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2)))))
% 1.45/1.65  (assume a36 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a37 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.45/1.65  (assume a38 (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 1.45/1.65  (assume a39 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.45/1.65  (assume a40 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))))
% 1.45/1.65  (assume a41 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a42 (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_w V_z)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z)))))
% 1.45/1.65  (assume a43 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 1.45/1.65  (assume a44 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 1.45/1.65  (assume a45 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 1.45/1.65  (assume a46 (forall ((V_ca_2 $$unsorted) (V_ab_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ab_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_ab_2)) (= V_b_2 V_ca_2)))))
% 1.45/1.65  (assume a47 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ca_2)) (= V_b_2 V_ca_2)))))
% 1.45/1.65  (assume a48 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.45/1.65  (assume a49 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oone T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.45/1.65  (assume a50 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 1.45/1.65  (assume a51 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.45/1.65  (assume a52 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.45/1.65  (assume a53 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ab_2)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a54 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 1.45/1.65  (assume a55 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 1.45/1.65  (assume a56 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a57 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_ab_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a58 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.45/1.65  (assume a59 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 1.45/1.65  (assume a60 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.45/1.65  (assume a61 (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__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.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 1.45/1.65  (assume a62 (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__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.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 1.45/1.65  (assume a63 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.45/1.65  (assume a64 (forall ((T_a $$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))))))
% 1.45/1.65  (assume a65 (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))))))
% 1.45/1.65  (assume a66 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a67 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a68 (forall ((T_a $$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)))))
% 1.45/1.65  (assume a69 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 1.45/1.65  (assume a70 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 1.45/1.65  (assume a71 (forall ((V_b $$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))))))
% 1.45/1.65  (assume a72 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a73 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))
% 1.45/1.65  (assume a74 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (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)))))))
% 1.45/1.65  (assume a75 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.45/1.65  (assume a76 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.45/1.65  (assume a77 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.45/1.65  (assume a78 (not (= (tptp.c_Polynomial_OpCons tptp.tc_Complex_Ocomplex tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))
% 1.45/1.65  (assume a79 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a80 (forall ((V_ab_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ab_2)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a81 (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))))
% 1.45/1.65  (assume a82 (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))))
% 1.45/1.65  (assume a83 (forall ((V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.45/1.65  (assume a84 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 1.45/1.65  (assume a85 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))))
% 1.45/1.65  (assume a86 (forall ((B_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_da____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_aa____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_OpCons tptp.tc_Complex_Ocomplex tptp.v_c____ tptp.v_cs____)) B_z))))))
% 1.45/1.65  (assume a87 (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.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (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__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)))))))))
% 1.45/1.65  (assume a88 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))))
% 1.45/1.65  (assume a89 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_ab_2)) V_e_2) V_db_2))))))
% 1.45/1.65  (assume a90 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2)) V_e_2) V_ca_2) V_db_2)))))
% 1.45/1.65  (assume a91 (forall ((V_db_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_ca_2 V_db_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 V_db_2))))))
% 1.45/1.65  (assume a92 (forall ((V_db_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_ca_2 V_db_2)) (= (= V_ab_2 V_b_2) (= V_ca_2 V_db_2))))))
% 1.45/1.65  (assume a93 (forall ((V_s $$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)))))))
% 1.45/1.65  (assume a94 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.45/1.65  (assume a95 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 1.45/1.65  (assume a96 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 1.45/1.65  (assume a97 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.45/1.65  (assume a98 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 1.45/1.65  (assume a99 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 1.45/1.65  (assume a100 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))))
% 1.45/1.65  (assume a101 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_b))))))
% 1.45/1.65  (assume a102 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)))))
% 1.45/1.65  (assume a103 (forall ((V_b $$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)))))
% 1.45/1.65  (assume a104 (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))))))
% 1.45/1.65  (assume a105 (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)))))
% 1.45/1.65  (assume a106 (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))))))
% 1.45/1.65  (assume a107 (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)))))
% 1.45/1.65  (assume a108 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)))))))
% 1.45/1.65  (assume a109 (forall ((V_ry $$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))))))
% 1.45/1.65  (assume a110 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 1.45/1.65  (assume a111 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a112 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.45/1.65  (assume a113 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 1.45/1.65  (assume a114 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 1.45/1.65  (assume a115 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 1.45/1.65  (assume a116 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 1.45/1.65  (assume a117 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 1.45/1.65  (assume a118 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 1.45/1.65  (assume a119 (forall ((V_a $$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))))))
% 1.45/1.65  (assume a120 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.45/1.65  (assume a121 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a122 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 1.45/1.65  (assume a123 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a124 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.45/1.65  (assume a125 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a126 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.45/1.65  (assume a127 (forall ((V_x_2 $$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))))))
% 1.45/1.65  (assume a128 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 1.45/1.65  (assume a129 (forall ((V_y_2 $$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))))))
% 1.45/1.65  (assume a130 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))))
% 1.45/1.65  (assume a131 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))))
% 1.45/1.65  (assume a132 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a133 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b))))))
% 1.45/1.65  (assume a134 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2)) V_e_2) V_ca_2) V_db_2)))))
% 1.45/1.65  (assume a135 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (= V_ca_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_ab_2)) V_e_2) V_db_2))))))
% 1.45/1.65  (assume a136 (forall ((V_b $$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)))))))
% 1.45/1.65  (assume a137 (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)))))))
% 1.45/1.65  (assume a138 (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)))))))
% 1.45/1.65  (assume a139 (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)))))))
% 1.45/1.65  (assume a140 (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)))))))
% 1.45/1.65  (assume a141 (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)))))))
% 1.45/1.65  (assume a142 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.45/1.65  (assume a143 (forall ((V_b $$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)))))))
% 1.45/1.65  (assume a144 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_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_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_ab_2))))))
% 1.45/1.65  (assume a145 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 1.45/1.65  (assume a146 (forall ((V_b $$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))))))
% 1.45/1.65  (assume a147 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a148 (forall ((V_b $$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)))))))
% 1.45/1.65  (assume a149 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.45/1.65  (assume a150 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2))))))
% 1.45/1.65  (assume a151 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_ab_2)))))))
% 1.45/1.65  (assume a152 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_ca_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_ab_2)))))))
% 1.45/1.65  (assume a153 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a154 (forall ((V_n $$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)))))))
% 1.45/1.65  (assume a155 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_y))))))
% 1.45/1.65  (assume a156 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))
% 1.45/1.65  (assume a157 (forall ((V_y_2 $$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)))))
% 1.45/1.65  (assume a158 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_b) V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)))))))
% 1.45/1.65  (assume a159 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a160 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a161 (forall ((V_ab_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_Osgn__class_Osgn T_a V_ab_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2)))))
% 1.45/1.65  (assume a162 (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)))))
% 1.45/1.65  (assume a163 (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)))))
% 1.45/1.65  (assume a164 (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))))))
% 1.45/1.65  (assume a165 (forall ((V_db_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_ab_2 V_b_2)) (not (= V_ca_2 V_db_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_db_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_db_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_ca_2))))))))
% 1.45/1.65  (assume a166 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.45/1.65  (assume a167 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))))
% 1.45/1.65  (assume a168 (forall ((V_za_2 $$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))))))
% 1.45/1.65  (assume a169 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_x))))
% 1.45/1.65  (assume a170 (forall ((V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_k) (tptp.c_Groups_Osgn__class_Osgn T_a V_k))))))
% 1.45/1.65  (assume a171 (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))))
% 1.45/1.65  (assume a172 (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))))
% 1.45/1.65  (assume a173 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (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_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ca_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_b_2 V_ab_2)) V_e_2) V_db_2))))))
% 1.45/1.65  (assume a174 (forall ((V_db_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (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_ab_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_db_2)) (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_ab_2 V_b_2)) V_e_2) V_ca_2) V_db_2)))))
% 1.45/1.65  (assume a175 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_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_ca_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 V_b_2))))))
% 1.45/1.65  (assume a176 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_ab_2))))))
% 1.45/1.65  (assume a177 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.45/1.65  (assume a178 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.45/1.65  (assume a179 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.45/1.65  (assume a180 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.45/1.65  (assume a181 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.45/1.65  (assume a182 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.45/1.65  (assume a183 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.45/1.65  (assume a184 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.45/1.65  (assume a185 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 1.45/1.65  (assume a186 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 1.45/1.65  (assume a187 (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)))))))
% 1.45/1.65  (assume a188 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 1.45/1.65  (assume a189 (forall ((V_y_2 $$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__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.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 1.45/1.65  (assume a190 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_za_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 1.45/1.65  (assume a191 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (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))))))
% 1.45/1.65  (assume a192 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_ab_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2)))))
% 1.45/1.65  (assume a193 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.45/1.65  (assume a194 (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))))
% 1.45/1.65  (assume a195 (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)))))
% 1.45/1.65  (assume a196 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_ab_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a197 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a198 (forall ((V_db_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_ca_2 V_db_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ca_2 V_db_2))))))
% 1.45/1.65  (assume a199 (forall ((V_x $$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_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a200 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 1.45/1.65  (assume a201 (forall ((V_b $$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))))
% 1.45/1.65  (assume a202 (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__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))))))
% 1.45/1.65  (assume a203 (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__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))))))
% 1.45/1.65  (assume a204 (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__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 1.45/1.65  (assume a205 (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__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 1.45/1.65  (assume a206 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.45/1.65  (assume a207 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (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))))))
% 1.45/1.65  (assume a208 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))))
% 1.45/1.65  (assume a209 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (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))))))
% 1.45/1.65  (assume a210 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 1.45/1.65  (assume a211 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (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))))))
% 1.45/1.65  (assume a212 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.45/1.65  (assume a213 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (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))))))
% 1.45/1.65  (assume a214 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 1.45/1.65  (assume a215 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (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)))))
% 1.45/1.65  (assume a216 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 1.45/1.65  (assume a217 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (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))))))
% 1.45/1.65  (assume a218 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))
% 1.45/1.65  (assume a219 (forall ((V_y_2 $$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.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (= V_x_2 V_y_2)))))))
% 1.45/1.65  (assume a220 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 1.45/1.65  (assume a221 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))))
% 1.45/1.65  (assume a222 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))
% 1.45/1.65  (assume a223 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a224 (forall ((V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a225 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a226 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a227 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a228 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a229 (forall ((V_b_2 $$unsorted) (V_ab_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_ab_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a230 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.45/1.65  (assume a231 (forall ((V_b $$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)))))))
% 1.45/1.65  (assume a232 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_ab_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_ab_2 V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a233 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_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_ca_2 V_ab_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ca_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a234 (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))))))
% 1.45/1.65  (assume a235 (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))))))
% 1.45/1.65  (assume a236 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.45/1.65  (assume a237 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 1.45/1.65  (assume a238 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 1.45/1.65  (assume a239 (forall ((V_b $$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))))))
% 1.45/1.65  (assume a240 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 1.45/1.65  (assume a241 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 1.45/1.65  (assume a242 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 1.45/1.65  (assume a243 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.45/1.65  (assume a244 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 1.45/1.65  (assume a245 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 1.45/1.65  (assume a246 (forall ((V_c $$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)))))
% 1.45/1.65  (assume a247 (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))))
% 1.45/1.65  (assume a248 (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))))
% 1.45/1.65  (assume a249 (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))))
% 1.45/1.65  (assume a250 (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))))
% 1.45/1.65  (assume a251 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted)) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ca_2) V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ca_2) V_b_2)) (= V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a252 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_ca_2 $$unsorted)) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ab_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b_2) V_ca_2)) (= V_ab_2 V_b_2)))))
% 1.45/1.65  (assume a253 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (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)))))
% 1.45/1.65  (assume a254 (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.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (not (= V_x_2 V_y_2))))))
% 1.45/1.65  (assume a255 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 1.45/1.65  (assume a256 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 1.45/1.65  (assume a257 (forall ((V_z $$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)))
% 1.45/1.65  (assume a258 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_w)))))
% 1.45/1.65  (assume a259 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a260 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 1.45/1.65  (assume a261 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.45/1.65  (assume a262 (forall ((V_a $$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)))))
% 1.45/1.65  (assume a263 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.45/1.65  (assume a264 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a265 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a266 (forall ((V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a267 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a268 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a269 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 1.45/1.65  (assume a270 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 1.45/1.65  (assume a271 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a272 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 1.45/1.65  (assume a273 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 1.45/1.65  (assume a274 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 1.45/1.65  (assume a275 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 1.45/1.65  (assume a276 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (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_ab_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.45/1.65  (assume a277 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ab_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b_2)))))))
% 1.45/1.65  (assume a278 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.45/1.65  (assume a279 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a280 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (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)))))))
% 1.45/1.65  (assume a281 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a282 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (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)))))))
% 1.45/1.65  (assume a283 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (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)))))))
% 1.45/1.65  (assume a284 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (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)))))))
% 1.45/1.65  (assume a285 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (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)))))))
% 1.45/1.65  (assume a286 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 1.45/1.65  (assume a287 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 1.45/1.65  (assume a288 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.45/1.65  (assume a289 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__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)))))))))
% 1.45/1.65  (assume a290 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 1.45/1.65  (assume a291 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (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__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))) (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))))))
% 1.45/1.65  (assume a292 (forall ((V_ab_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_ab_2 V_ab_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2)))))
% 1.45/1.65  (assume a293 (forall ((V_ab_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_ab_2 V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a294 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.45/1.65  (assume a295 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.45/1.65  (assume a296 (forall ((V_b $$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)))))))
% 1.45/1.65  (assume a297 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.45/1.65  (assume a298 (forall ((V_d $$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__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)))))))
% 1.45/1.65  (assume a299 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.45/1.65  (assume a300 (forall ((T_a $$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)))))
% 1.45/1.65  (assume a301 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (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)))))
% 1.45/1.65  (assume a302 (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))))))
% 1.45/1.65  (assume a303 (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))))))
% 1.45/1.65  (assume a304 (forall ((V_ab_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_ab_2)) (not (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a305 (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)))))
% 1.45/1.65  (assume a306 (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))))))
% 1.45/1.65  (assume a307 (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))))))
% 1.45/1.65  (assume a308 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 1.45/1.65  (assume a309 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.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)))))))
% 1.45/1.65  (assume a310 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.45/1.65  (assume a311 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.45/1.65  (assume a312 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.45/1.65  (assume a313 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.45/1.65  (assume a314 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a315 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a316 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) V_x)))))))
% 1.45/1.65  (assume a317 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (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__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (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)))))))
% 1.45/1.65  (assume a318 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.45/1.65  (assume a319 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (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))))))
% 1.45/1.65  (assume a320 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))))))
% 1.45/1.65  (assume a321 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (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)))))))
% 1.45/1.65  (assume a322 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring__abs T_a) (=> (and (or (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 1.45/1.65  (assume a323 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a324 (forall ((V_s $$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)))))))
% 1.45/1.65  (assume a325 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 1.45/1.65  (assume a326 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 1.45/1.65  (assume a327 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 1.45/1.65  (assume a328 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.45/1.65  (assume a329 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 1.45/1.65  (assume a330 (forall ((V_d $$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))))))
% 1.45/1.65  (assume a331 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))
% 1.45/1.65  (assume a332 (forall ((V_a $$unsorted) (V_d $$unsorted)) (=> (not (= tptp.v_cs____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (exists ((B_r $$unsorted)) (forall ((B_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_r (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_d (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_OpCons tptp.tc_Complex_Ocomplex V_a tptp.v_cs____)) B_z)))))))))
% 1.45/1.65  (assume a333 (not (forall ((B_r $$unsorted)) (not (forall ((B_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_r (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_da____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_aa____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_OpCons tptp.tc_Complex_Ocomplex tptp.v_c____ tptp.v_cs____)) B_z)))))))))
% 1.45/1.65  (assume a334 (forall ((V_x $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)))))))
% 1.45/1.65  (assume a335 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a336 (forall ((V_ra_2 $$unsorted) (V_ab_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x_2 V_ab_2)) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_ab_2 V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_ab_2 V_ra_2)))))))
% 1.45/1.65  (assume a337 (forall ((V_y $$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))))))
% 1.45/1.65  (assume a338 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2))) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.45/1.65  (assume a339 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y))))))
% 1.45/1.65  (assume a340 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a341 (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_b V_a)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_b)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_a))))
% 1.45/1.65  (assume a342 (forall ((V_z3 $$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)))))
% 1.45/1.65  (assume a343 (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))))
% 1.45/1.65  (assume a344 (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.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_g_2 V_f_2)))))))
% 1.45/1.65  (assume a345 (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)))))))
% 1.45/1.65  (assume a346 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_p))))
% 1.45/1.65  (assume a347 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) V_q))))
% 1.45/1.65  (assume a348 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.45/1.65  (assume a349 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_q) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.45/1.65  (assume a350 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_p))))
% 1.45/1.65  (assume a351 (forall ((V_q_2 $$unsorted) (V_b_2 $$unsorted) (V_pa_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_OpCons T_a V_ab_2 V_pa_2) (tptp.c_Polynomial_OpCons T_a V_b_2 V_q_2)) (and (= V_ab_2 V_b_2) (= V_pa_2 V_q_2))))))
% 1.45/1.65  (assume a352 (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pa_2) (tptp.c_Polynomial_Opoly T_a V_q_2)) (= V_pa_2 V_q_2)))))
% 1.45/1.65  (assume a353 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_p) (tptp.c_Polynomial_OpCons T_a V_b V_q)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q))))))
% 1.45/1.65  (assume a354 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_p) (tptp.c_Polynomial_OpCons T_a V_b V_q)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q))))))
% 1.45/1.65  (assume a355 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.45/1.65  (assume a356 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.45/1.65  (assume a357 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.45/1.65  (assume a358 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a359 (forall ((V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pa_2) (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.45/1.65  (assume a360 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.45/1.65  (assume a361 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (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))))))
% 1.45/1.65  (assume a362 (forall ((V_pa_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_OpCons T_a V_ab_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (and (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))))
% 1.45/1.65  (assume a363 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.45/1.65  (assume a364 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.45/1.65  (assume a365 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a366 (forall ((V_x_2 $$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)))))
% 1.45/1.65  (assume a367 (forall ((V_ab_2 $$unsorted) (V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pa_2) V_ab_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_ab_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.45/1.65  (assume a368 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a369 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 1.45/1.65  (assume a370 (forall ((T_a $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))
% 1.45/1.65  (assume a371 (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))))
% 1.45/1.65  (assume a372 (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))))
% 1.45/1.65  (assume a373 (forall ((V_n $$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)))
% 1.45/1.65  (assume a374 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a375 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 1.45/1.65  (assume a376 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_l_2) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))))
% 1.45/1.65  (assume a377 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))))
% 1.45/1.65  (assume a378 (forall ((V_k_2 $$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))))
% 1.45/1.65  (assume a379 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 1.45/1.65  (assume a380 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a381 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)))
% 1.45/1.65  (assume a382 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)))
% 1.45/1.65  (assume a383 (forall ((V_k $$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)))))
% 1.45/1.65  (assume a384 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2) V_i_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)))))
% 1.45/1.65  (assume a385 (forall ((V_k $$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)))))
% 1.45/1.65  (assume a386 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_r) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_q) V_r))))))
% 1.45/1.65  (assume a387 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a388 (forall ((V_n $$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))))
% 1.45/1.65  (assume a389 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a390 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.45/1.65  (assume a391 (forall ((V_m $$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)))))
% 1.45/1.65  (assume a392 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 1.45/1.65  (assume a393 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (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)))))
% 1.45/1.65  (assume a394 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 1.45/1.65  (assume a395 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.45/1.65  (assume a396 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a397 (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2)))))
% 1.45/1.65  (assume a398 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))))
% 1.45/1.65  (assume a399 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (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))))))
% 1.45/1.65  (assume a400 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))))
% 1.45/1.65  (assume a401 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a402 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))))
% 1.45/1.65  (assume a403 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 1.45/1.65  (assume a404 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.65  (assume a405 (forall ((V_k $$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))))
% 1.45/1.65  (assume a406 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 1.45/1.65  (assume a407 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))))
% 1.45/1.65  (assume a408 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))
% 1.45/1.65  (assume a409 (forall ((V_n $$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)))))
% 1.45/1.65  (assume a410 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.45/1.65  (assume a411 (forall ((V_k $$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))))
% 1.45/1.65  (assume a412 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.45/1.65  (assume a413 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 1.45/1.65  (assume a414 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 1.45/1.65  (assume a415 (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)))))
% 1.45/1.65  (assume a416 (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)))))
% 1.45/1.65  (assume a417 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))))
% 1.45/1.65  (assume a418 (forall ((V_l $$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))))))
% 1.45/1.65  (assume a419 (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (= V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))))))
% 1.45/1.65  (assume a420 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a421 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 1.45/1.65  (assume a422 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 1.45/1.65  (assume a423 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (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))))))
% 1.45/1.65  (assume a424 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))))
% 1.45/1.65  (assume a425 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_l))))))
% 1.45/1.65  (assume a426 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.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))))))
% 1.45/1.65  (assume a427 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a428 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (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))))
% 1.45/1.65  (assume a429 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))))
% 1.45/1.65  (assume a430 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (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)))))
% 1.45/1.65  (assume a431 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j)))))
% 1.45/1.65  (assume a432 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (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)))))
% 1.45/1.65  (assume a433 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a434 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))))
% 1.45/1.65  (assume a435 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))))
% 1.45/1.65  (assume a436 (forall ((V_n $$unsorted) (V_m $$unsorted)) (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)))
% 1.45/1.65  (assume a437 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m)))))
% 1.45/1.65  (assume a438 (forall ((V_m $$unsorted)) (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))))
% 1.45/1.65  (assume a439 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))))
% 1.45/1.65  (assume a440 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))))
% 1.45/1.65  (assume a441 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a442 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))))
% 1.45/1.65  (assume a443 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)))
% 1.45/1.65  (assume a444 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))))
% 1.45/1.65  (assume a445 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a446 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))))
% 1.45/1.65  (assume a447 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 1.45/1.65  (assume a448 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (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)))))
% 1.45/1.65  (assume a449 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 1.45/1.65  (assume a450 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (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)))))
% 1.45/1.65  (assume a451 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a452 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))
% 1.45/1.65  (assume a453 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))))
% 1.45/1.65  (assume a454 (forall ((V_k $$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)))))
% 1.45/1.65  (assume a455 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))))
% 1.45/1.65  (assume a456 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 1.45/1.65  (assume a457 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))))
% 1.45/1.65  (assume a458 (forall ((V_m $$unsorted) (V_n $$unsorted)) (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))))
% 1.45/1.65  (assume a459 (forall ((V_m $$unsorted) (V_n $$unsorted)) (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))))
% 1.45/1.65  (assume a460 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.65  (assume a461 (forall ((V_n $$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))))
% 1.45/1.65  (assume a462 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 1.45/1.65  (assume a463 (forall ((V_n $$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)))
% 1.45/1.65  (assume a464 (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.65  (assume a465 (forall ((V_m $$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)))
% 1.45/1.65  (assume a466 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 1.45/1.65  (assume a467 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a468 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.65  (assume a469 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.65  (assume a470 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a471 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a472 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a473 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a474 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a475 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a476 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a477 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m V_n)))))
% 1.45/1.65  (assume a478 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a479 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a480 (forall ((V_n_2 $$unsorted)) (= (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 1.45/1.65  (assume a481 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ab_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ab_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_ab_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))))
% 1.45/1.65  (assume a482 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ab_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ab_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_ab_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))
% 1.45/1.65  (assume a483 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a484 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 1.45/1.65  (assume a485 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 1.45/1.65  (assume a486 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a487 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a488 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a489 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a490 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (=> (tptp.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__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a491 (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)))))
% 1.45/1.65  (assume a492 (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))))))
% 1.45/1.65  (assume a493 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k))))))
% 1.45/1.65  (assume a494 (forall ((V_k $$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))))))
% 1.45/1.65  (assume a495 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 1.45/1.65  (assume a496 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (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_m_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_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_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_n_2))))))
% 1.45/1.65  (assume a497 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 1.45/1.65  (assume a498 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (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_m_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_n_2)) (= V_m_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_n_2))))))
% 1.45/1.65  (assume a499 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_i)) V_u) V_n))))))
% 1.45/1.65  (assume a500 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (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_m_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_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_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_n_2))))))
% 1.45/1.65  (assume a501 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2)))))
% 1.45/1.65  (assume a502 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))))
% 1.45/1.65  (assume a503 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a504 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (= V_m_2 V_n_2)))))
% 1.45/1.65  (assume a505 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 1.45/1.65  (assume a506 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 1.45/1.65  (assume a507 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a508 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 1.45/1.65  (assume a509 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a (tptp.c_Polynomial_OpCons T_a V_a V_p) V_q) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Polynomial_Opcompose T_a V_p V_q)))))))
% 1.45/1.65  (assume a510 (forall ((V_x $$unsorted)) (=> (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))))))
% 1.45/1.65  (assume a511 (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.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))))))))
% 1.45/1.65  (assume a512 (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.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))))))))
% 1.45/1.65  (assume a513 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.45/1.65  (assume a514 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.45/1.65  (assume a515 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))))
% 1.45/1.65  (assume a516 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_RComplete_Onatceiling V_y)))))
% 1.45/1.65  (assume a517 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.45/1.65  (assume a518 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q)) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.45/1.65  (assume a519 (forall ((V_x $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a520 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a521 (forall ((V_x $$unsorted)) (=> (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))))))
% 1.45/1.65  (assume a522 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 1.45/1.65  (assume a523 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y) (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)))))
% 1.45/1.65  (assume a524 (forall ((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__eq tptp.tc_Nat_Onat V_x V_y))))
% 1.45/1.65  (assume a525 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.45/1.65  (assume a526 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x))))
% 1.45/1.65  (assume a527 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_RComplete_Onatfloor V_y)))))
% 1.45/1.65  (assume a528 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.45/1.65  (assume a529 (forall ((V_x $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a530 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2))))
% 1.45/1.65  (assume a531 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_a)) (tptp.c_RComplete_Onatfloor V_b)) (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a) V_b)))))))
% 1.45/1.65  (assume a532 (forall ((V_y $$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)))))
% 1.45/1.65  (assume a533 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 1.45/1.65  (assume a534 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 1.45/1.65  (assume a535 (forall ((V_pa_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Polynomial_OpCons T_a V_ab_2 V_pa_2)) (or (tptp.c_Polynomial_Opos__poly T_a V_pa_2) (and (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ab_2)))))))
% 1.45/1.65  (assume a536 (forall ((V_p $$unsorted) (V_r $$unsorted)) (exists ((B_m $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_m) (forall ((B_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) V_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) B_z)) B_m)))))))
% 1.45/1.65  (assume a537 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))))
% 1.45/1.65  (assume a538 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))
% 1.45/1.65  (assume a539 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 1.45/1.65  (assume a540 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x))))
% 1.45/1.65  (assume a541 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))))
% 1.45/1.65  (assume a542 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 1.45/1.65  (assume a543 (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a544 (= (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)))
% 1.45/1.65  (assume a545 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a546 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 1.45/1.65  (assume a547 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 1.45/1.65  (assume a548 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.45/1.65  (assume a549 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.45/1.65  (assume a550 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.45/1.65  (assume a551 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.45/1.65  (assume a552 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))))
% 1.45/1.65  (assume a553 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)))))))
% 1.45/1.65  (assume a554 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))))
% 1.45/1.65  (assume a555 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_a) V_x_2 V_y_2) (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_y_2 V_x_2))))))
% 1.45/1.65  (assume a556 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_Polynomial_Opoly T_a) V_x_2 V_y_2) (or (= V_x_2 V_y_2) (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_y_2 V_x_2)))))))
% 1.45/1.65  (assume a557 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a558 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (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.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))))
% 1.45/1.65  (assume a559 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) V_x))))
% 1.45/1.65  (assume a560 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x) V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_RComplete_Onatfloor V_a)))))
% 1.45/1.65  (assume a561 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a))))
% 1.45/1.65  (assume a562 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 1.45/1.65  (assume a563 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)))))
% 1.45/1.65  (assume a564 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.45/1.65  (assume a565 (forall ((V_ab_2 $$unsorted) (V_x_2 $$unsorted)) (=> (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ab_2 (tptp.c_RComplete_Onatfloor V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_ab_2) V_x_2)))))
% 1.45/1.65  (assume a566 (forall ((V_ab_2 $$unsorted) (V_x_2 $$unsorted)) (=> (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2) V_ab_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_ab_2))))))
% 1.45/1.65  (assume a567 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a568 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 1.45/1.65  (assume a569 (forall ((V_x $$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.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)))))
% 1.45/1.65  (assume a570 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (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.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)))))
% 1.45/1.65  (assume a571 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (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.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)))))
% 1.45/1.65  (assume a572 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (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_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)))))
% 1.45/1.65  (assume a573 (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (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.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.45/1.65  (assume a574 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (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.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)))))
% 1.45/1.65  (assume a575 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (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_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)))))
% 1.45/1.65  (assume a576 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (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.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)))))))
% 1.45/1.65  (assume a577 (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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x B_y)) B_d) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_a B_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y V_b))))))))))
% 1.45/1.65  (assume a578 (forall ((V_pa_2 $$unsorted) (V_ab_2 $$unsorted) (T_a $$unsorted) (V_za_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (=> (= (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) V_za_2) V_za_2) (= (tptp.c_Polynomial_Opoly__rec T_a T_b V_za_2 V_f_2 (tptp.c_Polynomial_OpCons T_b V_ab_2 V_pa_2)) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 V_ab_2) V_pa_2) (tptp.c_Polynomial_Opoly__rec T_a T_b V_za_2 V_f_2 V_pa_2)))))))
% 1.45/1.65  (assume a579 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (exists ((B_k $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_k V_n_2) (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i B_k) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 1.45/1.65  (assume a580 (forall ((T_a $$unsorted) (V_za_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (=> (= (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) V_za_2) V_za_2) (= (tptp.c_Polynomial_Opoly__rec T_a T_b V_za_2 V_f_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) V_za_2)))))
% 1.45/1.65  (assume a581 (forall ((V_pa_2 $$unsorted) (V_ab_2 $$unsorted) (V_f_2 $$unsorted) (V_za_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (tptp.c_Polynomial_Opoly__rec T_a T_b V_za_2 V_f_2 (tptp.c_Polynomial_OpCons T_b V_ab_2 V_pa_2)) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 V_ab_2) V_pa_2) (tptp.c_If T_a (tptp.c_fequal V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) V_za_2 (tptp.c_Polynomial_Opoly__rec T_a T_b V_za_2 V_f_2 V_pa_2)))))))
% 1.45/1.65  (assume a582 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))
% 1.45/1.65  (assume a583 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 1.45/1.65  (assume a584 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 1.45/1.65  (assume a585 (forall ((V_z $$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))))))
% 1.45/1.65  (assume a586 (forall ((V_p $$unsorted) (V_z $$unsorted) (V_e $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_e) (exists ((B_d $$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_w $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w V_z))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w V_z)) B_d)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) B_w) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) V_z))) V_e))))))))
% 1.45/1.65  (assume a587 (forall ((V_b $$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.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a B_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y V_b))))))))))
% 1.45/1.65  (assume a588 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 1.45/1.65  (assume a589 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.45/1.65  (assume a590 (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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2 B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.hAPP V_X_2 V_M_2) (tptp.hAPP V_X_2 B_n))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((B_n $$unsorted)) (=> (tptp.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))))))))))
% 1.45/1.65  (assume a591 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (forall ((B_y $$unsorted)) (exists ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_x)))))))
% 1.45/1.65  (assume a592 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))
% 1.45/1.65  (assume a593 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m))))))))
% 1.45/1.65  (assume a594 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) V_n)))))
% 1.45/1.65  (assume a595 (forall ((V_X_2 $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) B_K))))))))
% 1.45/1.65  (assume a596 (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_q))))))
% 1.45/1.65  (assume a597 (forall ((V_n $$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)))))
% 1.45/1.65  (assume a598 (forall ((V_x $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) V_n)))))
% 1.45/1.65  (assume a599 (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))))))
% 1.45/1.65  (assume a600 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))))
% 1.45/1.65  (assume a601 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))))
% 1.45/1.65  (assume a602 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a603 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q))))))
% 1.45/1.65  (assume a604 (forall ((V_x $$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))))))
% 1.45/1.65  (assume a605 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 1.45/1.65  (assume a606 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))))
% 1.45/1.65  (assume a607 (forall ((V_n $$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)))))))
% 1.45/1.65  (assume a608 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2)) V_n_2)) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a609 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.45/1.65  (assume a610 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.65  (assume a611 (forall ((V_z $$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)))))
% 1.45/1.65  (assume a612 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 1.45/1.65  (assume a613 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n))))
% 1.45/1.65  (assume a614 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.45/1.65  (assume a615 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (= V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_n)))))
% 1.45/1.65  (assume a616 (forall ((V_p $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))))
% 1.45/1.65  (assume a617 (forall ((V_n $$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)))))))
% 1.45/1.65  (assume a618 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.45/1.65  (assume a619 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))
% 1.45/1.65  (assume a620 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.45/1.65  (assume a621 (forall ((V_n $$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)))))
% 1.45/1.65  (assume a622 (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)))))
% 1.45/1.65  (assume a623 (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))))
% 1.45/1.65  (assume a624 (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__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.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)))))))
% 1.45/1.65  (assume a625 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.45/1.65  (assume a626 (forall ((V_n $$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))))))
% 1.45/1.65  (assume a627 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.45/1.65  (assume a628 (forall ((V_n_2 $$unsorted) (V_ab_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_ab_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_ab_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.45/1.65  (assume a629 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_ab_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_ab_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_ab_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_ab_2) V_n_2)) (= V_m_2 V_n_2))))))
% 1.45/1.65  (assume a630 (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)))))
% 1.45/1.65  (assume a631 (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))))))
% 1.45/1.65  (assume a632 (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.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))))))
% 1.45/1.65  (assume a633 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.45/1.65  (assume a634 (forall ((V_n $$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)))))))
% 1.45/1.65  (assume a635 (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)))))))
% 1.45/1.65  (assume a636 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n)))))
% 1.45/1.65  (assume a637 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 1.45/1.65  (assume a638 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))))
% 1.45/1.65  (assume a639 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 1.45/1.65  (assume a640 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 1.45/1.65  (assume a641 (forall ((V_n $$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)))))))
% 1.45/1.65  (assume a642 (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))))))))
% 1.45/1.65  (assume a643 (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.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_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))))))))
% 1.45/1.65  (assume a644 (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__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (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))))))))
% 1.45/1.65  (assume a645 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_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_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 1.45/1.65  (assume a646 (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__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.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))))
% 1.45/1.65  (assume a647 (forall ((V_n $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) V_n)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 1.45/1.65  (assume a648 (forall ((T_a $$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))))))
% 1.45/1.65  (assume a649 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 1.45/1.65  (assume a650 (forall ((V_n $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (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))))
% 1.45/1.65  (assume a651 (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.45/1.65  (assume a652 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.45/1.65  (assume a653 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 1.45/1.65  (assume a654 (forall ((V_z $$unsorted)) (=> (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)))))
% 1.45/1.65  (assume a655 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.45/1.65  (assume a656 (forall ((V_za_2 $$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)))))
% 1.45/1.65  (assume a657 (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)))))
% 1.45/1.65  (assume a658 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))))
% 1.45/1.65  (assume a659 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 1.45/1.65  (assume a660 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_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))))))
% 1.45/1.65  (assume a661 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)))
% 1.45/1.65  (assume a662 (forall ((V_z $$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)))
% 1.45/1.65  (assume a663 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 1.45/1.65  (assume a664 (forall ((V_w $$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)))))
% 1.45/1.65  (assume a665 (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))))
% 1.45/1.65  (assume a666 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_z3)))))
% 1.45/1.65  (assume a667 (forall ((V_w_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_w_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2 V_w_2) (not (= V_za_2 V_w_2))))))
% 1.45/1.65  (assume a668 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 1.45/1.65  (assume a669 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))))
% 1.45/1.65  (assume a670 (forall ((V_k $$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)))))
% 1.45/1.65  (assume a671 (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 V_za_2))))
% 1.45/1.65  (assume a672 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (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))))
% 1.45/1.65  (assume a673 (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)))))
% 1.45/1.65  (assume a674 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (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))))
% 1.45/1.65  (assume a675 (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (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))))
% 1.45/1.65  (assume a676 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 1.45/1.65  (assume a677 (forall ((V_z2 $$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)))))
% 1.45/1.65  (assume a678 (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)))))
% 1.45/1.65  (assume a679 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)))
% 1.45/1.65  (assume a680 (forall ((V_z $$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)))
% 1.45/1.65  (assume a681 (forall ((V_ab_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_ab_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)))
% 1.45/1.65  (assume a682 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d)) V_z))))
% 1.45/1.65  (assume a683 (forall ((V_x $$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))))))
% 1.45/1.65  (assume a684 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_q))))))
% 1.45/1.65  (assume a685 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)))
% 1.45/1.65  (assume a686 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))))
% 1.45/1.65  (assume a687 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))))
% 1.45/1.65  (assume a688 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))))
% 1.45/1.65  (assume a689 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (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)))))
% 1.45/1.65  (assume a690 (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))))
% 1.45/1.65  (assume a691 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))))
% 1.45/1.65  (assume a692 (forall ((V_z3 $$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)))))
% 1.45/1.65  (assume a693 (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.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.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))))
% 1.45/1.65  (assume a694 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H)))))))
% 1.45/1.65  (assume a695 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H)))))))))
% 1.45/1.65  (assume a696 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (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.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.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))
% 1.45/1.65  (assume a697 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.45/1.65  (assume a698 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_q_H))))))
% 1.45/1.65  (assume a699 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 1.45/1.65  (assume a700 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)))))
% 1.45/1.65  (assume a701 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y))))))
% 1.45/1.65  (assume a702 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y))))))
% 1.45/1.65  (assume a703 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 1.45/1.65  (assume a704 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 1.45/1.65  (assume a705 (forall ((V_x $$unsorted) (V_y $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y))) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x)) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a706 (forall ((V_n $$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.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a)))))
% 1.45/1.65  (assume a707 (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.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))))))))
% 1.45/1.65  (assume a708 (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))))
% 1.45/1.65  (assume a709 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.45/1.65  (assume a710 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Nat__Transfer_Otsub V_x V_y))))))
% 1.45/1.65  (assume a711 (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))
% 1.45/1.65  (assume a712 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y)))))
% 1.45/1.65  (assume a713 (forall ((V_X_2 $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) V_K_2)) (tptp.c_SEQ_OBseq T_a V_X_2))))))
% 1.45/1.65  (assume a714 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_db_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_db_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x V_db_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_x $$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_db_2)))))))))))
% 1.45/1.65  (assume a715 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_db_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_db_2) (=> (forall ((B_x $$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_db_2))))) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_db_2)))))))))))
% 1.45/1.65  (assume a716 (forall ((V_a $$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 $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_y) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_y) V_n) V_a)) (= B_y B_x)))))))))
% 1.45/1.65  (assume a717 (forall ((V_a $$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)))))))
% 1.45/1.65  (assume a718 (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.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Transcendental_Oln V_x))))))
% 1.45/1.65  (assume a719 (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.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n))))))))
% 1.45/1.65  (assume a720 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) V_x))))
% 1.45/1.65  (assume a721 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2))))))
% 1.45/1.65  (assume a722 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 1.45/1.65  (assume a723 (= (tptp.c_Transcendental_Oln (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 1.45/1.65  (assume a724 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 1.45/1.65  (assume a725 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (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)))))
% 1.45/1.65  (assume a726 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)))))
% 1.45/1.65  (assume a727 (forall ((V_x_2 $$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)))))
% 1.45/1.65  (assume a728 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.45/1.65  (assume a729 (forall ((V_x_2 $$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))))))
% 1.45/1.65  (assume a730 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.45/1.65  (assume a731 (forall ((V_x $$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)))))
% 1.45/1.65  (assume a732 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)))))
% 1.45/1.65  (assume a733 (forall ((V_x_2 $$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__eq 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__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 1.45/1.65  (assume a734 (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)))))))
% 1.45/1.65  (assume a735 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)) V_x))))
% 1.45/1.65  (assume a736 (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)))
% 1.45/1.65  (assume a737 (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_n_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_n_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP V_f_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_i (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hAPP V_f_2 B_i))) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 (tptp.hAPP V_f_2 V_n_2)) (exists ((B_i $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i V_n_2) (= (tptp.hAPP V_f_2 B_i) V_k_2))))))))
% 1.45/1.65  (assume a738 (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)))))
% 1.45/1.65  (assume a739 (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_n_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_n_2) (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.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.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 (tptp.hAPP V_f_2 V_n_2)) (exists ((B_i $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i V_n_2) (= (tptp.hAPP V_f_2 B_i) V_k_2))))))))
% 1.45/1.65  (assume a740 (forall ((V_K_2 $$unsorted) (V_X_2 $$unsorted) (V_N_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_N_2 B_n) (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)))))
% 1.45/1.65  (assume a741 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (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.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 1.45/1.65  (assume a742 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (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.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 1.45/1.65  (assume a743 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a744 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))))
% 1.45/1.65  (assume a745 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))))
% 1.45/1.65  (assume a746 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.45/1.65  (assume a747 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))))
% 1.45/1.65  (assume a748 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))))
% 1.45/1.65  (assume a749 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))))
% 1.45/1.65  (assume a750 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))))
% 1.45/1.65  (assume a751 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a752 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a753 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a754 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))))
% 1.45/1.65  (assume a755 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))))
% 1.45/1.65  (assume a756 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a757 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.65  (assume a758 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a759 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc V_m))))
% 1.45/1.65  (assume a760 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.45/1.65  (assume a761 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.45/1.65  (assume a762 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a763 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 1.45/1.65  (assume a764 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a765 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))))
% 1.45/1.65  (assume a766 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 1.45/1.65  (assume a767 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 1.45/1.65  (assume a768 (forall ((V_n_2 $$unsorted) (V_ab_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_ab_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP (tptp.hAPP V_times_2 V_ab_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_ab_2) V_n_2)))))
% 1.45/1.65  (assume a769 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 1.45/1.65  (assume a770 (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))))
% 1.45/1.65  (assume a771 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a772 (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a773 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 1.45/1.65  (assume a774 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a775 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (= V_m_2 V_n_2))))
% 1.45/1.65  (assume a776 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a777 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a778 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))))
% 1.45/1.65  (assume a779 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))))
% 1.45/1.65  (assume a780 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= (tptp.c_Nat_OSuc V_m) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n)))))
% 1.45/1.65  (assume a781 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a782 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))))
% 1.45/1.65  (assume a783 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))))
% 1.45/1.65  (assume a784 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 1.45/1.65  (assume a785 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))))
% 1.45/1.65  (assume a786 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))))
% 1.45/1.65  (assume a787 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))))
% 1.45/1.65  (assume a788 (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))))
% 1.45/1.65  (assume a789 (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))))
% 1.45/1.65  (assume a790 (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a791 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.45/1.65  (assume a792 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.45/1.65  (assume a793 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (or (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.45/1.65  (assume a794 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))))
% 1.45/1.65  (assume a795 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a796 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))))
% 1.45/1.65  (assume a797 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q))))))
% 1.45/1.65  (assume a798 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 1.45/1.65  (assume a799 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 1.45/1.65  (assume a800 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a)))))
% 1.45/1.65  (assume a801 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.45/1.65  (assume a802 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a803 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a804 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.65  (assume a805 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.65  (assume a806 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))))
% 1.45/1.65  (assume a807 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))))
% 1.45/1.65  (assume a808 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 (tptp.c_Nat_OSuc V_n_2))))))
% 1.45/1.65  (assume a809 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 1.45/1.65  (assume a810 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a811 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)) (= V_m (tptp.c_Nat_OSuc V_n))))))
% 1.45/1.65  (assume a812 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a813 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))))
% 1.45/1.65  (assume a814 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.65  (assume a815 (forall ((V_m_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_m_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.45/1.65  (assume a816 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a817 (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__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.c_Nat_OSuc V_n))) (=> (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__eq T_a V_a V_b))))))
% 1.45/1.65  (assume a818 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (= V_a V_b)))))))
% 1.45/1.65  (assume a819 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)))))))
% 1.45/1.65  (assume a820 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.45/1.65  (assume a821 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))))
% 1.45/1.65  (assume a822 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.45/1.65  (assume a823 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) V_n))))
% 1.45/1.65  (assume a824 (forall ((V_i $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_i)) V_n))))
% 1.45/1.65  (assume a825 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)))))
% 1.45/1.65  (assume a826 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)))))
% 1.45/1.65  (assume a827 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (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_m (tptp.c_Nat_OSuc (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_m V_k) (tptp.c_Nat_OSuc V_j))))))
% 1.45/1.65  (assume a828 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m))))))
% 1.45/1.65  (assume a829 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.45/1.65  (assume a830 (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.45/1.65  (assume a831 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_i) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)))))
% 1.45/1.65  (assume a832 (forall ((V_n $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_r (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_r) (tptp.c_Nat_OSuc V_n)) V_r))))))
% 1.45/1.65  (assume a833 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.45/1.65  (assume a834 (forall ((V_y $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_p V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_p)) (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_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_p))) V_y))))))
% 1.45/1.65  (assume a835 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))))
% 1.45/1.65  (assume a836 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 1.45/1.65  (assume a837 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n)) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))))))
% 1.45/1.65  (assume a838 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 1.45/1.65  (assume a839 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 1.45/1.65  (assume a840 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y))))))
% 1.45/1.65  (assume a841 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n))) V_y))))))))
% 1.45/1.65  (assume a842 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))))
% 1.45/1.65  (assume a843 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.45/1.65  (assume a844 (forall ((V_a $$unsorted)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 1.45/1.65  (assume a845 (forall ((V_ab_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_ab_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a846 (forall ((V_ab_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_ab_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_ab_2)))))
% 1.45/1.65  (assume a847 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a848 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y))))))
% 1.45/1.65  (assume a849 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a850 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a851 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.45/1.65  (assume a852 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 1.45/1.65  (assume a853 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 1.45/1.65  (assume a854 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 1.45/1.65  (assume a855 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) V_a)))))
% 1.45/1.65  (assume a856 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) V_a)))))
% 1.45/1.65  (assume a857 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (and (=> (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.45/1.65  (assume a858 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a V_a_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))))))
% 1.45/1.65  (assume a859 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a V_a_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b))))))
% 1.45/1.65  (assume a860 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_a) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a861 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))))))
% 1.45/1.65  (assume a862 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a863 (forall ((V_ab_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_ab_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_ab_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a864 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a V_b) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a865 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.45/1.65  (assume a866 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H)))))))
% 1.45/1.65  (assume a867 (forall ((V_b_2 $$unsorted) (V_ab_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_ab_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_ab_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_2 V_ab_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2))))))
% 1.45/1.65  (assume a868 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_i_2)))))
% 1.45/1.65  (assume a869 (forall ((V_ab_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_ab_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_ab_2)))))
% 1.45/1.65  (assume a870 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_i_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i_2 V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_i_2))))))
% 1.45/1.65  (assume a871 (forall ((V_k $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_k) V_x)))))
% 1.45/1.65  (assume a872 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)))))
% 1.45/1.65  (assume a873 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.45/1.65  (assume a874 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.45/1.65  (assume a875 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.45/1.65  (assume a876 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.45/1.65  (assume a877 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i)))))))))
% 1.45/1.65  (assume a878 (forall ((V_r_1 $$unsorted) (V_y $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_y) V_r_1)) (=> (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_1 V_b_1))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_1 V_r_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 1.45/1.65  (assume a879 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n))))))))
% 1.45/1.65  (assume a880 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 1.45/1.65  (assume a881 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)))
% 1.45/1.65  (assume a882 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.45/1.65  (assume a883 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.45/1.65  (assume a884 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.65  (assume a885 (forall ((V_a $$unsorted)) (and (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a))))
% 1.45/1.65  (assume a886 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c))))
% 1.45/1.65  (assume a887 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 1.45/1.65  (assume a888 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 1.45/1.65  (assume a889 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 1.45/1.65  (assume a890 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 1.45/1.65  (assume a891 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) V_a))))
% 1.45/1.65  (assume a892 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_k) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n V_k)))))
% 1.45/1.65  (assume a893 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) V_m)))
% 1.45/1.65  (assume a894 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 1.45/1.66  (assume a895 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (and (=> (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))))
% 1.45/1.66  (assume a896 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z)) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_z)))))
% 1.45/1.66  (assume a897 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_H V_b_H) V_c)))))))
% 1.45/1.66  (assume a898 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 1.45/1.66  (assume a899 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 1.45/1.66  (assume a900 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a901 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 1.45/1.66  (assume a902 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a903 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.45/1.66  (assume a904 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.45/1.66  (assume a905 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.45/1.66  (assume a906 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_H V_b_H) V_c)))))))
% 1.45/1.66  (assume a907 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 1.45/1.66  (assume a908 (forall ((V_m $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_y V_m)) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 1.45/1.66  (assume a909 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a910 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 1.45/1.66  (assume a911 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a912 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.45/1.66  (assume a913 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.45/1.66  (assume a914 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b_H) V_c)))))))
% 1.45/1.66  (assume a915 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c)))))
% 1.45/1.66  (assume a916 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c))))
% 1.45/1.66  (assume a917 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c)))))
% 1.45/1.66  (assume a918 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))))))
% 1.45/1.66  (assume a919 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a920 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 1.45/1.66  (assume a921 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c))))
% 1.45/1.66  (assume a922 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.45/1.66  (assume a923 (forall ((V_db_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m_2 V_db_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_db_2) B_q))))))
% 1.45/1.66  (assume a924 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.45/1.66  (assume a925 (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.45/1.66  (assume a926 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.66  (assume a927 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.45/1.66  (assume a928 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.66  (assume a929 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.66  (assume a930 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.66  (assume a931 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_k) V_m))))
% 1.45/1.66  (assume a932 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_y))))))
% 1.45/1.66  (assume a933 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 1.45/1.66  (assume a934 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b))))
% 1.45/1.66  (assume a935 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.45/1.66  (assume a936 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m)) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y) V_m))))
% 1.45/1.66  (assume a937 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_m))))))
% 1.45/1.66  (assume a938 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m) V_n) V_m))))
% 1.45/1.66  (assume a939 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) V_n) V_m))))
% 1.45/1.66  (assume a940 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.66  (assume a941 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 1.45/1.66  (assume a942 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 1.45/1.66  (assume a943 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b)))))
% 1.45/1.66  (assume a944 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a V_b) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 1.45/1.66  (assume a945 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.45/1.66  (assume a946 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 1.45/1.66  (assume a947 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_a) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 1.45/1.66  (assume a948 (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 1.45/1.66  (assume a949 (forall ((V_k $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 1.45/1.66  (assume a950 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 1.45/1.66  (assume a951 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 1.45/1.66  (assume a952 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) V_n)))))
% 1.45/1.66  (assume a953 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n)))))
% 1.45/1.66  (assume a954 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n))))))))
% 1.45/1.66  (assume a955 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))))
% 1.45/1.66  (assume a956 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_k_2) (=> (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) B_i) B_j)) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))))))))
% 1.45/1.66  (assume a957 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b))))))
% 1.45/1.66  (assume a958 (forall ((V_m_2 $$unsorted) (V_q_2 $$unsorted) (V_n_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (= (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_q_2) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) (tptp.c_Nat_OSuc V_q_2)))) (= V_q_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 1.45/1.66  (assume a959 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m_2 V_n_2))) (or (and (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (exists ((B_q $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) B_q) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) (tptp.c_Nat_OSuc B_q))) (tptp.hBOOL (tptp.hAPP V_P_2 B_q))))))))
% 1.45/1.66  (assume a960 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))))
% 1.45/1.66  (assume a961 (forall ((V_y $$unsorted) (V_q_1 $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_q_1) V_y)) (=> (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_b_1))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 1.45/1.66  (assume a962 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.45/1.66  (assume a963 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r)))))))
% 1.45/1.66  (assume a964 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)))))))
% 1.45/1.66  (assume a965 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r)))))))
% 1.45/1.66  (assume a966 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j)))))))))
% 1.45/1.66  (assume a967 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 1.45/1.66  (assume a968 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 1.45/1.66  (assume a969 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_y) (= (tptp.c_RComplete_Onatfloor (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_y))) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_y))))))
% 1.45/1.66  (assume a970 (forall ((V_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_Complex_Ocis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n))) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) (tptp.c_Complex_Ocis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a))))))
% 1.45/1.66  (assume a971 (forall ((V_c $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_a) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) V_c)))))
% 1.45/1.66  (assume a972 (forall ((V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_d) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_d)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_x V_d)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_x V_d)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_d)))))))
% 1.45/1.66  (assume a973 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_b)))))
% 1.45/1.66  (assume a974 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_z)) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 1.45/1.66  (assume a975 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c)))))
% 1.45/1.66  (assume a976 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.66  (assume a977 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))
% 1.45/1.66  (assume a978 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n)))))
% 1.45/1.66  (assume a979 (forall ((V_x $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n V_x)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)))))
% 1.45/1.66  (assume a980 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c)))))
% 1.45/1.66  (assume a981 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m)))
% 1.45/1.66  (assume a982 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))
% 1.45/1.66  (assume a983 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))
% 1.45/1.66  (assume a984 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n))))))
% 1.45/1.66  (assume a985 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m))))
% 1.45/1.66  (assume a986 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n) V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n))))
% 1.45/1.66  (assume a987 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.45/1.66  (assume a988 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 1.45/1.66  (assume a989 (forall ((V_db_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m_2 V_db_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_db_2) B_q))))))
% 1.45/1.66  (assume a990 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_n))))
% 1.45/1.66  (assume a991 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))))
% 1.45/1.66  (assume a992 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.45/1.66  (assume a993 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n))))
% 1.45/1.66  (assume a994 (forall ((V_h $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)) V_h) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d) V_h)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c) V_h)) V_d))))))
% 1.45/1.66  (assume a995 (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__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_n))))
% 1.45/1.66  (assume a996 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n) V_m)) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))))
% 1.45/1.66  (assume a997 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a998 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a999 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1000 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1001 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1002 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 1.45/1.66  (assume a1003 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 1.45/1.66  (assume a1004 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 1.45/1.66  (assume a1005 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1006 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1007 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1008 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1009 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1010 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1011 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1012 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1013 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1014 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1015 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1016 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1017 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1018 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1019 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1020 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1021 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1022 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1023 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1024 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1025 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1026 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1027 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1028 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1029 (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1030 (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1031 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1032 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1033 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1034 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1035 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1036 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1037 (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1038 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1039 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1040 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1041 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1042 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1043 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1044 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1045 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1046 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1047 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1048 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1049 (tptp.class_Divides_Oring__div tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1050 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1051 (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1052 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1053 (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1054 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1055 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1056 (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1057 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1058 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1059 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1060 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1061 (tptp.class_Rings_Oidom tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1062 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 1.45/1.66  (assume a1063 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1064 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1065 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1066 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1067 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1068 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1069 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1070 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1071 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1072 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1073 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1074 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1075 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1076 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1077 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1078 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1079 (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1080 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1081 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1082 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1083 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1084 (tptp.class_Divides_Osemiring__div tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1085 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1086 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1087 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1088 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1089 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1090 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1091 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1092 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1093 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1094 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1095 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1096 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1097 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1098 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 1.45/1.66  (assume a1099 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 1.45/1.66  (assume a1100 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 1.45/1.66  (assume a1101 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 1.45/1.66  (assume a1102 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1103 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1104 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1105 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1106 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1107 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1108 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1109 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1110 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1111 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1112 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1113 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1114 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1115 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1116 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1117 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1118 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1119 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1120 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1121 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1122 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1123 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1124 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1125 (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1126 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1127 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1128 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1129 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1130 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1131 (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1132 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1133 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1134 (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1135 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1136 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1137 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1138 (tptp.class_RealVector_Oreal__field tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1139 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1140 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1141 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1142 (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1143 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1144 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1145 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1146 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1147 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1148 (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1149 (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1150 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1151 (tptp.class_Rings_Ocomm__ring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1152 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1153 (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1154 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1155 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1156 (tptp.class_Groups_Osgn__if tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1157 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1158 (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1159 (tptp.class_Power_Opower tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1160 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1161 (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1162 (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1163 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 1.45/1.66  (assume a1164 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1165 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1166 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1167 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1168 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1169 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1170 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1171 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1172 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1173 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1174 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1175 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1176 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1177 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1178 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1179 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1180 (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1181 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1182 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1183 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1184 (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1185 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1186 (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1187 (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1188 (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1189 (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1190 (tptp.class_Rings_Ocomm__ring tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1191 (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1192 (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1193 (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1194 (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1195 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1196 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1197 (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1198 (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1199 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex))
% 1.45/1.66  (assume a1200 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1201 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1202 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1203 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1204 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1205 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1206 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1207 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1208 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1209 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1210 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1211 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1212 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1213 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1214 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1215 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__comm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1216 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1217 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1218 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1219 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1220 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1221 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1222 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1223 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1224 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1225 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring__abs (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1226 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1227 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1228 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1229 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1230 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1231 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1232 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1233 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1234 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1235 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1236 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1237 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1238 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1239 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1240 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1241 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1242 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1243 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1244 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1245 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1246 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1247 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1248 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1249 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1250 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oord (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1251 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Osgn__if (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1252 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1253 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1254 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1255 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Oring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1256 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1257 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))))
% 1.45/1.66  (assume a1258 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.c_fequal V_x_2 V_y_2))) (= V_x_2 V_y_2))))
% 1.45/1.66  (assume a1259 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.c_fequal V_x_2 V_y_2)))))
% 1.45/1.66  (assume a1260 (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))))
% 1.45/1.66  (assume a1261 true)
% 1.45/1.66  (step t1 (cl (not (= (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))))) (not (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule equiv_pos2)
% 1.45/1.66  (step t2 (cl (= (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule refl)
% 1.45/1.66  (step t3 (cl (= (= (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) true) (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule equiv_simplify)
% 1.45/1.66  (step t4 (cl (not (= (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) true)) (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule equiv1 :premises (t3))
% 1.45/1.66  (step t5 (cl (= (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))))) :rule all_simplify)
% 1.45/1.66  (step t6 (cl (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule refl)
% 1.45/1.66  (step t7 (cl (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule all_simplify)
% 1.45/1.66  (step t8 (cl (= (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule cong :premises (t6 t7))
% 1.45/1.66  (step t9 (cl (= (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) true)) :rule all_simplify)
% 1.45/1.66  (step t10 (cl (= (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) true)) :rule trans :premises (t8 t9))
% 1.45/1.66  (step t11 (cl (= (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) true)) :rule trans :premises (t5 t10))
% 1.45/1.66  (step t12 (cl (= (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule resolution :premises (t4 t11))
% 1.45/1.66  (step t13 (cl (= (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule refl)
% 1.45/1.66  (step t14 (cl (= (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))))) :rule cong :premises (t2 t12 t13))
% 1.45/1.66  (step t15 (cl (not (= (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))))) (not (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule equiv_pos2)
% 1.45/1.66  (step t16 (cl (= (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule refl)
% 1.45/1.66  (step t17 (cl (= (= (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))))) :rule equiv_simplify)
% 1.45/1.66  (step t18 (cl (= (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (not (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))))) :rule equiv2 :premises (t17))
% 1.45/1.66  (step t19 (cl (not (not (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))))) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule not_not)
% 1.45/1.66  (step t20 (cl (= (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule resolution :premises (t18 t19))
% 1.45/1.66  (step t21 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t22)
% 1.45/1.66  (assume t22.a0 (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))
% 1.45/1.66  (assume t22.a1 (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.45/1.66  (assume t22.a2 (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))
% 1.45/1.66  (step t22.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 1.45/1.66  (step t22.t2 (cl (= (= false true) false)) :rule all_simplify)
% 1.45/1.66  (step t22.t3 (cl (= (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) false) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule equiv_simplify)
% 1.45/1.66  (step t22.t4 (cl (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) false) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule equiv2 :premises (t22.t3))
% 1.45/1.66  (step t22.t5 (cl (not (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) :rule not_not)
% 1.45/1.66  (step t22.t6 (cl (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) false) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) :rule resolution :premises (t22.t4 t22.t5))
% 1.45/1.66  (step t22.t7 (cl (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) false)) :rule resolution :premises (t22.t6 t22.a2))
% 1.45/1.66  (step t22.t8 (cl (= false (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule symm :premises (t22.t7))
% 1.45/1.66  (step t22.t9 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 1.45/1.66  (step t22.t10 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone 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 tptp.v_r____)))) :rule symm :premises (t22.a1))
% 1.45/1.66  (step t22.t11 (cl (= tptp.v_r____ tptp.v_r____)) :rule refl)
% 1.45/1.66  (step t22.t12 (cl (= (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule cong :premises (t22.t9 t22.t10 t22.t11))
% 1.45/1.66  (step t22.t13 (cl (= (= (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) true) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule equiv_simplify)
% 1.45/1.66  (step t22.t14 (cl (= (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) true) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule equiv2 :premises (t22.t13))
% 1.45/1.66  (step t22.t15 (cl (= (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) true)) :rule resolution :premises (t22.t14 t22.a0))
% 1.45/1.66  (step t22.t16 (cl (= false true)) :rule trans :premises (t22.t8 t22.t12 t22.t15))
% 1.45/1.66  (step t22.t17 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t16))
% 1.45/1.66  (step t22 (cl (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 1.45/1.66  (step t23 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) :rule and_pos)
% 1.45/1.66  (step t24 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 1.45/1.66  (step t25 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule and_pos)
% 1.45/1.66  (step t26 (cl false (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule resolution :premises (t22 t23 t24 t25))
% 1.45/1.66  (step t27 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) false) :rule reordering :premises (t26))
% 1.45/1.66  (step t28 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) false) :rule contraction :premises (t27))
% 1.45/1.66  (step t29 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) false) :rule resolution :premises (t21 t28))
% 1.45/1.66  (step t30 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (not false)) :rule implies_neg2)
% 1.45/1.66  (step t31 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false)) :rule resolution :premises (t29 t30))
% 1.45/1.66  (step t32 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false)) :rule contraction :premises (t31))
% 1.45/1.66  (step t33 (cl (= (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))))) :rule implies_simplify)
% 1.45/1.66  (step t34 (cl (not (=> (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false)) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule equiv1 :premises (t33))
% 1.45/1.66  (step t35 (cl (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule resolution :premises (t32 t34))
% 1.45/1.66  (step t36 (cl (= (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) false)) :rule resolution :premises (t20 t35))
% 1.45/1.66  (step t37 (cl (= (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) false))) :rule cong :premises (t16 t36))
% 1.45/1.66  (step t38 (cl (= (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) false) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))))) :rule all_simplify)
% 1.45/1.66  (step t39 (cl (= (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))))) :rule trans :premises (t37 t38))
% 1.45/1.66  (step t40 (cl (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t41)
% 1.45/1.66  (assume t41.a0 (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.45/1.66  (assume t41.a1 (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))
% 1.45/1.66  (assume t41.a2 (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))
% 1.45/1.66  (step t41.t1 (cl (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule and_neg)
% 1.45/1.66  (step t41.t2 (cl (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule resolution :premises (t41.t1 t41.a2 t41.a0 t41.a1))
% 1.45/1.66  (step t41 (cl (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 1.45/1.66  (step t42 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 1.45/1.66  (step t43 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule and_pos)
% 1.45/1.66  (step t44 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) :rule and_pos)
% 1.45/1.66  (step t45 (cl (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule resolution :premises (t41 t42 t43 t44))
% 1.45/1.66  (step t46 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule reordering :premises (t45))
% 1.45/1.66  (step t47 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule contraction :premises (t46))
% 1.45/1.66  (step t48 (cl (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule resolution :premises (t40 t47))
% 1.45/1.66  (step t49 (cl (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (not (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule implies_neg2)
% 1.45/1.66  (step t50 (cl (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule resolution :premises (t48 t49))
% 1.45/1.66  (step t51 (cl (=> (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) (and (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule contraction :premises (t50))
% 1.45/1.66  (step t52 (cl (not (and (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule resolution :premises (t15 t39 t51))
% 1.45/1.66  (step t53 (cl (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule not_and :premises (t52))
% 1.45/1.66  (step t54 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule or_neg)
% 1.45/1.66  (step t55 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))))) :rule or_neg)
% 1.45/1.66  (step t56 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule or_neg)
% 1.45/1.66  (step t57 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule resolution :premises (t53 t54 t55 t56))
% 1.45/1.66  (step t58 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule contraction :premises (t57))
% 1.45/1.66  (step t59 (cl (or (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule resolution :premises (t1 t14 t58))
% 1.45/1.66  (step t60 (cl (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule or :premises (t59))
% 1.45/1.66  (step t61 (cl (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____) (not (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule reordering :premises (t60))
% 1.45/1.66  (step t62 (cl (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq 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 tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq 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 tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) :rule or_pos)
% 1.45/1.66  (step t63 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq 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 tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.class_Orderings_Opreorder 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.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq 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 tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)))) :rule reordering :premises (t62))
% 1.45/1.66  (step t64 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) :rule or_pos)
% 1.45/1.66  (step t65 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (not (tptp.class_Orderings_Olinorder 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.v_z____) tptp.v_r____) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)))) :rule reordering :premises (t64))
% 1.45/1.66  (step t66 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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)))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t67)
% 1.45/1.66  (assume t67.a0 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))
% 1.45/1.66  (step t67.t1 (cl (or (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)))) :rule forall_inst :args ((:= V_x (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (:= V_y tptp.v_r____) (:= T_a tptp.tc_RealDef_Oreal)))
% 1.45/1.66  (step t67.t2 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule or :premises (t67.t1))
% 1.45/1.66  (step t67.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule resolution :premises (t67.t2 t67.a0))
% 1.45/1.66  (step t67 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule subproof :discharge (t67.a0))
% 1.45/1.66  (step t68 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule resolution :premises (t66 t67))
% 1.45/1.66  (step t69 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)))) :rule implies_neg2)
% 1.45/1.66  (step t70 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)))) :rule resolution :premises (t68 t69))
% 1.45/1.66  (step t71 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)))) :rule contraction :premises (t70))
% 1.45/1.66  (step t72 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule implies :premises (t71))
% 1.45/1.66  (step t73 (cl (not (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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))))) (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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)))) :rule equiv_pos2)
% 1.45/1.66  (step t74 (cl (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (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))))) :rule all_simplify)
% 1.45/1.66  (step t75 (cl (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) :rule resolution :premises (t73 t74 a215))
% 1.45/1.66  (step t76 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_r____ (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____))) :rule resolution :premises (t72 t75))
% 1.45/1.66  (step t77 (cl (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) :rule resolution :premises (t65 a1260 a1144 t76))
% 1.45/1.66  (step t78 (cl (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t79)
% 1.45/1.66  (assume t79.a0 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))
% 1.45/1.66  (step t79.t1 (cl (or (not (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____)))) :rule forall_inst :args ((:= V_z tptp.v_r____) (:= V_y (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____)) (:= V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____))) (:= T_a tptp.tc_RealDef_Oreal)))
% 1.45/1.66  (step t79.t2 (cl (not (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) :rule or :premises (t79.t1))
% 1.45/1.66  (step t79.t3 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) :rule resolution :premises (t79.t2 t79.a0))
% 1.45/1.66  (step t79 (cl (not (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) :rule subproof :discharge (t79.a0))
% 1.45/1.66  (step t80 (cl (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) :rule resolution :premises (t78 t79))
% 1.45/1.66  (step t81 (cl (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____)))) :rule implies_neg2)
% 1.45/1.66  (step t82 (cl (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____)))) :rule resolution :premises (t80 t81))
% 1.45/1.66  (step t83 (cl (=> (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____)))) :rule contraction :premises (t82))
% 1.45/1.66  (step t84 (cl (not (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) tptp.v_r____))) :rule implies :premises (t83))
% 1.45/1.66  (step t85 (cl (not (= (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (not (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) :rule equiv_pos2)
% 1.45/1.66  (step t86 (cl (= (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) :rule all_simplify)
% 1.45/1.66  (step t87 (cl (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z)))) :rule resolution :premises (t85 t86 a203))
% 1.45/1.66  (step t88 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq 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 tptp.v_r____)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z____) tptp.v_r____)) (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____))) :rule resolution :premises (t84 t87))
% 1.45/1.66  (step t89 (cl (tptp.c_Orderings_Oord__class_Oless 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 tptp.v_r____)) tptp.v_r____)) :rule resolution :premises (t63 a3 a1143 t77 t88))
% 1.45/1.66  (step t90 (cl (not (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule or_pos)
% 1.45/1.66  (step t91 (cl (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule reordering :premises (t90))
% 1.45/1.66  (step t92 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t93)
% 1.45/1.66  (assume t93.a0 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))))
% 1.45/1.66  (step t93.t1 (cl (or (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule forall_inst :args ((:= V_c (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (:= V_a (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (:= T_a tptp.tc_RealDef_Oreal)))
% 1.45/1.66  (step t93.t2 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule or :premises (t93.t1))
% 1.45/1.66  (step t93.t3 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t93.t2 t93.a0))
% 1.45/1.66  (step t93 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule subproof :discharge (t93.a0))
% 1.45/1.66  (step t94 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t92 t93))
% 1.45/1.66  (step t95 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule implies_neg2)
% 1.45/1.66  (step t96 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t94 t95))
% 1.45/1.66  (step t97 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule contraction :premises (t96))
% 1.45/1.66  (step t98 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule implies :premises (t97))
% 1.45/1.66  (step t99 (cl (not (= (forall ((V_c $$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)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))) (not (forall ((V_c $$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))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) :rule equiv_pos2)
% 1.45/1.66  (step t100 (cl (= (forall ((V_c $$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)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))) :rule all_simplify)
% 1.45/1.66  (step t101 (cl (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (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))))) :rule resolution :premises (t99 t100 a325))
% 1.45/1.66  (step t102 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t98 t101))
% 1.45/1.66  (step t103 (cl (= (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 tptp.v_r____)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t91 a1136 t102))
% 1.45/1.66  (step t104 (cl (=> (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (forall ((V_x $$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)))) :rule implies_neg1)
% 1.45/1.66  (anchor :step t105)
% 1.45/1.66  (assume t105.a0 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))
% 1.45/1.66  (step t105.t1 (cl (or (not (forall ((V_x $$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)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule forall_inst :args ((:= V_x tptp.v_r____)))
% 1.45/1.66  (step t105.t2 (cl (not (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule or :premises (t105.t1))
% 1.45/1.66  (step t105.t3 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule resolution :premises (t105.t2 t105.a0))
% 1.45/1.66  (step t105 (cl (not (forall ((V_x $$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)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule subproof :discharge (t105.a0))
% 1.45/1.66  (step t106 (cl (=> (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule resolution :premises (t104 t105))
% 1.45/1.66  (step t107 (cl (=> (forall ((V_x $$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))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (not (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule implies_neg2)
% 1.45/1.67  (step t108 (cl (=> (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) (=> (forall ((V_x $$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))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule resolution :premises (t106 t107))
% 1.45/1.67  (step t109 (cl (=> (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____)))) :rule contraction :premises (t108))
% 1.45/1.67  (step t110 (cl (not (forall ((V_x $$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)))) (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule implies :premises (t109))
% 1.45/1.67  (step t111 (cl (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 tptp.v_r____) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) tptp.v_r____))) :rule resolution :premises (t110 a331))
% 1.45/1.67  (step t112 (cl) :rule resolution :premises (t61 t89 t103 t111))
% 1.45/1.67  
% 1.45/1.67  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.LgoljnD4e3/cvc5---1.0.5_20042.smt2
% 1.45/1.67  % cvc5---1.0.5 exiting
% 1.45/1.67  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------