%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW231+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n010.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 18:18:54 EDT 2024

% Result   : Theorem 2.83s 3.04s
% Output   : Proof 2.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWW231+1 : TPTP v8.2.0. Released v5.2.0.
% 0.12/0.25  % Command    : do_cvc5 %s %d
% 0.24/0.46  % Computer : n010.cluster.edu
% 0.24/0.46  % Model    : x86_64 x86_64
% 0.24/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.46  % Memory   : 8042.1875MB
% 0.24/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.24/0.46  % CPULimit   : 300
% 0.24/0.46  % WCLimit    : 300
% 0.24/0.46  % DateTime   : Sun May 26 04:34:09 EDT 2024
% 0.24/0.46  % CPUTime    : 
% 0.55/0.83  %----Proving TF0_NAR, FOF, or CNF
% 2.83/3.04  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.83/3.04  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.Iu1zVElSdY/cvc5---1.0.5_13225.smt2
% 2.83/3.04  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.Iu1zVElSdY/cvc5---1.0.5_13225.smt2
% 2.83/3.04  (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 2.83/3.04  (assume a1 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_y))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_y (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x))))))
% 2.83/3.04  (assume a2 (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))))
% 2.83/3.04  (assume a3 (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x)))))
% 2.83/3.04  (assume a4 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))))
% 2.83/3.04  (assume a5 (forall ((V_w $$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)))))
% 2.83/3.04  (assume a6 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 2.83/3.04  (assume a7 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 2.83/3.04  (assume a8 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a9 (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)))))
% 2.83/3.04  (assume a10 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.04  (assume a11 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 2.83/3.04  (assume a12 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)) V_b))))
% 2.83/3.04  (assume a13 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 2.83/3.04  (assume a14 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 2.83/3.04  (assume a15 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 2.83/3.04  (assume a16 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 2.83/3.04  (assume a17 (forall ((V_c_2 $$unsorted) (V_aa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_aa_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_aa_2)) (= V_b_2 V_c_2)))))
% 2.83/3.04  (assume a18 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_c_2)) (= V_b_2 V_c_2)))))
% 2.83/3.04  (assume a19 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 2.83/3.04  (assume a20 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a21 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_b_2) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_aa_2)))))
% 2.83/3.04  (assume a22 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2))))))
% 2.83/3.04  (assume a23 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_a))))
% 2.83/3.04  (assume a24 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_z3)))))
% 2.83/3.04  (assume a25 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_w) V_z))))
% 2.83/3.04  (assume a26 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 2.83/3.04  (assume a27 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_NthRoot_Osqrt V_y_2)) (= V_x_2 V_y_2))))
% 2.83/3.04  (assume a28 (forall ((V_c $$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)))))
% 2.83/3.04  (assume a29 (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))))))
% 2.83/3.04  (assume a30 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_b_2)) (or (= V_aa_2 V_b_2) (= V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)))))))
% 2.83/3.04  (assume a31 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))
% 2.83/3.04  (assume a32 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.04  (assume a33 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b)))))
% 2.83/3.04  (assume a34 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.04  (assume a35 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_b))))
% 2.83/3.04  (assume a36 (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)))))
% 2.83/3.04  (assume a37 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y))))))
% 2.83/3.04  (assume a38 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 2.83/3.04  (assume a39 (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x))))))
% 2.83/3.04  (assume a40 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 2.83/3.04  (assume a41 (forall ((V_z_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w_2) V_y_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_z_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w_2) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_y_2))) (or (= V_w_2 V_x_2) (= V_y_2 V_z_2))))))
% 2.83/3.04  (assume a42 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))))
% 2.83/3.04  (assume a43 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 2.83/3.04  (assume a44 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 2.83/3.04  (assume a45 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 2.83/3.04  (assume a46 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_aa_2 V_b_2)) (not (= V_c_2 V_d_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_d_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_d_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_c_2))))))))
% 2.83/3.04  (assume a47 (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))))))
% 2.83/3.04  (assume a48 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)))))
% 2.83/3.04  (assume a49 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ry))))))
% 2.83/3.04  (assume a50 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ry)))))
% 2.83/3.04  (assume a51 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_rx))))))
% 2.83/3.04  (assume a52 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ly)))))
% 2.83/3.04  (assume a53 (forall ((V_ry $$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)))))))
% 2.83/3.04  (assume a54 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_ry))))))
% 2.83/3.04  (assume a55 (forall ((V_ry $$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))))))
% 2.83/3.04  (assume a56 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 2.83/3.04  (assume a57 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 2.83/3.04  (assume a58 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 2.83/3.04  (assume a59 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 2.83/3.04  (assume a60 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 2.83/3.04  (assume a61 (forall ((V_d $$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))))))
% 2.83/3.04  (assume a62 (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))))))
% 2.83/3.04  (assume a63 (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))))))
% 2.83/3.04  (assume a64 (forall ((V_m $$unsorted) (V_l $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_l) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_m)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_l))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_y (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_m)))))))
% 2.83/3.04  (assume a65 (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_NthRoot_Osqrt (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) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y) V_y))))))
% 2.83/3.04  (assume a66 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_x))))
% 2.83/3.04  (assume a67 (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ouminus T_a) (= (tptp.hAPP (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_fun T_b T_a) V_A_2) V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP V_A_2 V_x_2))))))
% 2.83/3.04  (assume a68 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y_2)) (= V_x_2 V_y_2)))))
% 2.83/3.04  (assume a69 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) V_a))))
% 2.83/3.04  (assume a70 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) V_x))))
% 2.83/3.04  (assume a71 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (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_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))
% 2.83/3.04  (assume a72 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) (tptp.c_Complex_Ocis V_b)) (tptp.c_Complex_Ocis (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))
% 2.83/3.04  (assume a73 (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)))))
% 2.83/3.04  (assume a74 (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))))))
% 2.83/3.04  (assume a75 (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)))))
% 2.83/3.04  (assume a76 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))))
% 2.83/3.04  (assume a77 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))))
% 2.83/3.04  (assume a78 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)))))
% 2.83/3.04  (assume a79 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)))
% 2.83/3.04  (assume a80 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x))))))
% 2.83/3.04  (assume a81 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))
% 2.83/3.04  (assume a82 (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)))))
% 2.83/3.04  (assume a83 (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)))))
% 2.83/3.04  (assume a84 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 2.83/3.04  (assume a85 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 2.83/3.04  (assume a86 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 2.83/3.04  (assume a87 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_aa_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a88 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a89 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__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_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 2.83/3.04  (assume a90 (forall ((V_aa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a91 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_aa_2)))))
% 2.83/3.04  (assume a92 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2))))))
% 2.83/3.04  (assume a93 (forall ((V_b $$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)))))
% 2.83/3.04  (assume a94 (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)))))
% 2.83/3.04  (assume a95 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))))
% 2.83/3.04  (assume a96 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y)))))
% 2.83/3.04  (assume a97 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))
% 2.83/3.04  (assume a98 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a99 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))))
% 2.83/3.04  (assume a100 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x))))))
% 2.83/3.04  (assume a101 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a102 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))))
% 2.83/3.04  (assume a103 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b))))))
% 2.83/3.04  (assume a104 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_aa_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_b_2))))))
% 2.83/3.04  (assume a105 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 2.83/3.04  (assume a106 (forall ((V_x $$unsorted) (V_u $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_u) V_u)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x))))
% 2.83/3.04  (assume a107 (forall ((V_ra_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x_2) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_ra_2)))))
% 2.83/3.04  (assume a108 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_x))))
% 2.83/3.04  (assume a109 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))))
% 2.83/3.04  (assume a110 (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y) V_y))))))
% 2.83/3.04  (assume a111 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))))
% 2.83/3.04  (assume a112 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))))
% 2.83/3.04  (assume a113 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_Orcis V_r V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocis V_a)))))
% 2.83/3.04  (assume a114 (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_w V_z)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z)))))
% 2.83/3.04  (assume a115 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 2.83/3.04  (assume a116 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a117 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a118 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_y)) V_x) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)))))))
% 2.83/3.04  (assume a119 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a120 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a121 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a122 (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a123 (forall ((T_a $$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)))))
% 2.83/3.04  (assume a124 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (= (tptp.c_RealVector_Oof__real T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a125 (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))))))
% 2.83/3.04  (assume a126 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (= (tptp.c_RealVector_Oof__real T_a V_x_2) (tptp.c_RealVector_Oof__real T_a V_y_2)) (= V_x_2 V_y_2)))))
% 2.83/3.04  (assume a127 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))))
% 2.83/3.04  (assume a128 (forall ((V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_RealVector_Oof__real T_a V_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))))
% 2.83/3.04  (assume a129 (forall ((V_r $$unsorted)) (= (tptp.c_Complex_Orcis V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r))))
% 2.83/3.04  (assume a130 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 2.83/3.04  (assume a131 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))))
% 2.83/3.04  (assume a132 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))
% 2.83/3.04  (assume a133 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a134 (forall ((V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a135 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a136 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a137 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a138 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a139 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a140 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a141 (forall ((V_b_2 $$unsorted) (V_aa_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_aa_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a142 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 2.83/3.04  (assume a143 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a144 (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))))
% 2.83/3.04  (assume a145 (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))))
% 2.83/3.04  (assume a146 (forall ((V_aa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_aa_2)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a147 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 2.83/3.04  (assume a148 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 2.83/3.04  (assume a149 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a150 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 2.83/3.04  (assume a151 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 2.83/3.04  (assume a152 (forall ((V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_RealVector_Oof__real T_a V_r)) (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_r))))))
% 2.83/3.04  (assume a153 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a154 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a155 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a156 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a157 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_aa_2) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a158 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a159 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a160 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_aa_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b_2) V_c_2)) (= V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a161 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_b_2)) (= V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a162 (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a163 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a164 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a165 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a166 (forall ((T_a $$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)))))
% 2.83/3.04  (assume a167 (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))))))
% 2.83/3.04  (assume a168 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_RealVector_Oof__real T_a V_x)) (tptp.c_RealVector_Oof__real T_a V_y))))))
% 2.83/3.04  (assume a169 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a170 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_RealVector_Oof__real T_a V_x) (tptp.c_RealVector_Oof__real T_a V_y))))))
% 2.83/3.04  (assume a171 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_RealVector_Oof__real T_a V_x) (tptp.c_RealVector_Oof__real T_a V_y))))))
% 2.83/3.04  (assume a172 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_RealVector_Oof__real T_a V_x))))))
% 2.83/3.04  (assume a173 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_RealVector_Oof__real T_a V_x))))))
% 2.83/3.04  (assume a174 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))))
% 2.83/3.04  (assume a175 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a176 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 2.83/3.04  (assume a177 (forall ((V_d $$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)))))))))
% 2.83/3.04  (assume a178 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 2.83/3.04  (assume a179 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 2.83/3.04  (assume a180 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 2.83/3.04  (assume a181 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 2.83/3.04  (assume a182 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 2.83/3.04  (assume a183 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 2.83/3.04  (assume a184 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a185 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a186 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a187 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a188 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a189 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b_2)))))))
% 2.83/3.04  (assume a190 (forall ((V_b_2 $$unsorted) (V_aa_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_aa_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_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_aa_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))))))))
% 2.83/3.04  (assume a191 (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)))))
% 2.83/3.04  (assume a192 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a193 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 2.83/3.04  (assume a194 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 2.83/3.04  (assume a195 (forall ((V_y_2 $$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)))))))))
% 2.83/3.04  (assume a196 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 2.83/3.04  (assume a197 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a198 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a199 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 2.83/3.04  (assume a200 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_aa_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a201 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a202 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a203 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a204 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a205 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a206 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a207 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 2.83/3.04  (assume a208 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2))))))
% 2.83/3.04  (assume a209 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))))
% 2.83/3.04  (assume a210 (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)))))
% 2.83/3.04  (assume a211 (forall ((V_aa_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_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a212 (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)))))
% 2.83/3.04  (assume a213 (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))))))
% 2.83/3.04  (assume a214 (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))))
% 2.83/3.04  (assume a215 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (= (tptp.c_NthRoot_Osqrt V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a216 (forall ((V_x $$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_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)))))
% 2.83/3.04  (assume a217 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a218 (forall ((V_y_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2))))
% 2.83/3.04  (assume a219 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))))
% 2.83/3.04  (assume a220 (forall ((V_aa_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_aa_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 V_aa_2))))
% 2.83/3.04  (assume a221 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 2.83/3.04  (assume a222 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a223 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 2.83/3.04  (assume a224 (forall ((V_x_2 $$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))))))
% 2.83/3.04  (assume a225 (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))))))
% 2.83/3.04  (assume a226 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))))
% 2.83/3.04  (assume a227 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))))
% 2.83/3.04  (assume a228 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a229 (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))))))
% 2.83/3.04  (assume a230 (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))))))
% 2.83/3.04  (assume a231 (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))))))
% 2.83/3.04  (assume a232 (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))))))
% 2.83/3.04  (assume a233 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 2.83/3.04  (assume a234 (forall ((V_x_2 $$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))))))
% 2.83/3.04  (assume a235 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 2.83/3.04  (assume a236 (forall ((V_y_2 $$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))))))
% 2.83/3.04  (assume a237 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 2.83/3.04  (assume a238 (forall ((V_g_2 $$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)))))))
% 2.83/3.04  (assume a239 (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)))))))
% 2.83/3.04  (assume a240 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a241 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a242 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a243 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.c_Transcendental_Opi))
% 2.83/3.04  (assume a244 (forall ((V_y_2 $$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)))))))
% 2.83/3.04  (assume a245 (not (= tptp.c_Transcendental_Opi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a246 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a247 (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (exists ((B_K $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_RealVector_Oof__real T_a B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal B_x)) B_K))))))))
% 2.83/3.04  (assume a248 (forall ((V_r $$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))))
% 2.83/3.04  (assume a249 (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_RealVector_Oof__real T_a B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal B_x)) B_K)))))))
% 2.83/3.04  (assume a250 (forall ((T_a $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))
% 2.83/3.04  (assume a251 (forall ((V_x $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 2.83/3.04  (assume a252 (forall ((V_y $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 2.83/3.04  (assume a253 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))
% 2.83/3.04  (assume a254 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))
% 2.83/3.04  (assume a255 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))
% 2.83/3.04  (assume a256 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 2.83/3.04  (assume a257 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 2.83/3.04  (assume a258 (forall ((V_d $$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)))))))
% 2.83/3.04  (assume a259 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y V_x) (=> (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_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_y) (tptp.c_Transcendental_Ocos V_x)))))))
% 2.83/3.04  (assume a260 (forall ((V_x $$unsorted)) (=> (not (tptp.c_RealDef_Opositive V_x)) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (tptp.c_RealDef_Opositive (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x))))))
% 2.83/3.04  (assume a261 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r) (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r V_x) V_y))))
% 2.83/3.04  (assume a262 (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_x V_y) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_r) V_y))))
% 2.83/3.04  (assume a263 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_Complex_Ocomplex_OComplex V_c V_d)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_b V_d)))))
% 2.83/3.04  (assume a264 (forall ((V_real2_H_2 $$unsorted) (V_real1_H_2 $$unsorted) (V_real2_2 $$unsorted) (V_real1_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2) (tptp.c_Complex_Ocomplex_OComplex V_real1_H_2 V_real2_H_2)) (and (= V_real1_2 V_real1_H_2) (= V_real2_2 V_real2_H_2)))))
% 2.83/3.04  (assume a265 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_aa_2 V_b_2) (= V_c_2 V_d_2))))))
% 2.83/3.04  (assume a266 (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))))))
% 2.83/3.04  (assume a267 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_x_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_x_2) (tptp.hAPP V_B_2 V_x_2))))))
% 2.83/3.04  (assume a268 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_aa_2 V_b_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (and (= V_aa_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a269 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_RealVector_Oof__real T_a V_x) (tptp.c_RealVector_Oof__real T_a V_y))))))
% 2.83/3.04  (assume a270 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_RealVector_Oof__real T_a V_x) (tptp.c_RealVector_Oof__real T_a V_y))))))
% 2.83/3.04  (assume a271 (forall ((T_a $$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)))))
% 2.83/3.04  (assume a272 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 2.83/3.04  (assume a273 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a274 (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a275 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a276 (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)))))))
% 2.83/3.04  (assume a277 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 2.83/3.04  (assume a278 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a279 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a280 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_aa_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a281 (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)))))
% 2.83/3.04  (assume a282 (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))))
% 2.83/3.04  (assume a283 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))))
% 2.83/3.04  (assume a284 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 2.83/3.04  (assume a285 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 2.83/3.04  (assume a286 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 2.83/3.04  (assume a287 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 2.83/3.04  (assume a288 (forall ((V_b $$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))))
% 2.83/3.04  (assume a289 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 2.83/3.04  (assume a290 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a)))))
% 2.83/3.04  (assume a291 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 2.83/3.04  (assume a292 (forall ((T_a $$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))))))
% 2.83/3.04  (assume a293 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 2.83/3.04  (assume a294 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a295 (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))))
% 2.83/3.04  (assume a296 (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))))
% 2.83/3.04  (assume a297 (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))))
% 2.83/3.04  (assume a298 (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))))
% 2.83/3.04  (assume a299 (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))))
% 2.83/3.04  (assume a300 (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))))
% 2.83/3.04  (assume a301 (= (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 2.83/3.04  (assume a302 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Transcendental_Ocos V_x))))
% 2.83/3.04  (assume a303 (forall ((T_a $$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)))))
% 2.83/3.04  (assume a304 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b)))))
% 2.83/3.04  (assume a305 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a306 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)))
% 2.83/3.04  (assume a307 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a308 (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a309 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 2.83/3.04  (assume a310 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_y)))))
% 2.83/3.04  (assume a311 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a312 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) (tptp.c_Complex_Ocomplex_OComplex V_c V_d)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b) V_d)) (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_a) V_d) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b) V_c))))))
% 2.83/3.04  (assume a313 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a314 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2)) V_e_2) V_c_2) V_d_2)))))
% 2.83/3.04  (assume a315 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_aa_2)) V_e_2) V_d_2))))))
% 2.83/3.04  (assume a316 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a317 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)))))))
% 2.83/3.04  (assume a318 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)))))
% 2.83/3.04  (assume a319 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))
% 2.83/3.04  (assume a320 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.04  (assume a321 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.04  (assume a322 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y))))))
% 2.83/3.04  (assume a323 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a324 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 2.83/3.04  (assume a325 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a326 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a327 (forall ((T_a $$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)))))
% 2.83/3.04  (assume a328 (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)))))
% 2.83/3.04  (assume a329 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 2.83/3.04  (assume a330 (forall ((V_a $$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)))))
% 2.83/3.04  (assume a331 (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)))))
% 2.83/3.04  (assume a332 (not (tptp.c_RealDef_Opositive (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a333 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (or (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_a)) (= V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))))))))
% 2.83/3.04  (assume a334 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_x)))))
% 2.83/3.04  (assume a335 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_RealDef_Opositive V_x) (=> (tptp.c_RealDef_Opositive V_y) (tptp.c_RealDef_Opositive (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))
% 2.83/3.04  (assume a336 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_RealDef_Opositive V_x) (=> (tptp.c_RealDef_Opositive V_y) (tptp.c_RealDef_Opositive (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y))))))
% 2.83/3.04  (assume a337 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_y)))))
% 2.83/3.04  (assume a338 (forall ((V_s $$unsorted) (V_r $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_r V_s) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_s)))))
% 2.83/3.04  (assume a339 (forall ((V_xa_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_x_2 V_y_2) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_xa_2)) (and (= V_x_2 V_xa_2) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a340 (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r) (tptp.c_Complex_Ocomplex_OComplex V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a341 (forall ((V_y_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_y_2))))
% 2.83/3.04  (assume a342 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a343 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)))))
% 2.83/3.04  (assume a344 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (and (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a345 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a346 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_Complex_Ocomplex_OComplex V_c V_d)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_b V_d)))))
% 2.83/3.04  (assume a347 (= (tptp.c_Complex_Ocis (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)))
% 2.83/3.04  (assume a348 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Ocis V_a) (tptp.c_Complex_Orcis (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_a))))
% 2.83/3.04  (assume a349 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_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_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_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_aa_2 V_b_2)) V_e_2) V_c_2) V_d_2)))))
% 2.83/3.04  (assume a350 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_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_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_aa_2)) V_e_2) V_d_2))))))
% 2.83/3.04  (assume a351 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))))
% 2.83/3.04  (assume a352 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a353 (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)))
% 2.83/3.04  (assume a354 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq 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 V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y)))))))
% 2.83/3.04  (assume a355 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) V_x)))))))
% 2.83/3.04  (assume a356 (forall ((V_y $$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)))))))
% 2.83/3.04  (assume a357 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))
% 2.83/3.04  (assume a358 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a359 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))))
% 2.83/3.04  (assume a360 (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocomplex_OComplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y) V_r)))))
% 2.83/3.04  (assume a361 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) (tptp.c_Complex_Ocomplex_OComplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_y)))))
% 2.83/3.04  (assume a362 (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_b V_a)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_b)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_a))))
% 2.83/3.04  (assume a363 (forall ((V_y $$unsorted)) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a364 (forall ((V_real2 $$unsorted) (V_real1 $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__size (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 2.83/3.04  (assume a365 (forall ((V_real2_2 $$unsorted) (V_real1_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__case T_a V_f1_2 (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_real1_2) V_real2_2))))
% 2.83/3.04  (assume a366 (forall ((V_real2_2 $$unsorted) (V_real1_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__rec T_a V_f1_2 (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_real1_2) V_real2_2))))
% 2.83/3.04  (assume a367 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi) V_x) (= (tptp.c_Transcendental_Oarccos (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x))))))
% 2.83/3.04  (assume a368 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 2.83/3.04  (assume a369 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))))
% 2.83/3.04  (assume a370 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)))))))
% 2.83/3.04  (assume a371 (forall ((V_x $$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 V_x tptp.c_Transcendental_Opi) (= (tptp.c_Transcendental_Oarccos (tptp.c_Transcendental_Ocos V_x)) V_x)))))
% 2.83/3.04  (assume a372 (forall ((V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= (tptp.c_Transcendental_Ocos (tptp.c_Transcendental_Oarccos V_y)) V_y))))
% 2.83/3.04  (assume a373 (forall ((V_real2 $$unsorted) (V_real1 $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 2.83/3.04  (assume a374 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 2.83/3.04  (assume a375 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Transcendental_Ocos V_a) (tptp.c_Transcendental_Osin V_a)))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 2.83/3.04  (assume a376 (forall ((V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) tptp.c_Complex_Oii) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r))))
% 2.83/3.04  (assume a377 (forall ((V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_r)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r))))
% 2.83/3.04  (assume a378 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)))
% 2.83/3.04  (assume a379 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a380 (forall ((V_n $$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)))
% 2.83/3.04  (assume a381 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 2.83/3.04  (assume a382 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a383 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a384 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))))
% 2.83/3.04  (assume a385 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)))
% 2.83/3.04  (assume a386 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)))
% 2.83/3.04  (assume a387 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a388 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 2.83/3.04  (assume a389 (forall ((V_n $$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))))
% 2.83/3.04  (assume a390 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))))
% 2.83/3.04  (assume a391 (forall ((V_i_2 $$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)))))
% 2.83/3.04  (assume a392 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_k)))))
% 2.83/3.04  (assume a393 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 2.83/3.04  (assume a394 (forall ((V_i $$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)))))
% 2.83/3.04  (assume a395 (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2)))))
% 2.83/3.04  (assume a396 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))))
% 2.83/3.04  (assume a397 (forall ((V_k_2 $$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))))))
% 2.83/3.04  (assume a398 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))))
% 2.83/3.04  (assume a399 (forall ((V_i $$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)))))
% 2.83/3.04  (assume a400 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))))
% 2.83/3.04  (assume a401 (forall ((V_n_2 $$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))))))
% 2.83/3.04  (assume a402 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 2.83/3.04  (assume a403 (forall ((V_n_2 $$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))))))
% 2.83/3.04  (assume a404 (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))))
% 2.83/3.04  (assume a405 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))))
% 2.83/3.04  (assume a406 (forall ((V_l $$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)))))
% 2.83/3.04  (assume a407 (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)))
% 2.83/3.04  (assume a408 (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a409 (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))))
% 2.83/3.04  (assume a410 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 2.83/3.04  (assume a411 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 2.83/3.04  (assume a412 (forall ((V_z $$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)))))
% 2.83/3.04  (assume a413 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))))
% 2.83/3.04  (assume a414 (forall ((V_n_2 $$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))))
% 2.83/3.04  (assume a415 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))
% 2.83/3.04  (assume a416 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a417 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 2.83/3.04  (assume a418 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))))
% 2.83/3.04  (assume a419 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 2.83/3.04  (assume a420 (forall ((V_l_2 $$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))))))
% 2.83/3.04  (assume a421 (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 $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))))
% 2.83/3.04  (assume a422 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (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))))
% 2.83/3.04  (assume a423 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 2.83/3.04  (assume a424 (forall ((V_m $$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)))))
% 2.83/3.04  (assume a425 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 2.83/3.04  (assume a426 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 2.83/3.04  (assume a427 (forall ((V_n $$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))))
% 2.83/3.04  (assume a428 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 2.83/3.04  (assume a429 (forall ((V_n $$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)))))))
% 2.83/3.04  (assume a430 (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)))))
% 2.83/3.04  (assume a431 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))))
% 2.83/3.04  (assume a432 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 2.83/3.04  (assume a433 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))))
% 2.83/3.04  (assume a434 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)))
% 2.83/3.04  (assume a435 (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))))))
% 2.83/3.04  (assume a436 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j)))))
% 2.83/3.04  (assume a437 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a438 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m)))))
% 2.83/3.04  (assume a439 (forall ((V_m $$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))))
% 2.83/3.04  (assume a440 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))))
% 2.83/3.04  (assume a441 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 2.83/3.04  (assume a442 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 2.83/3.04  (assume a443 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a444 (= (tptp.c_Transcendental_Osin tptp.c_Transcendental_Opi) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a445 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x))))))
% 2.83/3.04  (assume a446 (forall ((V_x $$unsorted)) (=> (= (tptp.c_Transcendental_Ocos V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= (tptp.c_Transcendental_Osin V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a447 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) (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_Transcendental_Osin V_x)) (tptp.c_Transcendental_Ocos V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Transcendental_Osin V_y))))))
% 2.83/3.04  (assume a448 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a449 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x)) (tptp.c_Transcendental_Ocos V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Transcendental_Osin V_y))))))
% 2.83/3.04  (assume a450 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_y)) (tptp.c_Transcendental_Osin V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_y)) (tptp.c_Transcendental_Ocos V_x))))))
% 2.83/3.04  (assume a451 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))))
% 2.83/3.04  (assume a452 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))))
% 2.83/3.04  (assume a453 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Ocis V_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Transcendental_Ocos V_a) (tptp.c_Transcendental_Osin V_a)))))
% 2.83/3.04  (assume a454 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 2.83/3.04  (assume a455 (forall ((V_m $$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))))
% 2.83/3.04  (assume a456 (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))))))
% 2.83/3.04  (assume a457 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a458 (forall ((V_n_2 $$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))))))
% 2.83/3.04  (assume a459 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)))
% 2.83/3.04  (assume a460 (forall ((V_m $$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)))
% 2.83/3.04  (assume a461 (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))))))
% 2.83/3.04  (assume a462 (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)))))
% 2.83/3.04  (assume a463 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a464 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 2.83/3.04  (assume a465 (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))))
% 2.83/3.04  (assume a466 (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)))))
% 2.83/3.04  (assume a467 (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))))
% 2.83/3.04  (assume a468 (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)))))
% 2.83/3.04  (assume a469 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 2.83/3.04  (assume a470 (forall ((V_m $$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)))
% 2.83/3.04  (assume a471 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 2.83/3.04  (assume a472 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a473 (forall ((V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_x))))
% 2.83/3.04  (assume a474 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Transcendental_Ocos V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x)) (tptp.c_Transcendental_Osin V_x))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a475 (forall ((V_x $$unsorted)) (=> (= (tptp.c_Transcendental_Osin V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a476 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_x)) (tptp.c_Transcendental_Ocos V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x)) (tptp.c_Transcendental_Osin V_y))))))
% 2.83/3.04  (assume a477 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (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_Transcendental_Ocos V_x)) (tptp.c_Transcendental_Ocos V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x)) (tptp.c_Transcendental_Osin V_y))))))
% 2.83/3.04  (assume a478 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y)) (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_Transcendental_Ocos V_y)) (tptp.c_Transcendental_Ocos V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_y)) (tptp.c_Transcendental_Osin V_x))))))
% 2.83/3.04  (assume a479 (forall ((V_a $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Transcendental_Ocos V_a) (tptp.c_Transcendental_Osin V_a))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a480 (= tptp.c_Complex_Oii (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a481 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_x_2 V_y_2) tptp.c_Complex_Oii) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a482 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) tptp.c_Complex_Oii) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b) V_a))))
% 2.83/3.04  (assume a483 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b) V_a))))
% 2.83/3.04  (assume a484 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) tptp.c_Complex_Oii) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 2.83/3.04  (assume a485 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a486 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_i) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j)) V_u) V_m) V_n)))))
% 2.83/3.04  (assume a487 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a488 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_n_2))))))
% 2.83/3.04  (assume a489 (forall ((V_n $$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))))))
% 2.83/3.04  (assume a490 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2)))))
% 2.83/3.04  (assume a491 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))))
% 2.83/3.04  (assume a492 (forall ((V_n_2 $$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))))))
% 2.83/3.04  (assume a493 (forall ((V_z $$unsorted)) (=> (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a494 (forall ((V_y $$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)))))
% 2.83/3.04  (assume a495 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 2.83/3.04  (assume a496 (forall ((V_x $$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))))))
% 2.83/3.04  (assume a497 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2))))))
% 2.83/3.04  (assume a498 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_aa_2)))))
% 2.83/3.04  (assume a499 (forall ((V_aa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a500 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (not (= V_x_2 V_y_2))))))
% 2.83/3.04  (assume a501 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (= V_x_2 V_y_2)))))
% 2.83/3.04  (assume a502 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))
% 2.83/3.04  (assume a503 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y)))))
% 2.83/3.04  (assume a504 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a505 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 2.83/3.04  (assume a506 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 2.83/3.04  (assume a507 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 2.83/3.04  (assume a508 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 2.83/3.04  (assume a509 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 2.83/3.04  (assume a510 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 2.83/3.04  (assume a511 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 2.83/3.04  (assume a512 (forall ((V_a $$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))))))
% 2.83/3.04  (assume a513 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 2.83/3.04  (assume a514 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a515 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 2.83/3.04  (assume a516 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a517 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 2.83/3.04  (assume a518 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a519 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 2.83/3.04  (assume a520 (forall ((V_x_2 $$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))))))
% 2.83/3.04  (assume a521 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 2.83/3.04  (assume a522 (forall ((V_y_2 $$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))))))
% 2.83/3.04  (assume a523 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))))
% 2.83/3.04  (assume a524 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))))
% 2.83/3.04  (assume a525 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a526 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2))))))
% 2.83/3.04  (assume a527 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a528 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_aa_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2)))))
% 2.83/3.04  (assume a529 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 2.83/3.04  (assume a530 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 2.83/3.04  (assume a531 (forall ((V_d $$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)))))))
% 2.83/3.04  (assume a532 (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)))))
% 2.83/3.04  (assume a533 (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)))))
% 2.83/3.04  (assume a534 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))
% 2.83/3.04  (assume a535 (forall ((V_y_2 $$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)))))
% 2.83/3.04  (assume a536 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 2.83/3.04  (assume a537 (forall ((V_y_2 $$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)))))))
% 2.83/3.04  (assume a538 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))
% 2.83/3.04  (assume a539 (forall ((V_y_2 $$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))))))
% 2.83/3.04  (assume a540 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 2.83/3.04  (assume a541 (forall ((V_x $$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)))))
% 2.83/3.04  (assume a542 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 2.83/3.04  (assume a543 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a544 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 2.83/3.04  (assume a545 (forall ((V_x $$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))))))
% 2.83/3.04  (assume a546 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 2.83/3.04  (assume a547 (forall ((V_y_2 $$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))))))
% 2.83/3.04  (assume a548 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))))
% 2.83/3.04  (assume a549 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a550 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 2.83/3.04  (assume a551 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 2.83/3.04  (assume a552 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 2.83/3.04  (assume a553 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 2.83/3.04  (assume a554 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 2.83/3.04  (assume a555 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 2.83/3.04  (assume a556 (forall ((V_x $$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))))
% 2.83/3.04  (assume a557 (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)))))
% 2.83/3.04  (assume a558 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 2.83/3.04  (assume a559 (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)))))))
% 2.83/3.04  (assume a560 (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)))))))
% 2.83/3.04  (assume a561 (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)))))))
% 2.83/3.04  (assume a562 (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)))))))
% 2.83/3.04  (assume a563 (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)))))))
% 2.83/3.04  (assume a564 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 2.83/3.04  (assume a565 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a566 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_aa_2))))))
% 2.83/3.04  (assume a567 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 2.83/3.04  (assume a568 (forall ((V_b $$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))))))
% 2.83/3.04  (assume a569 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a570 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a571 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 2.83/3.04  (assume a572 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2))))))
% 2.83/3.04  (assume a573 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_aa_2)))))))
% 2.83/3.04  (assume a574 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_aa_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_c_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_aa_2)))))))
% 2.83/3.04  (assume a575 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a576 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a577 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a578 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a579 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a580 (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)))))))
% 2.83/3.04  (assume a581 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a582 (forall ((V_d $$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)))))))
% 2.83/3.04  (assume a583 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 2.83/3.04  (assume a584 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a585 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 2.83/3.04  (assume a586 (forall ((T_a $$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))))))
% 2.83/3.04  (assume a587 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a588 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a589 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) (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_aa_2)))))
% 2.83/3.04  (assume a590 (forall ((V_aa_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_Ouminus__class_Ouminus T_a V_aa_2) V_aa_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a591 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n)))))))
% 2.83/3.04  (assume a592 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))))
% 2.83/3.04  (assume a593 (forall ((V_ra_2 $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x_2 V_aa_2)) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_aa_2 V_ra_2)))))))
% 2.83/3.04  (assume a594 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a595 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_aa_2)) (not (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a596 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 2.83/3.04  (assume a597 (forall ((V_d $$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)))))))
% 2.83/3.04  (assume a598 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_aa_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_aa_2) V_b_2))))))
% 2.83/3.04  (assume a599 (forall ((V_x_2 $$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)))))
% 2.83/3.04  (assume a600 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_z_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 2.83/3.04  (assume a601 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))
% 2.83/3.04  (assume a602 (forall ((V_y $$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))))))
% 2.83/3.04  (assume a603 (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))))))
% 2.83/3.04  (assume a604 (forall ((V_aa_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_aa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a605 (forall ((V_aa_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_aa_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_aa_2)))))
% 2.83/3.04  (assume a606 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a607 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.c_Transcendental_Opi))
% 2.83/3.04  (assume a608 (forall ((V_y_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2))))
% 2.83/3.04  (assume a609 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt 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_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a610 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (not (= (tptp.c_NthRoot_Osqrt V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a611 (forall ((V_x $$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_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)))))
% 2.83/3.04  (assume a612 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a613 (forall ((V_y_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_y_2))))
% 2.83/3.04  (assume a614 (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) (tptp.c_RealDef_Opositive (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_y_2 V_x_2)))))
% 2.83/3.04  (assume a615 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a616 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_aa_2 V_b_2))))))
% 2.83/3.04  (assume a617 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_aa_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_aa_2))))))
% 2.83/3.04  (assume a618 (forall ((V_d $$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)))))))))
% 2.83/3.04  (assume a619 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 2.83/3.04  (assume a620 (forall ((V_d $$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)))))))))
% 2.83/3.04  (assume a621 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 2.83/3.04  (assume a622 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 2.83/3.04  (assume a623 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 2.83/3.04  (assume a624 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 2.83/3.04  (assume a625 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 2.83/3.04  (assume a626 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 2.83/3.04  (assume a627 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 2.83/3.04  (assume a628 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a629 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a630 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 2.83/3.04  (assume a631 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 2.83/3.04  (assume a632 (forall ((V_b $$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)))))))
% 2.83/3.04  (assume a633 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 2.83/3.04  (assume a634 (forall ((V_y_2 $$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))))))))
% 2.83/3.04  (assume a635 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a636 (forall ((T_a $$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))))))
% 2.83/3.04  (assume a637 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_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_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_aa_2 V_b_2)) V_e_2) V_c_2) V_d_2)))))
% 2.83/3.04  (assume a638 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_aa_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_aa_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_aa_2)) V_e_2) V_d_2))))))
% 2.83/3.04  (assume a639 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 2.83/3.04  (assume a640 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oabs__if T_a) (and (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a))))))
% 2.83/3.04  (assume a641 (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)))))))
% 2.83/3.04  (assume a642 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_aa_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_aa_2)))))
% 2.83/3.04  (assume a643 (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))))))
% 2.83/3.04  (assume a644 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_s)))))))
% 2.83/3.04  (assume a645 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z_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_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_z_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 2.83/3.04  (assume a646 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 2.83/3.04  (assume a647 (forall ((V_s $$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)))))))
% 2.83/3.04  (assume a648 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))))
% 2.83/3.04  (assume a649 (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) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))))
% 2.83/3.04  (assume a650 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Osin V_x))))))
% 2.83/3.04  (assume a651 (forall ((V_r $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_r))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r) V_r)))))
% 2.83/3.04  (assume a652 (forall ((V_a $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_a) V_a)))))
% 2.83/3.04  (assume a653 (forall ((V_x $$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))))
% 2.83/3.04  (assume a654 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a655 (forall ((V_x_2 $$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)))))
% 2.83/3.04  (assume a656 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 2.83/3.04  (assume a657 (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_aa_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Orderings_Oord__class_Oless T_a V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a658 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))))))))))
% 2.83/3.04  (assume a659 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq 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 V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y)))))))
% 2.83/3.04  (assume a660 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))))
% 2.83/3.04  (assume a661 (forall ((V_a $$unsorted)) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))))
% 2.83/3.04  (assume a662 (forall ((V_x $$unsorted)) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))))
% 2.83/3.04  (assume a663 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 2.83/3.04  (assume a664 (forall ((V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a665 (forall ((V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a666 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi) V_y) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_y) (tptp.c_Transcendental_Ocos V_x)))))))
% 2.83/3.04  (assume a667 (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__algebra__1 T_a) (tptp.class_RealVector_Oreal__normed__vector 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.c_RealVector_Oof__real T_a B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal B_x)) B_K))))))))
% 2.83/3.04  (assume a668 (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))))))))
% 2.83/3.04  (assume a669 (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))))))))
% 2.83/3.04  (assume a670 (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))))))))
% 2.83/3.04  (assume a671 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a672 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a673 (forall ((V_n_2 $$unsorted)) (= (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 2.83/3.04  (assume a674 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a675 (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))))))
% 2.83/3.04  (assume a676 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 2.83/3.04  (assume a677 (forall ((V_k $$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))))
% 2.83/3.04  (assume a678 (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)))))
% 2.83/3.04  (assume a679 (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))))))
% 2.83/3.04  (assume a680 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 2.83/3.04  (assume a681 (forall ((V_m $$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)))))
% 2.83/3.04  (assume a682 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 2.83/3.04  (assume a683 (forall ((V_n_2 $$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))))
% 2.83/3.04  (assume a684 (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))))
% 2.83/3.04  (assume a685 (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))))
% 2.83/3.04  (assume a686 (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))))))
% 2.83/3.04  (assume a687 (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)))))
% 2.83/3.04  (assume a688 (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))))
% 2.83/3.04  (assume a689 (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)))))
% 2.83/3.04  (assume a690 (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))))
% 2.83/3.04  (assume a691 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 2.83/3.04  (assume a692 (forall ((V_n $$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))))
% 2.83/3.04  (assume a693 (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))))
% 2.83/3.04  (assume a694 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 2.83/3.04  (assume a695 (forall ((V_z $$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)))))
% 2.83/3.04  (assume a696 (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)))))))
% 2.83/3.04  (assume a697 (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)))))
% 2.83/3.04  (assume a698 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (= V_m_2 V_n_2)))))
% 2.83/3.04  (assume a699 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a700 (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)))))
% 2.83/3.04  (assume a701 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 2.83/3.04  (assume a702 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a703 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k))))))
% 2.83/3.04  (assume a704 (forall ((V_k $$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))))))
% 2.83/3.04  (assume a705 (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)))))
% 2.83/3.04  (assume a706 (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))))
% 2.83/3.04  (assume a707 (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))))
% 2.83/3.04  (assume a708 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))))
% 2.83/3.04  (assume a709 (forall ((V_c $$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))))))
% 2.83/3.04  (assume a710 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 2.83/3.04  (assume a711 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a712 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 2.83/3.04  (assume a713 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a714 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_aa_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_aa_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_aa_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))))))))
% 2.83/3.04  (assume a715 (forall ((V_b_2 $$unsorted) (V_aa_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_aa_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_aa_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_aa_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))))))))))
% 2.83/3.04  (assume a716 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_n_2))))))
% 2.83/3.04  (assume a717 (forall ((V_n_2 $$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)))))
% 2.83/3.04  (assume a718 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a719 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 2.83/3.04  (assume a720 (forall ((V_b $$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))))))))))
% 2.83/3.04  (assume a721 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))
% 2.83/3.04  (assume a722 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 2.83/3.04  (assume a723 (forall ((V_P_2 $$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)))))))
% 2.83/3.04  (assume a724 (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)))))
% 2.83/3.04  (assume a725 (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)))))
% 2.83/3.04  (assume a726 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 2.83/3.04  (assume a727 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 2.83/3.04  (assume a728 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))))
% 2.83/3.04  (assume a729 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 2.83/3.04  (assume a730 (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)))))
% 2.83/3.04  (assume a731 (forall ((V_aa_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_aa_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_aa_2) V_x_2)))))
% 2.83/3.04  (assume a732 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a733 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 2.83/3.04  (assume a734 (forall ((V_x $$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)))))
% 2.83/3.04  (assume a735 (= (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)))
% 2.83/3.04  (assume a736 (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a737 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a738 (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))))
% 2.83/3.04  (assume a739 (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)))))
% 2.83/3.04  (assume a740 (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)))))
% 2.83/3.04  (assume a741 (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)))))
% 2.83/3.04  (assume a742 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x))))
% 2.83/3.04  (assume a743 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))))
% 2.83/3.04  (assume a744 (forall ((V_x $$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))))
% 2.83/3.04  (assume a745 (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)))))
% 2.83/3.04  (assume a746 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 2.83/3.04  (assume a747 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 2.83/3.04  (assume a748 (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)))))
% 2.83/3.04  (assume a749 (= (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)))
% 2.83/3.04  (assume a750 (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)))))
% 2.83/3.04  (assume a751 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))))
% 2.83/3.04  (assume a752 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 2.83/3.04  (assume a753 (forall ((V_x $$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))))
% 2.83/3.04  (assume a754 (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)))))
% 2.83/3.04  (assume a755 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 2.83/3.04  (assume a756 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a757 (forall ((V_n_2 $$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))))
% 2.83/3.04  (assume a758 (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)))))
% 2.83/3.04  (assume a759 (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))))))
% 2.83/3.04  (assume a760 (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))))
% 2.83/3.04  (assume a761 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 2.83/3.04  (assume a762 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a763 (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.c_Transcendental_Opi) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a764 (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a765 (forall ((V_aa_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2) V_aa_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_aa_2))))))
% 2.83/3.04  (assume a766 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 2.83/3.04  (assume a767 (forall ((V_x_2 $$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))))
% 2.83/3.04  (assume a768 (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)))))
% 2.83/3.04  (assume a769 (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)))))))
% 2.83/3.04  (assume a770 (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)))))))
% 2.83/3.04  (assume a771 (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))))))))))
% 2.83/3.04  (assume a772 (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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x B_y)) B_d) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a B_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y V_b))))))))))
% 2.83/3.04  (assume a773 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2 B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 V_M_2))))))))))
% 2.83/3.04  (assume a774 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m))))))))
% 2.83/3.04  (assume a775 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) V_n)))))
% 2.83/3.04  (assume a776 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a777 (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))))))
% 2.83/3.04  (assume a778 (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))))))
% 2.83/3.04  (assume a779 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__algebra__1 T_a) (= (tptp.c_RealVector_Oof__real T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_RealVector_Oof__real T_a V_x)) V_n)))))
% 2.83/3.04  (assume a780 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a781 (forall ((V_k $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) V_k))))
% 2.83/3.04  (assume a782 (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))))
% 2.83/3.04  (assume a783 (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))))))
% 2.83/3.04  (assume a784 (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)))))
% 2.83/3.04  (assume a785 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 2.83/3.04  (assume a786 (forall ((V_x $$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))))))
% 2.83/3.04  (assume a787 (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))))))))
% 2.83/3.04  (assume a788 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 2.83/3.04  (assume a789 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2)) V_n_2)) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 2.83/3.04  (assume a790 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a791 (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))))))
% 2.83/3.04  (assume a792 (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)))))
% 2.83/3.04  (assume a793 (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))))
% 2.83/3.04  (assume a794 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 2.83/3.04  (assume a795 (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_x)) V_n) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)))))
% 2.83/3.04  (assume a796 (forall ((V_z $$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)))))
% 2.83/3.04  (assume a797 (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)))))
% 2.83/3.04  (assume a798 (forall ((V_n $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) V_n) (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)))))
% 2.83/3.04  (assume a799 (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)))))))))
% 2.83/3.04  (assume a800 (forall ((V_n $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r V_a)) V_n) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_r) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a)))))
% 2.83/3.04  (assume a801 (forall ((V_n $$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)))))))
% 2.83/3.04  (assume a802 (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))))))
% 2.83/3.04  (assume a803 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 2.83/3.04  (assume a804 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 2.83/3.04  (assume a805 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) V_n)))))
% 2.83/3.04  (assume a806 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a807 (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))))
% 2.83/3.04  (assume a808 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 2.83/3.04  (assume a809 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)))))))
% 2.83/3.04  (assume a810 (forall ((V_n $$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))))))
% 2.83/3.04  (assume a811 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 2.83/3.04  (assume a812 (forall ((V_n_2 $$unsorted) (V_aa_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_aa_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_aa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 2.83/3.04  (assume a813 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_aa_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_aa_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_aa_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_aa_2) V_n_2)) (= V_m_2 V_n_2))))))
% 2.83/3.04  (assume a814 (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)))))
% 2.83/3.04  (assume a815 (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))))))
% 2.83/3.04  (assume a816 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_n)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 2.83/3.04  (assume a817 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 2.83/3.04  (assume a818 (forall ((V_n $$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)))))))
% 2.83/3.04  (assume a819 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 2.83/3.04  (assume a820 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 2.83/3.04  (assume a821 (forall ((V_n $$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)))))
% 2.83/3.04  (assume a822 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 2.83/3.04  (assume a823 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 2.83/3.04  (assume a824 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))))
% 2.83/3.04  (assume a825 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 2.83/3.04  (assume a826 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 2.83/3.04  (assume a827 (forall ((V_n $$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)))))))
% 2.83/3.04  (assume a828 (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))))))))
% 2.83/3.04  (assume a829 (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))))))))
% 2.83/3.04  (assume a830 (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))))))))
% 2.83/3.04  (assume a831 (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))))))
% 2.83/3.04  (assume a832 (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))))))
% 2.83/3.04  (assume a833 (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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) V_n)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 2.83/3.04  (assume a834 (forall ((T_a $$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))))))
% 2.83/3.04  (assume a835 (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))))
% 2.83/3.04  (assume a836 (forall ((V_i $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_i) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_i))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_i) V_i)))))
% 2.83/3.04  (assume a837 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 2.83/3.04  (assume a838 (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 V_w_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_2 V_w_2) (not (= V_z_2 V_w_2))))))
% 2.83/3.04  (assume a839 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))))
% 2.83/3.04  (assume a840 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a841 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_j))))))
% 2.83/3.04  (assume a842 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z_2))))
% 2.83/3.04  (assume a843 (forall ((V_z_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_z_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_z_2))))
% 2.83/3.04  (assume a844 (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))))
% 2.83/3.04  (assume a845 (forall ((V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z)))))
% 2.83/3.04  (assume a846 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) V_z_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 2.83/3.04  (assume a847 (forall ((V_z_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_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2))))
% 2.83/3.04  (assume a848 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 V_z_2))))
% 2.83/3.04  (assume a849 (forall ((V_i $$unsorted)) (and (=> (= V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_Int_Oint V_i) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (not (= V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_i) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_Int_Oint V_i) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_i)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_Int_Oint V_i) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))))
% 2.83/3.04  (assume a850 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 2.83/3.04  (assume a851 (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)))))
% 2.83/3.04  (assume a852 (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)))
% 2.83/3.04  (assume a853 (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)))))))
% 2.83/3.04  (assume a854 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2) (= V_w_2 V_z_2)))))
% 2.83/3.04  (assume a855 (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)))))
% 2.83/3.04  (assume a856 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 2.83/3.04  (assume a857 (forall ((V_z2 $$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)))))
% 2.83/3.04  (assume a858 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)))
% 2.83/3.04  (assume a859 (forall ((V_z $$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)))
% 2.83/3.04  (assume a860 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 2.83/3.04  (assume a861 (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 2.83/3.04  (assume a862 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 2.83/3.04  (assume a863 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 2.83/3.04  (assume a864 (forall ((V_z $$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)))
% 2.83/3.04  (assume a865 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_w) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w)))))
% 2.83/3.04  (assume a866 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 2.83/3.04  (assume a867 (forall ((V_w $$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)))))
% 2.83/3.04  (assume a868 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_z3)))))
% 2.83/3.04  (assume a869 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z))))
% 2.83/3.04  (assume a870 (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 2.83/3.04  (assume a871 (forall ((V_aa_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_aa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)))
% 2.83/3.04  (assume a872 (forall ((V_x $$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))))))
% 2.83/3.04  (assume a873 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d)) V_z))))
% 2.83/3.04  (assume a874 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_z)))
% 2.83/3.04  (assume a875 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)))
% 2.83/3.04  (assume a876 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))))
% 2.83/3.04  (assume a877 (forall ((V_k $$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)))))
% 2.83/3.04  (assume a878 (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)))))
% 2.83/3.04  (assume a879 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j)))))
% 2.83/3.04  (assume a880 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))
% 2.83/3.04  (assume a881 (forall ((V_z $$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)))))
% 2.83/3.04  (assume a882 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))))
% 2.83/3.04  (assume a883 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))
% 2.83/3.04  (assume a884 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))
% 2.83/3.04  (assume a885 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w))))
% 2.83/3.04  (assume a886 (forall ((V_q $$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))))))
% 2.83/3.04  (assume a887 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 2.83/3.04  (assume a888 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))))
% 2.83/3.04  (assume a889 (forall ((V_r $$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)))))))
% 2.83/3.04  (assume a890 (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)))))))))
% 2.83/3.04  (assume a891 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))
% 2.83/3.04  (assume a892 (forall ((V_r_H $$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)))))))
% 2.83/3.04  (assume a893 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_q_H))))))
% 2.83/3.04  (assume a894 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)))))
% 2.83/3.04  (assume a895 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 2.83/3.04  (assume a896 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 2.83/3.04  (assume a897 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 2.83/3.04  (assume a898 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y))))))
% 2.83/3.04  (assume a899 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y))))))
% 2.83/3.04  (assume a900 (forall ((V_x $$unsorted) (V_y $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y))) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x)) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 2.83/3.04  (assume a901 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_d_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x V_d_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_d_2)))))))))))
% 2.83/3.04  (assume a902 (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))))))
% 2.83/3.04  (assume a903 (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)))))
% 2.83/3.04  (assume a904 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_d_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x V_d_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_d_2)))))))))))
% 2.83/3.04  (assume a905 (forall ((V_a $$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)))))))
% 2.83/3.04  (assume a906 (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)))))))))
% 2.83/3.04  (assume a907 (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))))))
% 2.83/3.04  (assume a908 (= (tptp.c_Transcendental_Oln (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a909 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) V_x))))
% 2.83/3.04  (assume a910 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2))))))
% 2.83/3.04  (assume a911 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 2.83/3.04  (assume a912 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 2.83/3.04  (assume a913 (forall ((V_x $$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)))))
% 2.83/3.04  (assume a914 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)))))
% 2.83/3.04  (assume a915 (forall ((V_x $$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))))))
% 2.83/3.04  (assume a916 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 2.83/3.04  (assume a917 (forall ((V_x_2 $$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))))))
% 2.83/3.04  (assume a918 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 2.83/3.04  (assume a919 (forall ((V_x $$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)))))
% 2.83/3.04  (assume a920 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 2.83/3.04  (assume a921 (forall ((V_x $$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)))))
% 2.83/3.04  (assume a922 (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)))))))
% 2.83/3.04  (assume a923 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)) V_x))))
% 2.83/3.04  (assume a924 (forall ((V_X_2 $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) B_K))))))))
% 2.83/3.04  (assume a925 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n))))))))
% 2.83/3.04  (assume a926 (forall ((V_X_2 $$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) (exists ((B_x $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP V_X_2 B_n) (tptp.c_Groups_Ouminus__class_Ouminus T_a B_x))) B_k)))))))))
% 2.83/3.04  (assume a927 (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 $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_k) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP V_X_2 B_n) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP V_X_2 B_N)))) B_k)))))))))
% 2.83/3.04  (assume a928 (forall ((V_X_2 $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) B_K))))))))
% 2.83/3.04  (assume a929 (forall ((V_X_2 $$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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) V_K_2)) (tptp.c_SEQ_OBseq T_a V_X_2))))))
% 2.83/3.04  (assume a930 (forall ((V_k_2 $$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))))))))
% 2.83/3.04  (assume a931 (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 $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i V_n_2) (= (tptp.hAPP V_f_2 B_i) V_k_2))))))))
% 2.83/3.04  (assume a932 (forall ((V_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a)) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) V_n)))))
% 2.83/3.04  (assume a933 (forall ((V_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a)) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) V_n)))))
% 2.83/3.04  (assume a934 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))))
% 2.83/3.04  (assume a935 (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq 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_x V_y)) (tptp.c_Groups_Oplus__class_Oplus 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_Complex_ORe V_x) (tptp.c_Complex_ORe V_y))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y)))))))
% 2.83/3.04  (assume a936 (= (tptp.c_Complex_ORe tptp.c_Complex_Oii) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a937 (forall ((V_z $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_z)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 2.83/3.04  (assume a938 (= (tptp.c_Complex_ORe (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a939 (= (tptp.c_Complex_OIm (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a940 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) V_x)))
% 2.83/3.04  (assume a941 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) V_y)))
% 2.83/3.04  (assume a942 (forall ((V_z $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex V_z)) V_z)))
% 2.83/3.04  (assume a943 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Complex_ORe V_x) (tptp.c_Complex_ORe V_y)) (=> (= (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y)) (= V_x V_y)))))
% 2.83/3.04  (assume a944 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= V_x_2 V_y_2) (and (= (tptp.c_Complex_ORe V_x_2) (tptp.c_Complex_ORe V_y_2)) (= (tptp.c_Complex_OIm V_x_2) (tptp.c_Complex_OIm V_y_2))))))
% 2.83/3.04  (assume a945 (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z)))
% 2.83/3.04  (assume a946 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Ocis V_a)) (tptp.c_Transcendental_Osin V_a))))
% 2.83/3.04  (assume a947 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Ocis V_a)) (tptp.c_Transcendental_Ocos V_a))))
% 2.83/3.04  (assume a948 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))))
% 2.83/3.04  (assume a949 (= (tptp.c_Complex_OIm tptp.c_Complex_Oii) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a950 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x) (tptp.c_Complex_ORe V_y)))))
% 2.83/3.04  (assume a951 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y)))))
% 2.83/3.04  (assume a952 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_x) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x))))))
% 2.83/3.04  (assume a953 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_x V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x) (tptp.c_Complex_ORe V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y))))))
% 2.83/3.04  (assume a954 (forall ((V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x)))))
% 2.83/3.04  (assume a955 (forall ((V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x)))))
% 2.83/3.04  (assume a956 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y)))))
% 2.83/3.04  (assume a957 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x) (tptp.c_Complex_ORe V_y)))))
% 2.83/3.04  (assume a958 (= (tptp.c_Complex_ORe (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a959 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))))
% 2.83/3.04  (assume a960 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))
% 2.83/3.04  (assume a961 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))))
% 2.83/3.04  (assume a962 (= (tptp.c_Complex_OIm (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 2.83/3.04  (assume a963 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_x)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))))
% 2.83/3.04  (assume a964 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))))
% 2.83/3.04  (assume a965 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))))
% 2.83/3.04  (assume a966 (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 tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_x)) B_K))))))
% 2.83/3.04  (assume a967 (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 tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_x)) B_K))))))
% 2.83/3.04  (assume a968 (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 tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_x)) B_K))))))
% 2.83/3.04  (assume a969 (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 tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_x)) B_K))))))
% 2.83/3.04  (assume a970 (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Oexpi V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Oof__real tptp.tc_Complex_Ocomplex (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal (tptp.c_Complex_ORe V_z)))) (tptp.c_Complex_Ocis (tptp.c_Complex_OIm V_z))))))
% 2.83/3.04  (assume a971 (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Complex_OIm B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_x)) B_K)))))
% 2.83/3.04  (assume a972 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y)))))
% 2.83/3.04  (assume a973 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a974 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))))
% 2.83/3.04  (assume a975 (forall ((V_x $$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_Oexp tptp.tc_RealDef_Oreal V_x))))
% 2.83/3.04  (assume a976 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a977 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a978 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))
% 2.83/3.04  (assume a979 (forall ((T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.c_Transcendental_Oexp T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 2.83/3.04  (assume a980 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Transcendental_Oexp T_a V_x)) (tptp.c_Transcendental_Oexp T_a V_y)) (tptp.c_Transcendental_Oexp T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y))))))
% 2.83/3.04  (assume a981 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.c_Transcendental_Oexp T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Transcendental_Oexp T_a V_x)) (tptp.c_Transcendental_Oexp T_a V_y))))))
% 2.83/3.04  (assume a982 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (= (tptp.c_Transcendental_Oexp T_a (tptp.c_RealVector_Oof__real T_a V_x)) (tptp.c_RealVector_Oof__real T_a (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x))))))
% 2.83/3.04  (assume a983 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y_2)) (= V_x_2 V_y_2))))
% 2.83/3.04  (assume a984 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__field T_a) (tptp.class_SEQ_Obanach T_a)) (not (= (tptp.c_Transcendental_Oexp T_a V_x) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 2.83/3.04  (assume a985 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x)) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x))))
% 2.83/3.04  (assume a986 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a987 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x))))
% 2.83/3.04  (assume a988 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))
% 2.83/3.04  (assume a989 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y))))
% 2.83/3.04  (assume a990 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_y) V_x) (= (tptp.c_Transcendental_Oln V_x) V_y))))
% 2.83/3.04  (assume a991 (forall ((V_x $$unsorted) (V_u $$unsorted)) (=> (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_u) V_x) (= (tptp.c_Transcendental_Oln V_x) V_u))))
% 2.83/3.04  (assume a992 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Oln (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x)) V_x)))
% 2.83/3.04  (assume a993 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp 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_x_2))))
% 2.83/3.04  (assume a994 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 2.83/3.04  (assume a995 (forall ((V_x $$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_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal V_x)))))
% 2.83/3.04  (assume a996 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x)) V_x))))
% 2.83/3.04  (assume a997 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_Transcendental_Oexp tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2)) V_x_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2))))
% 2.83/3.04  (assume a998 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Oboolean__algebra T_1) (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a999 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a1000 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a1001 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a1002 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ouminus T_1) (tptp.class_Groups_Ouminus (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a1003 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))))
% 2.83/3.04  (assume a1004 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1005 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1006 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1007 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1008 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1009 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1010 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1011 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1012 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1013 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1014 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1015 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1016 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1017 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1018 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1019 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1020 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1021 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1022 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1023 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1024 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1025 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1026 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1027 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1028 (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1029 (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1030 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1031 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1032 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1033 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1034 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1035 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1036 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1037 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1038 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1039 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1040 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1041 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1042 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1043 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1044 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1045 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1046 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1047 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1048 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1049 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1050 (tptp.class_Groups_Ouminus tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1051 (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1052 (tptp.class_Groups_Oabs__if tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1053 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1054 (tptp.class_Groups_Ominus tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1055 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1056 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1057 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1058 (tptp.class_Rings_Oidom tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1059 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 2.83/3.04  (assume a1060 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1061 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1062 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1063 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1064 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1065 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1066 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1067 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1068 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1069 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1070 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1071 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1072 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1073 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1074 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1075 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1076 (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1077 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1078 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1079 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1080 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1081 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1082 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1083 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1084 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1085 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1086 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1087 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1088 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1089 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1090 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1091 (tptp.class_Groups_Ominus tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1092 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1093 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1094 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 2.83/3.04  (assume a1095 (tptp.class_Lattices_Oboolean__algebra tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1096 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1097 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1098 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1099 (tptp.class_Groups_Ouminus tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1100 (tptp.class_Groups_Ominus tptp.tc_HOL_Obool))
% 2.83/3.04  (assume a1101 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1102 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1103 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1104 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1105 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1106 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1107 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1108 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1109 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1110 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1111 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1112 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1113 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1114 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1115 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1116 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1117 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1118 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1119 (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1120 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1121 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1122 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1123 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1124 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1125 (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1126 (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1127 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1128 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1129 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1130 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1131 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1132 (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1133 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1134 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1135 (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1136 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1137 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1138 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1139 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1140 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1141 (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1142 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1143 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1144 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1145 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1146 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1147 (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1148 (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1149 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1150 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1151 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1152 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1153 (tptp.class_Groups_Ouminus tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1154 (tptp.class_Groups_Osgn__if tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1155 (tptp.class_Groups_Oabs__if tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1156 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1157 (tptp.class_Groups_Ominus tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1158 (tptp.class_Power_Opower tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1159 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1160 (tptp.class_SEQ_Obanach tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1161 (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1162 (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1163 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 2.83/3.04  (assume a1164 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1165 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1166 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1167 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1168 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1169 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1170 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1171 (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1172 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1173 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1174 (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1175 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1176 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1177 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1178 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1179 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1180 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1181 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1182 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1183 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1184 (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1185 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1186 (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1187 (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1188 (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1189 (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1190 (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1191 (tptp.class_Groups_Ouminus tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1192 (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1193 (tptp.class_Groups_Ominus tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1194 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1195 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1196 (tptp.class_SEQ_Obanach tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1197 (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1198 (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1199 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex))
% 2.83/3.04  (assume a1200 (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))
% 2.83/3.04  (assume a1201 true)
% 2.83/3.04  (step t1 (cl (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule and_neg)
% 2.83/3.04  (step t2 (cl (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule implies_neg1)
% 2.83/3.04  (anchor :step t3)
% 2.83/3.04  (assume t3.a0 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))
% 2.83/3.04  (assume t3.a1 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))
% 2.83/3.04  (assume t3.a2 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))
% 2.83/3.04  (assume t3.a3 (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))
% 2.83/3.04  (assume t3.a4 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))
% 2.83/3.04  (assume t3.a5 (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))
% 2.83/3.04  (assume t3.a6 (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))
% 2.83/3.04  (assume t3.a7 (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))
% 2.83/3.04  (assume t3.a8 (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))
% 2.83/3.04  (assume t3.a9 (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))
% 2.83/3.04  (assume t3.a10 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))
% 2.83/3.04  (assume t3.a11 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))
% 2.83/3.04  (assume t3.a12 (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))
% 2.83/3.04  (assume t3.a13 (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.04  (assume t3.a14 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))
% 2.83/3.04  (assume t3.a15 (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.04  (assume t3.a16 (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.04  (step t3.t1 (cl (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule implies_neg1)
% 2.83/3.04  (anchor :step t3.t2)
% 2.83/3.04  (assume t3.t2.a0 (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.04  (assume t3.t2.a1 (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))
% 2.83/3.04  (assume t3.t2.a2 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))
% 2.83/3.04  (assume t3.t2.a3 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))
% 2.83/3.04  (assume t3.t2.a4 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))
% 2.83/3.04  (assume t3.t2.a5 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))
% 2.83/3.04  (assume t3.t2.a6 (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))
% 2.83/3.04  (assume t3.t2.a7 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))
% 2.83/3.04  (assume t3.t2.a8 (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))
% 2.83/3.05  (assume t3.t2.a9 (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))
% 2.83/3.05  (assume t3.t2.a10 (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.05  (assume t3.t2.a11 (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))
% 2.83/3.05  (assume t3.t2.a12 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))
% 2.83/3.05  (assume t3.t2.a13 (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))
% 2.83/3.05  (assume t3.t2.a14 (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))
% 2.83/3.05  (assume t3.t2.a15 (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))
% 2.83/3.05  (assume t3.t2.a16 (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))
% 2.83/3.05  (step t3.t2.t1 (cl (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule symm :premises (t3.t2.a16))
% 2.83/3.05  (step t3.t2.t2 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule symm :premises (t3.t2.t1))
% 2.83/3.05  (step t3.t2.t3 (cl (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule symm :premises (t3.t2.a10))
% 2.83/3.05  (step t3.t2.t4 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule symm :premises (t3.t2.t3))
% 2.83/3.05  (step t3.t2.t5 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)))) :rule symm :premises (t3.t2.a9))
% 2.83/3.05  (step t3.t2.t6 (cl (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))))) :rule cong :premises (t3.t2.t5))
% 2.83/3.05  (step t3.t2.t7 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))))) :rule trans :premises (t3.t2.t4 t3.t2.t6))
% 2.83/3.05  (step t3.t2.t8 (cl (= (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))))) :rule symm :premises (t3.t2.a8))
% 2.83/3.05  (step t3.t2.t9 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule symm :premises (t3.t2.t8))
% 2.83/3.05  (step t3.t2.t10 (cl (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) :rule refl)
% 2.83/3.05  (step t3.t2.t11 (cl (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule symm :premises (t3.t2.a5))
% 2.83/3.05  (step t3.t2.t12 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule symm :premises (t3.t2.t11))
% 2.83/3.05  (step t3.t2.t13 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) :rule symm :premises (t3.t2.a4))
% 2.83/3.05  (step t3.t2.t14 (cl (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule cong :premises (t3.t2.t13))
% 2.83/3.05  (step t3.t2.t15 (cl (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule symm :premises (t3.t2.a3))
% 2.83/3.05  (step t3.t2.t16 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule trans :premises (t3.t2.t12 t3.t2.t14 t3.t2.t15))
% 2.83/3.05  (step t3.t2.t17 (cl (= (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule cong :premises (t3.t2.t10 t3.t2.t16))
% 2.83/3.05  (step t3.t2.t18 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) :rule symm :premises (t3.t2.a7))
% 2.83/3.05  (step t3.t2.t19 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) :rule symm :premises (t3.t2.t18))
% 2.83/3.05  (step t3.t2.t20 (cl (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule cong :premises (t3.t2.t19))
% 2.83/3.05  (step t3.t2.t21 (cl (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule symm :premises (t3.t2.a6))
% 2.83/3.05  (step t3.t2.t22 (cl (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule trans :premises (t3.t2.t20 t3.t2.t21))
% 2.83/3.05  (step t3.t2.t23 (cl (= (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule cong :premises (t3.t2.t17 t3.t2.t22))
% 2.83/3.05  (step t3.t2.t24 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule symm :premises (t3.t2.a2))
% 2.83/3.05  (step t3.t2.t25 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule symm :premises (t3.t2.a1))
% 2.83/3.05  (step t3.t2.t26 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule trans :premises (t3.t2.t9 t3.t2.t23 t3.t2.t24 t3.t2.t25))
% 2.83/3.05  (step t3.t2.t27 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule trans :premises (t3.t2.t7 t3.t2.t26))
% 2.83/3.05  (step t3.t2.t28 (cl (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule symm :premises (t3.t2.a15))
% 2.83/3.05  (step t3.t2.t29 (cl (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule symm :premises (t3.t2.t28))
% 2.83/3.05  (step t3.t2.t30 (cl (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))))) :rule cong :premises (t3.t2.t5))
% 2.83/3.05  (step t3.t2.t31 (cl (= (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))))) :rule symm :premises (t3.t2.a14))
% 2.83/3.05  (step t3.t2.t32 (cl (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule symm :premises (t3.t2.t31))
% 2.83/3.05  (step t3.t2.t33 (cl (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) :rule symm :premises (t3.t2.a13))
% 2.83/3.05  (step t3.t2.t34 (cl (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule symm :premises (t3.t2.t33))
% 2.83/3.05  (step t3.t2.t35 (cl (= (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule cong :premises (t3.t2.t17 t3.t2.t34))
% 2.83/3.05  (step t3.t2.t36 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule symm :premises (t3.t2.a12))
% 2.83/3.05  (step t3.t2.t37 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule symm :premises (t3.t2.a11))
% 2.83/3.05  (step t3.t2.t38 (cl (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule trans :premises (t3.t2.t29 t3.t2.t30 t3.t2.t32 t3.t2.t35 t3.t2.t36 t3.t2.t37))
% 2.83/3.05  (step t3.t2.t39 (cl (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule cong :premises (t3.t2.t27 t3.t2.t38))
% 2.83/3.05  (step t3.t2.t40 (cl (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule symm :premises (t3.t2.a0))
% 2.83/3.05  (step t3.t2.t41 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule trans :premises (t3.t2.a9 t3.t2.t2 t3.t2.t39 t3.t2.t40))
% 2.83/3.05  (step t3.t2 (cl (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4 t3.t2.a5 t3.t2.a6 t3.t2.a7 t3.t2.a8 t3.t2.a9 t3.t2.a10 t3.t2.a11 t3.t2.a12 t3.t2.a13 t3.t2.a14 t3.t2.a15 t3.t2.a16))
% 2.83/3.05  (step t3.t3 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t4 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t3.t5 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t6 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule and_pos)
% 2.83/3.05  (step t3.t7 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule and_pos)
% 2.83/3.05  (step t3.t8 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule and_pos)
% 2.83/3.05  (step t3.t9 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule and_pos)
% 2.83/3.05  (step t3.t10 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) :rule and_pos)
% 2.83/3.05  (step t3.t11 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t12 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t3.t13 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t14 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t3.t15 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t16 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t3.t17 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t18 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t3.t19 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule and_pos)
% 2.83/3.05  (step t3.t20 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7 t3.t8 t3.t9 t3.t10 t3.t11 t3.t12 t3.t13 t3.t14 t3.t15 t3.t16 t3.t17 t3.t18 t3.t19))
% 2.83/3.05  (step t3.t21 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule reordering :premises (t3.t20))
% 2.83/3.05  (step t3.t22 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule contraction :premises (t3.t21))
% 2.83/3.05  (step t3.t23 (cl (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule resolution :premises (t3.t1 t3.t22))
% 2.83/3.05  (step t3.t24 (cl (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule implies_neg2)
% 2.83/3.05  (step t3.t25 (cl (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule resolution :premises (t3.t23 t3.t24))
% 2.83/3.05  (step t3.t26 (cl (=> (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule contraction :premises (t3.t25))
% 2.83/3.05  (step t3.t27 (cl (not (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule implies :premises (t3.t26))
% 2.83/3.05  (step t3.t28 (cl (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule and_neg)
% 2.83/3.05  (step t3.t29 (cl (and (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule resolution :premises (t3.t28 t3.a13 t3.a9 t3.a11 t3.a0 t3.a2 t3.a1 t3.a12 t3.a4 t3.a8 t3.a3 t3.a16 t3.a7 t3.a10 t3.a5 t3.a6 t3.a15 t3.a14))
% 2.83/3.05  (step t3.t30 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule resolution :premises (t3.t27 t3.t29))
% 2.83/3.05  (step t3 (cl (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4 t3.a5 t3.a6 t3.a7 t3.a8 t3.a9 t3.a10 t3.a11 t3.a12 t3.a13 t3.a14 t3.a15 t3.a16))
% 2.83/3.05  (step t4 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule and_pos)
% 2.83/3.05  (step t5 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule and_pos)
% 2.83/3.05  (step t6 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule and_pos)
% 2.83/3.05  (step t7 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t8 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) :rule and_pos)
% 2.83/3.05  (step t9 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t10 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t11 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t12 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t13 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule and_pos)
% 2.83/3.05  (step t14 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t15 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t16 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule and_pos)
% 2.83/3.05  (step t17 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t18 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule and_pos)
% 2.83/3.05  (step t19 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t20 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule and_pos)
% 2.83/3.05  (step t21 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20))
% 2.83/3.06  (step t22 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule reordering :premises (t21))
% 2.83/3.06  (step t23 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule contraction :premises (t22))
% 2.83/3.06  (step t24 (cl (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule resolution :premises (t2 t23))
% 2.83/3.06  (step t25 (cl (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule implies_neg2)
% 2.83/3.06  (step t26 (cl (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule resolution :premises (t24 t25))
% 2.83/3.06  (step t27 (cl (=> (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule contraction :premises (t26))
% 2.83/3.06  (step t28 (cl (not (and (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule implies :premises (t27))
% 2.83/3.06  (step t29 (cl (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) :rule resolution :premises (t1 t28))
% 2.83/3.06  (step t30 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (not (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (not (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule reordering :premises (t29))
% 2.83/3.06  (step t31 (cl (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule or_pos)
% 2.83/3.06  (step t32 (cl (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))))) :rule reordering :premises (t31))
% 2.83/3.06  (step t33 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t34)
% 2.83/3.06  (assume t34.a0 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.06  (step t34.t1 (cl (or (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))))) :rule forall_inst :args ((:= V_b (tptp.c_Transcendental_Ocos tptp.v_a)) (:= V_a (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (:= T_a tptp.tc_RealDef_Oreal)))
% 2.83/3.06  (step t34.t2 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule or :premises (t34.t1))
% 2.83/3.06  (step t34.t3 (cl (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule resolution :premises (t34.t2 t34.a0))
% 2.83/3.06  (step t34 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule subproof :discharge (t34.a0))
% 2.83/3.06  (step t35 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule resolution :premises (t33 t34))
% 2.83/3.06  (step t36 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))))) :rule implies_neg2)
% 2.83/3.06  (step t37 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))))) :rule resolution :premises (t35 t36))
% 2.83/3.06  (step t38 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))))) :rule contraction :premises (t37))
% 2.83/3.06  (step t39 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule implies :premises (t38))
% 2.83/3.06  (step t40 (cl (not (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))) (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) :rule equiv_pos2)
% 2.83/3.06  (step t41 (cl (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))) :rule all_simplify)
% 2.83/3.06  (step t42 (cl (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) :rule resolution :premises (t40 t41 a32))
% 2.83/3.06  (step t43 (cl (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))))) :rule resolution :premises (t39 t42))
% 2.83/3.06  (step t44 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule resolution :premises (t32 a1161 t43))
% 2.83/3.06  (step t45 (cl (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule or_pos)
% 2.83/3.06  (step t46 (cl (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))))) :rule reordering :premises (t45))
% 2.83/3.06  (step t47 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t48)
% 2.83/3.06  (assume t48.a0 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 2.83/3.06  (step t48.t1 (cl (or (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))))) :rule forall_inst :args ((:= V_b (tptp.c_Transcendental_Osin tptp.v_a)) (:= V_a (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (:= T_a tptp.tc_RealDef_Oreal)))
% 2.83/3.06  (step t48.t2 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule or :premises (t48.t1))
% 2.83/3.06  (step t48.t3 (cl (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule resolution :premises (t48.t2 t48.a0))
% 2.83/3.06  (step t48 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule subproof :discharge (t48.a0))
% 2.83/3.06  (step t49 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule resolution :premises (t47 t48))
% 2.83/3.06  (step t50 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) (not (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))))) :rule implies_neg2)
% 2.83/3.06  (step t51 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))))) :rule resolution :premises (t49 t50))
% 2.83/3.06  (step t52 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))))) :rule contraction :premises (t51))
% 2.83/3.06  (step t53 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule implies :premises (t52))
% 2.83/3.06  (step t54 (cl (or (not (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))))) :rule resolution :premises (t53 t42))
% 2.83/3.06  (step t55 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule resolution :premises (t46 a1161 t54))
% 2.83/3.06  (step t56 (cl (not (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule equiv_pos2)
% 2.83/3.06  (step t57 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))))) :rule refl)
% 2.83/3.06  (step t58 (cl (= (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule all_simplify)
% 2.83/3.06  (step t59 (cl (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule cong :premises (t57 t58))
% 2.83/3.06  (step t60 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y)))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t61)
% 2.83/3.06  (assume t61.a0 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))))
% 2.83/3.06  (step t61.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y)))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule forall_inst :args ((:= V_y (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (:= V_x (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))))
% 2.83/3.06  (step t61.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y)))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule or :premises (t61.t1))
% 2.83/3.06  (step t61.t3 (cl (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t61.t2 t61.a0))
% 2.83/3.06  (step t61 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y)))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule subproof :discharge (t61.a0))
% 2.83/3.06  (step t62 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t60 t61))
% 2.83/3.06  (step t63 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule implies_neg2)
% 2.83/3.06  (step t64 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t62 t63))
% 2.83/3.06  (step t65 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule contraction :premises (t64))
% 2.83/3.06  (step t66 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t56 t59 t65))
% 2.83/3.06  (step t67 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y)))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule implies :premises (t66))
% 2.83/3.06  (step t68 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_ORe (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t67 a961))
% 2.83/3.06  (step t69 (cl (not (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule equiv_pos2)
% 2.83/3.06  (step t70 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) :rule refl)
% 2.83/3.06  (step t71 (cl (= (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule all_simplify)
% 2.83/3.06  (step t72 (cl (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule cong :premises (t70 t71))
% 2.83/3.06  (step t73 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t74)
% 2.83/3.06  (assume t74.a0 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))
% 2.83/3.06  (step t74.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule forall_inst :args ((:= V_y (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (:= V_x (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))))
% 2.83/3.06  (step t74.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule or :premises (t74.t1))
% 2.83/3.06  (step t74.t3 (cl (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t74.t2 t74.a0))
% 2.83/3.06  (step t74 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule subproof :discharge (t74.a0))
% 2.83/3.06  (step t75 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t73 t74))
% 2.83/3.06  (step t76 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule implies_neg2)
% 2.83/3.06  (step t77 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t75 t76))
% 2.83/3.06  (step t78 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule contraction :premises (t77))
% 2.83/3.06  (step t79 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t69 t72 t78))
% 2.83/3.06  (step t80 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y)) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule implies :premises (t79))
% 2.83/3.06  (step t81 (cl (= (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (tptp.c_Complex_OIm (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t80 a960))
% 2.83/3.06  (step t82 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t83)
% 2.83/3.06  (assume t83.a0 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))))
% 2.83/3.06  (step t83.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule forall_inst :args ((:= V_y (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (:= V_x (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))))
% 2.83/3.06  (step t83.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule or :premises (t83.t1))
% 2.83/3.06  (step t83.t3 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t83.t2 t83.a0))
% 2.83/3.06  (step t83 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule subproof :discharge (t83.a0))
% 2.83/3.06  (step t84 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t82 t83))
% 2.83/3.06  (step t85 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule implies_neg2)
% 2.83/3.06  (step t86 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule resolution :premises (t84 t85))
% 2.83/3.06  (step t87 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y)))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))))) :rule contraction :premises (t86))
% 2.83/3.06  (step t88 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_x) V_y) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe V_x)) (tptp.c_Complex_ORe V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_OIm V_y))) (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_Complex_ORe V_x)) (tptp.c_Complex_OIm V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm V_x)) (tptp.c_Complex_ORe V_y))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule implies :premises (t87))
% 2.83/3.06  (step t89 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) (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_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi))) (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))))) :rule resolution :premises (t88 a959))
% 2.83/3.06  (step t90 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t91)
% 2.83/3.06  (assume t91.a0 (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))))
% 2.83/3.06  (step t91.t1 (cl (or (not (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule forall_inst :args ((:= V_z (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))
% 2.83/3.06  (step t91.t2 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule or :premises (t91.t1))
% 2.83/3.06  (step t91.t3 (cl (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t91.t2 t91.a0))
% 2.83/3.06  (step t91 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule subproof :discharge (t91.a0))
% 2.83/3.06  (step t92 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t90 t91))
% 2.83/3.06  (step t93 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (not (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule implies_neg2)
% 2.83/3.06  (step t94 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule resolution :premises (t92 t93))
% 2.83/3.06  (step t95 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule contraction :premises (t94))
% 2.83/3.06  (step t96 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule implies :premises (t95))
% 2.83/3.06  (step t97 (cl (not (= (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z)) (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))))) (not (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z))) (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) :rule equiv_pos2)
% 2.83/3.06  (anchor :step t98 :args ((V_z $$unsorted) (:= V_z V_z)))
% 2.83/3.06  (step t98.t1 (cl (= V_z V_z)) :rule refl)
% 2.83/3.06  (step t98.t2 (cl (= (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) :rule all_simplify)
% 2.83/3.06  (step t98 (cl (= (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z)) (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)))))) :rule bind)
% 2.83/3.06  (step t99 (cl (forall ((V_z $$unsorted)) (= V_z (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z))))) :rule resolution :premises (t97 t98 a945))
% 2.83/3.06  (step t100 (cl (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t96 t99))
% 2.83/3.06  (step t101 (cl (not (= (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))))) (not (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule equiv_pos2)
% 2.83/3.06  (step t102 (cl (= (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))))) :rule refl)
% 2.83/3.06  (step t103 (cl (= (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule all_simplify)
% 2.83/3.06  (step t104 (cl (= (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))))) :rule cong :premises (t102 t103))
% 2.83/3.06  (step t105 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t106)
% 2.83/3.06  (assume t106.a0 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))))
% 2.83/3.06  (step t106.t1 (cl (or (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x))))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule forall_inst :args ((:= V_x tptp.v_a)))
% 2.83/3.06  (step t106.t2 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x))))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule or :premises (t106.t1))
% 2.83/3.06  (step t106.t3 (cl (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule resolution :premises (t106.t2 t106.a0))
% 2.83/3.06  (step t106 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x))))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule subproof :discharge (t106.a0))
% 2.83/3.06  (step t107 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule resolution :premises (t105 t106))
% 2.83/3.06  (step t108 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule implies_neg2)
% 2.83/3.06  (step t109 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule resolution :premises (t107 t108))
% 2.83/3.06  (step t110 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule contraction :premises (t109))
% 2.83/3.06  (step t111 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule resolution :premises (t101 t104 t110))
% 2.83/3.06  (step t112 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x))))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule implies :premises (t111))
% 2.83/3.06  (step t113 (cl (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos tptp.v_a)) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule resolution :premises (t112 a359))
% 2.83/3.06  (step t114 (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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) :rule or_pos)
% 2.83/3.06  (step t115 (cl (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)) (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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule reordering :premises (t114))
% 2.83/3.06  (step t116 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (forall ((V_c $$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)
% 2.83/3.06  (anchor :step t117)
% 2.83/3.06  (assume t117.a0 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 2.83/3.06  (step t117.t1 (cl (or (not (forall ((V_c $$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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule forall_inst :args ((:= V_c tptp.v_a) (:= V_a tptp.c_Transcendental_Opi) (:= T_a tptp.tc_RealDef_Oreal)))
% 2.83/3.06  (step t117.t2 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule or :premises (t117.t1))
% 2.83/3.06  (step t117.t3 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule resolution :premises (t117.t2 t117.a0))
% 2.83/3.06  (step t117 (cl (not (forall ((V_c $$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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule subproof :discharge (t117.a0))
% 2.83/3.06  (step t118 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule resolution :premises (t116 t117))
% 2.83/3.06  (step t119 (cl (=> (forall ((V_c $$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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule implies_neg2)
% 2.83/3.06  (step t120 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) (=> (forall ((V_c $$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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule resolution :premises (t118 t119))
% 2.83/3.06  (step t121 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))))) :rule contraction :premises (t120))
% 2.83/3.06  (step t122 (cl (not (forall ((V_c $$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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule implies :premises (t121))
% 2.83/3.06  (step t123 (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)
% 2.83/3.06  (step t124 (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)
% 2.83/3.06  (step t125 (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 (t123 t124 a56))
% 2.83/3.06  (step t126 (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_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi)))) :rule resolution :premises (t122 t125))
% 2.83/3.06  (step t127 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_a tptp.c_Transcendental_Opi))) :rule resolution :premises (t115 a1137 t126))
% 2.83/3.06  (step t128 (cl (not (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule or_pos)
% 2.83/3.06  (step t129 (cl (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (not (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule reordering :premises (t128))
% 2.83/3.06  (step t130 (cl (not (= (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))) (not (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule equiv_pos2)
% 2.83/3.06  (step t131 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (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)))))) :rule refl)
% 2.83/3.06  (step t132 (cl (= (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)))) :rule refl)
% 2.83/3.06  (step t133 (cl (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule all_simplify)
% 2.83/3.06  (step t134 (cl (= (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule cong :premises (t132 t133))
% 2.83/3.06  (step t135 (cl (= (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))) :rule cong :premises (t131 t134))
% 2.83/3.06  (step t136 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t137)
% 2.83/3.06  (assume t137.a0 (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 2.83/3.06  (step t137.t1 (cl (or (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule forall_inst :args ((:= V_a tptp.v_r) (:= T_a tptp.tc_RealDef_Oreal)))
% 2.83/3.06  (step t137.t2 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule or :premises (t137.t1))
% 2.83/3.06  (step t137.t3 (cl (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule resolution :premises (t137.t2 t137.a0))
% 2.83/3.06  (step t137 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule subproof :discharge (t137.a0))
% 2.83/3.06  (step t138 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule resolution :premises (t136 t137))
% 2.83/3.06  (step t139 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (not (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule implies_neg2)
% 2.83/3.06  (step t140 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule resolution :premises (t138 t139))
% 2.83/3.06  (step t141 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule contraction :premises (t140))
% 2.83/3.06  (step t142 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule resolution :premises (t130 t135 t141))
% 2.83/3.06  (step t143 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule implies :premises (t142))
% 2.83/3.06  (step t144 (cl (not (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))) (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) :rule equiv_pos2)
% 2.83/3.06  (step t145 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))) :rule all_simplify)
% 2.83/3.06  (step t146 (cl (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) :rule resolution :premises (t144 t145 a9))
% 2.83/3.06  (step t147 (cl (or (not (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule resolution :premises (t143 t146))
% 2.83/3.06  (step t148 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule resolution :premises (t129 a1136 t147))
% 2.83/3.06  (step t149 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t150)
% 2.83/3.06  (assume t150.a0 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))))
% 2.83/3.06  (step t150.t1 (cl (or (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule forall_inst :args ((:= V_a tptp.v_a) (:= V_r (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))
% 2.83/3.06  (step t150.t2 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule or :premises (t150.t1))
% 2.83/3.06  (step t150.t3 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule resolution :premises (t150.t2 t150.a0))
% 2.83/3.06  (step t150 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule subproof :discharge (t150.a0))
% 2.83/3.06  (step t151 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule resolution :premises (t149 t150))
% 2.83/3.06  (step t152 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule implies_neg2)
% 2.83/3.06  (step t153 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule resolution :premises (t151 t152))
% 2.83/3.06  (step t154 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a))))) :rule contraction :premises (t153))
% 2.83/3.06  (step t155 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule implies :premises (t154))
% 2.83/3.06  (step t156 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Ocos tptp.v_a)))) :rule resolution :premises (t155 a965))
% 2.83/3.06  (step t157 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t158)
% 2.83/3.06  (assume t158.a0 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))))
% 2.83/3.06  (step t158.t1 (cl (or (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule forall_inst :args ((:= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (:= V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))
% 2.83/3.06  (step t158.t2 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule or :premises (t158.t1))
% 2.83/3.06  (step t158.t3 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t158.t2 t158.a0))
% 2.83/3.06  (step t158 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule subproof :discharge (t158.a0))
% 2.83/3.06  (step t159 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t157 t158))
% 2.83/3.06  (step t160 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule implies_neg2)
% 2.83/3.06  (step t161 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule resolution :premises (t159 t160))
% 2.83/3.06  (step t162 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a)))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule contraction :premises (t161))
% 2.83/3.06  (step t163 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Ocos V_a))))) (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule implies :premises (t162))
% 2.83/3.06  (step t164 (cl (= (tptp.c_Complex_ORe (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Ocos (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t163 a965))
% 2.83/3.06  (step t165 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t166)
% 2.83/3.06  (assume t166.a0 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))))
% 2.83/3.06  (step t166.t1 (cl (or (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))) :rule forall_inst :args ((:= V_a tptp.v_a) (:= V_r (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))
% 2.83/3.06  (step t166.t2 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule or :premises (t166.t1))
% 2.83/3.06  (step t166.t3 (cl (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t166.t2 t166.a0))
% 2.83/3.06  (step t166 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule subproof :discharge (t166.a0))
% 2.83/3.06  (step t167 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t165 t166))
% 2.83/3.06  (step t168 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))) :rule implies_neg2)
% 2.83/3.06  (step t169 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))) :rule resolution :premises (t167 t168))
% 2.83/3.06  (step t170 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a))))) :rule contraction :premises (t169))
% 2.83/3.06  (step t171 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule implies :premises (t170))
% 2.83/3.06  (step t172 (cl (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t171 a964))
% 2.83/3.06  (step t173 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t174)
% 2.83/3.06  (assume t174.a0 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))))
% 2.83/3.06  (step t174.t1 (cl (or (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule forall_inst :args ((:= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (:= V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))
% 2.83/3.06  (step t174.t2 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule or :premises (t174.t1))
% 2.83/3.06  (step t174.t3 (cl (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t174.t2 t174.a0))
% 2.83/3.06  (step t174 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule subproof :discharge (t174.a0))
% 2.83/3.06  (step t175 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t173 t174))
% 2.83/3.06  (step t176 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (not (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule implies_neg2)
% 2.83/3.06  (step t177 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule resolution :premises (t175 t176))
% 2.83/3.06  (step t178 (cl (=> (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a)))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))))) :rule contraction :premises (t177))
% 2.83/3.06  (step t179 (cl (not (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis V_r V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) (tptp.c_Transcendental_Osin V_a))))) (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule implies :premises (t178))
% 2.83/3.06  (step t180 (cl (= (tptp.c_Complex_OIm (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (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_Transcendental_Opi tptp.v_a))) (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_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t179 a964))
% 2.83/3.06  (step t181 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t182)
% 2.83/3.06  (assume t182.a0 (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))))
% 2.83/3.06  (step t182.t1 (cl (or (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule forall_inst :args ((:= V_x tptp.v_a)))
% 2.83/3.06  (step t182.t2 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule or :premises (t182.t1))
% 2.83/3.06  (step t182.t3 (cl (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t182.t2 t182.a0))
% 2.83/3.06  (step t182 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule subproof :discharge (t182.a0))
% 2.83/3.06  (step t183 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t181 t182))
% 2.83/3.06  (step t184 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (not (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule implies_neg2)
% 2.83/3.06  (step t185 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule resolution :premises (t183 t184))
% 2.83/3.06  (step t186 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x)))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a))))) :rule contraction :premises (t185))
% 2.83/3.06  (step t187 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin V_x))))) (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule implies :premises (t186))
% 2.83/3.06  (step t188 (cl (= (tptp.c_Transcendental_Osin (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Osin tptp.v_a)))) :rule resolution :premises (t187 a452))
% 2.83/3.06  (step t189 (cl (not (= (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) (not (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule equiv_pos2)
% 2.83/3.06  (step t190 (cl (= (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))) :rule refl)
% 2.83/3.06  (step t191 (cl (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule all_simplify)
% 2.83/3.06  (step t192 (cl (= (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))))) :rule cong :premises (t190 t191))
% 2.83/3.06  (step t193 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t194)
% 2.83/3.06  (assume t194.a0 (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))
% 2.83/3.06  (step t194.t1 (cl (or (not (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule forall_inst :args ((:= V_b tptp.v_a) (:= V_r2 (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (:= V_a tptp.c_Transcendental_Opi) (:= V_r1 (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))
% 2.83/3.06  (step t194.t2 (cl (not (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) :rule or :premises (t194.t1))
% 2.83/3.06  (step t194.t3 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) :rule resolution :premises (t194.t2 t194.a0))
% 2.83/3.06  (step t194 (cl (not (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) :rule subproof :discharge (t194.a0))
% 2.83/3.06  (step t195 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) :rule resolution :premises (t193 t194))
% 2.83/3.06  (step t196 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule implies_neg2)
% 2.83/3.06  (step t197 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)))) (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule resolution :premises (t195 t196))
% 2.83/3.06  (step t198 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a))))) :rule contraction :premises (t197))
% 2.83/3.06  (step t199 (cl (=> (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a))))) :rule resolution :premises (t189 t192 t198))
% 2.83/3.06  (step t200 (cl (not (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b))))) (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule implies :premises (t199))
% 2.83/3.06  (step t201 (cl (= (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi tptp.v_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.c_Transcendental_Opi)) (tptp.c_Complex_Orcis (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) tptp.v_a)))) :rule resolution :premises (t200 a36))
% 2.83/3.06  (step t202 (cl (not (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))) (not (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule equiv_pos2)
% 2.83/3.06  (step t203 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))))) :rule refl)
% 2.83/3.06  (step t204 (cl (= (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule all_simplify)
% 2.83/3.06  (step t205 (cl (= (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))))) :rule cong :premises (t203 t204))
% 2.83/3.06  (step t206 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t207)
% 2.83/3.06  (assume t207.a0 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))))
% 2.83/3.06  (step t207.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule forall_inst :args ((:= V_y (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (:= V_x (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))
% 2.83/3.06  (step t207.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule or :premises (t207.t1))
% 2.83/3.06  (step t207.t3 (cl (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule resolution :premises (t207.t2 t207.a0))
% 2.83/3.06  (step t207 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule subproof :discharge (t207.a0))
% 2.83/3.06  (step t208 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule resolution :premises (t206 t207))
% 2.83/3.06  (step t209 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (not (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule implies_neg2)
% 2.83/3.06  (step t210 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule resolution :premises (t208 t209))
% 2.83/3.06  (step t211 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule contraction :premises (t210))
% 2.83/3.06  (step t212 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))))) :rule resolution :premises (t202 t205 t211))
% 2.83/3.06  (step t213 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule implies :premises (t212))
% 2.83/3.06  (step t214 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))))) :rule resolution :premises (t213 a4))
% 2.83/3.06  (step t215 (cl (not (= (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))))) (not (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule equiv_pos2)
% 2.83/3.06  (step t216 (cl (= (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))))) :rule refl)
% 2.83/3.06  (step t217 (cl (= (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule all_simplify)
% 2.83/3.06  (step t218 (cl (= (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))))) :rule cong :premises (t216 t217))
% 2.83/3.06  (step t219 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) :rule implies_neg1)
% 2.83/3.06  (anchor :step t220)
% 2.83/3.06  (assume t220.a0 (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))))
% 2.83/3.06  (step t220.t1 (cl (or (not (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule forall_inst :args ((:= V_x tptp.v_r)))
% 2.83/3.06  (step t220.t2 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule or :premises (t220.t1))
% 2.83/3.06  (step t220.t3 (cl (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule resolution :premises (t220.t2 t220.a0))
% 2.83/3.06  (step t220 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule subproof :discharge (t220.a0))
% 2.83/3.06  (step t221 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) :rule resolution :premises (t219 t220))
% 2.83/3.06  (step t222 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (not (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule implies_neg2)
% 2.83/3.06  (step t223 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r))) (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule resolution :premises (t221 t222))
% 2.83/3.06  (step t224 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r)))) :rule contraction :premises (t223))
% 2.83/3.06  (step t225 (cl (=> (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r))))) :rule resolution :premises (t215 t218 t224))
% 2.83/3.06  (step t226 (cl (not (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule implies :premises (t225))
% 2.83/3.06  (step t227 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal tptp.v_r) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) tptp.v_r) tptp.v_r)))) :rule resolution :premises (t226 a2))
% 2.83/3.08  (step t228 (cl) :rule resolution :premises (t30 t44 t55 t68 t81 t89 t100 t113 t127 t148 t156 t164 t172 t180 t188 t201 t214 t227 a1200))
% 2.83/3.08  
% 2.83/3.08  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.Iu1zVElSdY/cvc5---1.0.5_13225.smt2
% 2.83/3.08  % cvc5---1.0.5 exiting
% 2.83/3.08  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------