%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW192+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 : Fri Sep  1 00:19:54 EDT 2023

% Result   : Theorem 3.20s 3.47s
% Output   : Proof 3.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.24  % Problem    : SWW192+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.25  % Command    : do_cvc5 %s %d
% 0.25/0.46  % Computer : n023.cluster.edu
% 0.25/0.46  % Model    : x86_64 x86_64
% 0.25/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46  % Memory   : 8042.1875MB
% 0.25/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46  % CPULimit   : 300
% 0.25/0.46  % WCLimit    : 300
% 0.25/0.46  % DateTime   : Sun Aug 27 20:59:56 EDT 2023
% 0.25/0.46  % CPUTime    : 
% 0.42/0.71  %----Proving TF0_NAR, FOF, or CNF
% 3.20/3.47  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EyF15NDFA1/cvc5---1.0.5_28330.p...
% 3.20/3.47  ------- get file name : TPTP file name is SWW192+1
% 3.20/3.47  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28330.smt2...
% 3.20/3.47  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.20/3.47  % SZS status Theorem for SWW192+1
% 3.20/3.47  % SZS output start Proof for SWW192+1
% 3.20/3.47  (
% 3.20/3.47  (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (let ((_let_3 (tptp.c_Int_OBit0 _let_2))) (let ((_let_4 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_3))) (let ((_let_5 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (let ((_let_6 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_5 tptp.v_x____) _let_4) (tptp.hAPP (tptp.hAPP _let_5 tptp.v_y____) _let_4)))) (let ((_let_7 (not (= _let_6 _let_1)))) (let ((_let_8 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_9 (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) tptp.c_Complex_Oii))) (let ((_let_11 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Complex_Ocomplex tptp.c_Int_OMin))) (let ((_let_12 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_13 (tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_3)))) (let ((_let_14 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_15 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (let ((_let_16 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_17 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls))) (let ((_let_18 (tptp.c_Int_OBit1 _let_2))) (let ((_let_19 (tptp.c_Nat_OSuc _let_14))) (let ((_let_20 (tptp.c_Nat_OSuc _let_19))) (let ((_let_21 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_2))) (let ((_let_22 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_23 (tptp.c_NthRoot_Osqrt _let_1))) (let ((_let_24 (= _let_23 _let_1))) (let ((_let_25 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_NthRoot_Osqrt V_xa_2) (tptp.c_NthRoot_Osqrt V_ya_2)) (= V_xa_2 V_ya_2))))) (let ((_let_26 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls))) (let ((_let_27 (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))))))) (let ((_let_28 (tptp.c_Complex_Ocomplex_OComplex tptp.v_x____ tptp.v_y____))) (let ((_let_29 (= tptp.v_z _let_28))) (let ((_let_30 (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_z) _let_1))) (let ((_let_31 (= _let_1 _let_23))) (let ((_let_32 (tptp.c_NthRoot_Osqrt _let_6))) (let ((_let_33 (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_28) _let_32))) (let ((_let_34 (= _let_23 _let_32))) (let ((_let_35 (ASSUME :args (_let_30)))) (let ((_let_36 (ASSUME :args (_let_29)))) (let ((_let_37 (SYMM (ASSUME :args (_let_24))))) (let ((_let_38 (_let_27))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (= _let_1 _let_6))) (let ((_let_41 (= _let_40 _let_34))) (let ((_let_42 (not _let_34))) (let ((_let_43 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_NthRoot_Osqrt V_xa_2) (tptp.c_NthRoot_Osqrt V_ya_2)) (= V_ya_2 V_xa_2))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (= _let_1 _let_32))) (let ((_let_46 (ASSUME :args (_let_42)))) (let ((_let_47 (SYMM _let_35))) (let ((_let_48 (SYMM _let_47))) (let ((_let_49 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_46 _let_37 _let_35 (MODUS_PONENS (AND_INTRO _let_49 _let_36 _let_35) (SCOPE (TRANS _let_47 (CONG (REFL :args (tptp.tc_Complex_Ocomplex)) (SYMM (SYMM _let_36)) :args (APPLY_UF tptp.c_RealVector_Onorm__class_Onorm)) (SYMM (SYMM _let_49))) :args (_let_33 _let_29 _let_30)))) :args (_let_30 _let_29 _let_31 _let_33 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (TRANS (SYMM (TRANS _let_48 (SYMM (SYMM _let_37)))) _let_48 (SYMM (SYMM (ASSUME :args (_let_45))))))) (FALSE_INTRO _let_46))) :args (_let_42 _let_31 _let_30 _let_45)) :args ((not (and _let_30 _let_29 _let_31 _let_33 _let_42)) SB_LITERAL))) (CONG (REFL :args ((not _let_30))) (REFL :args ((not _let_29))) (REFL :args ((not _let_31))) (REFL :args ((not _let_33))) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_34))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_41)) :args ((or _let_40 _let_42 (not _let_41)))) (SYMM (ASSUME :args (_let_7))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_6 _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.c_NthRoot_Osqrt V_xa_2) (tptp.c_NthRoot_Osqrt V_ya_2)))) :args (_let_43)))) _let_44 :args (_let_41 false _let_43)) :args (_let_42 true _let_40 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.v_y____ tptp.v_x____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Complex_Ocomplex_OComplex V_x V_y)))) :args _let_38)) _let_39 :args (_let_33 false _let_27)) _let_37 _let_36 _let_35 :args (false true _let_34 false _let_33 false _let_31 false _let_29 false _let_30)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_30 _let_29 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_w))))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) _let_1) _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) V_a) V_a))) (= (tptp.c_Int_OBit0 tptp.c_Int_OPls) tptp.c_Int_OPls) (forall ((V_l_2 $$unsorted)) (= (= tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l_2)) (= tptp.c_Int_OPls V_l_2))) (forall ((V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (= V_k_2 tptp.c_Int_OPls))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit1 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) V_k))) (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))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))) (forall ((V_z3 $$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)))) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls V_k) V_k)) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit0 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_k))) (= _let_15 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_2)) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_22 _let_22) _let_4) (= _let_21 _let_22) (= _let_22 _let_21) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_xa_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (=> (tptp.class_Int_Onumber T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls))) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OPls (tptp.c_Int_OBit1 V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (not (= tptp.v_z (tptp.c_Complex_Ocomplex_OComplex B_x B_y))))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z)) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))) (forall ((T_a $$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)))) (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)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) _let_3) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_3) (tptp.hAPP (tptp.hAPP _let_4 V_y) _let_3)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a _let_1)) V_x)) V_y))))))))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Code__Numeral_Ocode__numeral) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Code__Numeral_Ocode__numeral _let_2)) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_3 V_xa_2) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_ya_2) _let_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))))) (forall ((V_w $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_w))) (=> (and (tptp.class_Groups_Omonoid__mult T_b) (tptp.class_Int_Onumber T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) _let_1) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) _let_1) _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1) (or (= V_a_2 _let_1) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))) _let_27 (not (= _let_16 _let_15)) (= _let_12 (tptp.c_Complex_Ocomplex_OComplex _let_8 _let_8)) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k) V_k)) (forall ((V_w $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b)))) (forall ((V_y $$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))))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)) (forall ((V_z $$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)) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x))) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a V_xa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 V_v) V_w))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) V_z) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))) V_z))))) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2) _let_1) (and (= V_a_2 _let_1) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Complex_Ocomplex_OComplex V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (and (= V_a_2 _let_1) (= V_b_2 _let_1))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_x)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_b)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_y) _let_1)))) (forall ((V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w))) V_z))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xa_2) (tptp.hAPP (tptp.hAPP _let_2 V_ya_2) V_ya_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1))))))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_b_H)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b)))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_1 (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 _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (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)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a _let_1)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Code__Numeral_Ocode__numeral tptp.c_Int_OPls)) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n))) (let ((_let_3 (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((V_w_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_a_2 V_b_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Complex_Ocomplex V_w_2)) (and (= V_a_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_w_2)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls) tptp.c_Int_OPls) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k)))) (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)))) (forall ((V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) tptp.c_Int_OPls) V_w) tptp.c_Int_OPls)) (forall ((V_l $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_OBit0 V_k)) V_l) (tptp.c_Int_OBit0 (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_z1) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_w))))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w))) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_z1) (tptp.hAPP _let_1 V_z2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (= V_a_2 _let_1))))) (= tptp.c_Int_OPls _let_16) (= _let_16 _let_17) (forall ((V_z $$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)) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)) (forall ((V_z $$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)))) (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)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_a_2 V_b_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (and (= V_a_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= _let_9 (tptp.c_Complex_Ocomplex_OComplex _let_1 _let_8)) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c)))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_b))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b)) _let_1) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (= _let_14 _let_26) (= _let_26 _let_14) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a) V_a))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_OBit1 V_k)) V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l)) V_l)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) _let_1) _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))) (forall ((V_real2_H_2 $$unsorted) (V_real1_H_2 $$unsorted) (V_real2_2 $$unsorted) (V_real1_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2) (tptp.c_Complex_Ocomplex_OComplex V_real1_H_2 V_real2_H_2)) (and (= V_real1_2 V_real1_H_2) (= V_real2_2 V_real2_H_2)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_a)) V_a))))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_z) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) _let_3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_3) (tptp.hAPP (tptp.hAPP _let_4 V_y) _let_3)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) V_x)) V_y)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) _let_1) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_n)) _let_1))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) _let_1) (= V_a_2 _let_1))))) (forall ((V_ya $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_xa) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ya) _let_1))))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_NthRoot_Osqrt _let_3)) _let_1) _let_3))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (=> (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) V_x) (= V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (=> (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) V_y) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_3 V_xa_2) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_ya_2) _let_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1))))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_2) _let_2)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 _let_1))) (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) V_x)) _let_2))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) _let_2))) (let ((_let_4 (= _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> _let_4 (= _let_3 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_4) (= _let_3 _let_1))))))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q)))))) (forall ((V_w_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) _let_1) _let_2) (and (= V_a_2 _let_2) (not (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))) (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)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint _let_16) _let_16) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_z)) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_w) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_z1))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z2)) V_z3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_z3)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2))) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (= V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_c_2)) (= V_a_2 V_b_2))))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.hAPP _let_1 V_z1))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z2)) V_z3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_z3)))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))) (forall ((V_c $$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_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_p)) V_q) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) V_q))))))) (not (= _let_8 _let_1)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_z1) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_w))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xa_2) (tptp.hAPP (tptp.hAPP _let_2 V_ya_2) V_ya_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))) (forall ((V_a_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_xa_2 V_a_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_ya_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_xa_2)))) (= (tptp.c_NthRoot_Osqrt _let_8) _let_8) (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_NthRoot_Osqrt V_y))))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (= V_xa_2 _let_1)))) _let_25 (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_za_2 $$unsorted) (V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_xa_2))) (let ((_let_3 (tptp.hAPP _let_1 V_w_2))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_3 V_ya_2) (tptp.hAPP _let_2 V_za_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_3 V_za_2) (tptp.hAPP _let_2 V_ya_2))) (or (= V_w_2 V_xa_2) (= V_ya_2 V_za_2)))))))) (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_m) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b_2))) (let ((_let_3 (tptp.hAPP _let_1 V_a_2))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_c_2 V_d_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_3 V_c_2) (tptp.hAPP _let_2 V_d_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_3 V_d_2) (tptp.hAPP _let_2 V_c_2)))))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_q)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_q))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))) (forall ((V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (= (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP _let_1 V_x) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_NthRoot_Osqrt V_x)) V_k)))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (= (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (= V_xa_2 _let_1)))) _let_24 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r))) (=> (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 _let_1 V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP _let_1 V_d))))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ya_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_xa_2))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m))))) (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.hAPP (tptp.hAPP _let_1 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m))))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) V_m))))) (forall ((V_real2 $$unsorted) (V_real1 $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__size (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa_2) V_xa_2) _let_1) (or (= V_xa_2 _let_1) (= V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))) (forall ((V_b $$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)))) (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)))) (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)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_b_2 V_c_2)))) (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_b_2 V_c_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Oone T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (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))) (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))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))) (forall ((V_k $$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)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))) (forall ((V_n_2 $$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))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1) (or (= V_a _let_1) (= V_b _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2) _let_1) (or (= V_a_2 _let_1) (= V_b_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (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))) (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))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 _let_1))))) (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))) (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))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$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))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_e) V_c))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= _let_1 V_a_2))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1) _let_1)))) (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))) (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))) (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))) (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))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_a_2) (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_b_2)) (or (= V_a_2 V_b_2) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_b $$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))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_b $$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))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_b))) (forall ((V_n $$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)) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) _let_1) V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) _let_1) _let_1))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (or (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (= (tptp.hAPP _let_1 (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 _let_1 V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))))) (forall ((V_n $$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)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_ya_2))))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_ya $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_xa) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ya) _let_1)))))))) (forall ((V_real2 $$unsorted) (V_real1 $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize tptp.tc_Complex_Ocomplex (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls))))))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_ya_2))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_xa_2 V_ya_2)))) (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)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (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 _let_1 V_n) (tptp.hAPP _let_1 V_N))))))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (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))))) (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))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$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))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_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_a_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_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_z $$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)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2))) (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)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_xa_2 tptp.c_Int_OPls)))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_ya_2)))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (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 _let_1 V_N) (tptp.hAPP _let_1 V_n)))))))) (forall ((V_za_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.c_Int_Oiszero T_a V_za_2) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_xa_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_ya_2)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Oone__class_Oone T_a))))) (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)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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_a_2) V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (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) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 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) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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 _let_2 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1))) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (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)))))) (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)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_xa_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_ya_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_xa_2 V_ya_2) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$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))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_a_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_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (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 _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))) (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)))) (forall ((V_ya_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_ya_2)))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (=> (= (tptp.c_NthRoot_Osqrt V_x) _let_1) (= V_x _let_1))))) (forall ((V_x $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes 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.hAPP (tptp.hAPP _let_1 V_u) V_u)) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 _let_1)))) (forall ((V_ya_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_ya_2)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) _let_1))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xa_2) (tptp.hAPP (tptp.hAPP _let_2 V_ya_2) V_ya_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (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 _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x) V_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 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))))))) (forall ((V_xa_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_xa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))) (forall ((V_y $$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))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_ya_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_xa_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_xa_2) V_ya_2))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y)))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((V_w_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w_2))) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))))) (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)))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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 _let_2 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 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 _let_1 V_u) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_v) V_y)) V_a)))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (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 _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_ya_2))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y) (= V_x V_y))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) (=> (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_x V_y))))))) (forall ((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) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_8 _let_13) (forall ((V_x $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_u) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_3 V_xa_2) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_ya_2) _let_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))))) (forall ((V_k $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_k)) _let_1) (= V_a _let_1))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (= (tptp.c_NthRoot_Osqrt V_x) V_y)))) (forall ((V_x $$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.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x))) (forall ((V_xa_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_xa_2)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_xa_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa_2))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_c)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_b V_d)) _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_real2_2 $$unsorted) (V_real1_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__rec T_a V_f1_2 (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_real1_2) V_real2_2))) (forall ((V_real2_2 $$unsorted) (V_real1_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complex_Ocomplex_Ocomplex__case T_a V_f1_2 (tptp.c_Complex_Ocomplex_OComplex V_real1_2 V_real2_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_real1_2) V_real2_2))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) _let_1)))) (forall ((V_xa_2 $$unsorted)) (= (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2)) (exists ((B_y $$unsorted)) (= V_xa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) B_y) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m _let_1) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)) (= V_m _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))) (forall ((V_k $$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)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (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))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 _let_1) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 _let_1))))) (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))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))) (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)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)) (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 $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1 V_i) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n))))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 V_v_H_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_m_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_xa_2) V_m_2) _let_2) (or (= V_m_2 _let_1) (= V_xa_2 _let_2)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) _let_1) V_n) _let_1))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 _let_1) (= V_n_2 _let_1)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_n $$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)))))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$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))) (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))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_m $$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)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_n_2 $$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))) (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 $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (=> (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 _let_1 V_i) (tptp.hAPP _let_1 V_j))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m))) (forall ((V_k $$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)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint _let_16) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint _let_15)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y)) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y)) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_ya_2))) (let ((_let_2 (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2))) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_xa_2 V_ya_2)) (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_xa_2) V_ya_2)) (or (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_ya_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_y)) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))))) (forall ((V_xa_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_xa_2)) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_x)) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Nat_OSuc V_n)) _let_1)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP _let_1 V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_n)) V_a))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_q)))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_q)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= _let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_2) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (= _let_22 _let_19) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m))) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.hAPP _let_1 V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_m)) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_xa_2) V_n_2)) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Nat_OSuc V_n))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_3 V_a) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_b) _let_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (= V_a V_b))))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ya_2) _let_1)) (or (= V_xa_2 V_ya_2) (= V_xa_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_ya_2)))))))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_xa_2 $$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_xa_2) (tptp.hAPP V_g_2 V_xa_2))))) (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))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))) (forall ((V_y $$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))))) (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))))) (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))))) (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))))) (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))))) (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))) (forall ((V_xa_2 $$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_xa_2) (tptp.hAPP V_g_2 V_xa_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_g_2 $$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)))))) (forall ((V_n $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_r (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_r) (tptp.c_Nat_OSuc V_n)) V_r))))) (= _let_21 _let_19) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_18) (tptp.c_Nat_OSuc _let_20)) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_n))) (= _let_20 _let_4) (= _let_4 _let_20) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_n) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n)))) (forall ((V_xa_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Int_Oint V_xa_2) (exists ((B_y $$unsorted)) (= V_xa_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) B_y))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_3 (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) _let_1) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_n)) _let_1)))))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) (tptp.hAPP (tptp.hAPP _let_3 V_x) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_2)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_16 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_3)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_n))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_n))))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_16 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_18)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_16 _let_17) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_16 _let_16) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_16 _let_15) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) _let_1))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))) _let_1)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$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))))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2)))) (forall ((V_y $$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)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_f_2 V_g_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_g_2 V_f_2))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (not (= V_xa_2 V_ya_2)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))) (forall ((V_y $$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)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$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))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_y $$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)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= V_xa_2 V_ya_2))))) (forall ((V_y $$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))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_a $$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))))) (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))))) (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))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_x $$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))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OMin) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OMin))) (forall ((V_w_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_w_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2 V_w_2) (not (= V_za_2 V_w_2))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OMin (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin V_k_2))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OMin tptp.c_Int_OMin) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2))) (=> (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 _let_1 V_xa_2) (tptp.hAPP _let_1 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_xa_2 V_ya_2)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (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 _let_1 V_m) (tptp.hAPP _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (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 _let_1 V_n) (tptp.hAPP _let_1 V_N))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (not (= V_xa_2 V_ya_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (= V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2))) (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)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_xa_2 tptp.c_Int_OPls)))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_ya_2)))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (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 _let_1 V_N) (tptp.hAPP _let_1 V_n)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))) (forall ((V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin _let_16) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_xa_2 V_ya_2)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OMin) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OMin))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin tptp.c_Int_OPls) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OMin)) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin V_k_2))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OMin tptp.c_Int_OMin)) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k $$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)))) (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))) (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))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m $$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)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_k $$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)))) (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))))) (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)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls)) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (not (= V_n_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (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))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_n _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n)))) (forall ((V_a_2 $$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_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (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_a_2))))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) tptp.c_Int_OMin))) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OMin (tptp.c_Int_OBit0 V_l)))) (not (= tptp.c_Int_OPls tptp.c_Int_OMin)) (not (= tptp.c_Int_OMin tptp.c_Int_OPls)) (forall ((V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OMin) (= V_k_2 tptp.c_Int_OMin))) (forall ((V_l_2 $$unsorted)) (= (= tptp.c_Int_OMin (tptp.c_Int_OBit1 V_l_2)) (= tptp.c_Int_OMin V_l_2))) (= (tptp.c_Int_OBit1 tptp.c_Int_OMin) tptp.c_Int_OMin) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (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))))) (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))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_2 V_v_H_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (and (=> _let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_H_2)) _let_1)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_m))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))) (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)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2) (= V_xa_2 V_ya_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= V_xa_2 V_ya_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$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))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$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))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))) (forall ((V_y $$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))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_a $$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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$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))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (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 _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n)))))))) (forall ((V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_ya_2)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_xa_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (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 _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (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 _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (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 _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (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 _let_1 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (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 _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 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) _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2))) (=> (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 _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_2 V_a_2) (tptp.hAPP _let_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_2 V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (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)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_d $$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)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 _let_2) (not (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$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)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))) (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))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2)))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OMin) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OMin))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OMin (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OMin V_k_2))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OMin)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OMin tptp.c_Int_OPls) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OMin) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OMin))) (not (= _let_17 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OMin))) (forall ((V_w_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_w_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 _let_1)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls _let_16)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc _let_2)) (or (= V_x _let_1) (= V_x _let_2)))))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc _let_1)) (= V_n_2 _let_1)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_w_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_w_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 _let_1)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_16 _let_15) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (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 _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP _let_1 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))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (=> (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 _let_1 V_i) (tptp.hAPP _let_1 V_j)))))) (= tptp.c_Int_OMin (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint _let_15)) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j)))))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_xa_2) V_xa_2))) (= V_xa_2 _let_1)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_1 V_xa_2) V_za_2) (tptp.hAPP (tptp.hAPP _let_1 V_ya_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z))) (=> (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 _let_1 V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) tptp.c_Int_OMin) V_k) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (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))))) (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))))) (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2) (= V_w_2 V_za_2)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1))))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 _let_1)))) (forall ((V_ya_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_ya_2)))) (forall ((V_ya_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_NthRoot_Osqrt V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_ya_2)))) (forall ((V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_xa_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 _let_1)))) (forall ((V_n_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_xa_2) V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_xa_2) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_xa_2) V_n_2)) (or (= V_n_2 _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_xa_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 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)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 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)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 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)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 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)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 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)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 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)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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 _let_2 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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 _let_2 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2))) (=> (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 _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2))) (=> (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 _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (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)))))) (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)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xa_2) (tptp.hAPP (tptp.hAPP _let_2 V_ya_2) V_ya_2))) (or (not (= V_xa_2 _let_1)) (not (= V_ya_2 _let_1)))))))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_z)))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin)) V_z) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_z)))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 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)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (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))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n))))))) (forall ((V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OMin) _let_2) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2))) (= (tptp.hAPP _let_1 (tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP (tptp.hAPP V_times_2 V_a_2) (tptp.hAPP _let_1 V_n_2))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_xa_2)) (not (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OMin))) (let ((_let_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) _let_2) (or (and (= V_m_2 _let_2) (= V_n_2 _let_2)) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m) V_n) _let_1) (or (= V_m _let_1) (= V_m (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OMin)))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_1 V_xa_2) V_za_2) (tptp.hAPP (tptp.hAPP _let_1 V_ya_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_za_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_za_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_xa_2) (tptp.hAPP _let_1 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2))))) (forall ((V_s $$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)))))) (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 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))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_k_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 _let_1)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1)))))) (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r V_s)))))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))) (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2))) (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 V_za_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_xa_2) V_ya_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_ya_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_xa_2)))) (forall ((V_w_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_xa_2) _let_2)) (or (= _let_2 _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_xa_2)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (=> (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) _let_1) _let_1)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) _let_1)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_xa_2) (tptp.hAPP _let_1 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_xa_2 V_ya_2)))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_a V_b))))))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_2 _let_1))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_H tptp.c_Int_OPls))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_v_H))))))))))))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z))))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (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 _let_2 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 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 _let_1 V_u) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_v) V_y)) V_a)))))))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_14 _let_4) (forall ((V_k $$unsorted) (V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) V_k)))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_3) (= _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_v_H))) V_k)))))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_v_H)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (not (= V_a_2 _let_1)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_n _let_1) (= V_n (tptp.c_Nat_OSuc _let_1)))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_8 _let_13) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 _let_13) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_3 V_xa_2) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_ya_2) _let_2))) (or (not (= V_xa_2 _let_1)) (not (= V_ya_2 _let_1))))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_x _let_1) (= V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_NthRoot_Osqrt V_x)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 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 _let_1 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))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_q))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_2 V_b_H) V_q_H) V_r_H))) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_2 V_b) V_q) V_r) _let_3) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_3 _let_1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q))))))))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 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))))))) (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))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (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)))) (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)))) (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (=> (=> (= V_m_2 V_n_2) _let_1) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) _let_1) _let_1))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_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 _let_1 V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_q_H)))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H _let_1)))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP _let_1 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))))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_2 V_b_H) V_q_H) V_r_H))) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_2 V_b) V_q) V_r) _let_3) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 _let_3) (=> (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 _let_1 V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 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))))))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_5 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 V_u) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_5) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y _let_5) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_4 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_4 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2))) V_u)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) V_b) (= V_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) (tptp.c_Groups_Oone__class_Oone T_a)) (= V_a_2 V_b_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (= V_a _let_2))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.c_Groups_Oone__class_Oone T_a))))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_a)) V_n)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_xa_2 V_ya_2)) (and (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_xa_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_ya_2 _let_1)))))) (forall ((V_a_2 $$unsorted) (V_w_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> (not _let_3) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2))) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_w_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (= V_c_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_2) (and (=> (not _let_3) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_2) V_c_2))) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (= V_c_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> (not _let_3) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_2) V_c_2) V_b_2)) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_w_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> (not _let_3) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2) V_b_2)) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))))) (forall ((V_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r))) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_r)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_a V_r)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP _let_1 V_b) V_c))))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_y) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_a) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)))) (forall ((V_a_2 $$unsorted) (V_w_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))))))))))) (forall ((V_w_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_2) V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_w_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))))))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OMin) V_x) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_x))))) (forall ((V_w_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_2) V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_w_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_a_2 $$unsorted) (V_w_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_r_2 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_r_2))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_r) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_r (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) (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 V_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (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_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_y))) (forall ((T_a $$unsorted)) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2))))) (forall ((V_u $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_u) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) V_u))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) 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 tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 _let_1) V_x))) (forall ((V_za_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (= V_xa_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_ya_2 (tptp.hAPP _let_1 V_za_2))) (= (tptp.hAPP _let_1 V_xa_2) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_ya_2 V_za_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_w $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_z V_w)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_w)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero 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 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero 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.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_c_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> (not _let_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2)) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_c_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> (not _let_2) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2))) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))))) (forall ((V_w_2 $$unsorted) (V_xa_2 $$unsorted) (V_za_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_ya_2 _let_2)) (=> (not (= V_za_2 _let_2)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_xa_2 V_ya_2) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w_2 V_za_2)) (= (tptp.hAPP (tptp.hAPP _let_1 V_xa_2) V_za_2) (tptp.hAPP (tptp.hAPP _let_1 V_w_2) V_ya_2))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field 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.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field 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 V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2)))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2)))))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1)))))))))))) (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y _let_2)) (=> (not (= V_z _let_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_y)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_x) V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) V_b))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1)))))))))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) V_b_2))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) _let_4) _let_11) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Transcendental_Oarctan V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1)) (tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_2 (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1)))))))))))) (= (tptp.c_Transcendental_Oarctan _let_8) _let_8) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Oarctan (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_w $$unsorted)) (not (= tptp.c_Complex_Oii (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Complex_Ocomplex V_w)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_x)))) (not (= tptp.c_Complex_Oii _let_9)) (not (= tptp.c_Complex_Oii _let_12)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii) (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex V_a V_b)) tptp.c_Complex_Oii) (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_b) V_a))) (= _let_10 _let_11) (= _let_10 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex _let_9)) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_Complex_Ocomplex_OComplex V_xa_2 V_ya_2) tptp.c_Complex_Oii) (and (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_ya_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= tptp.c_Complex_Oii (tptp.c_Complex_Ocomplex_OComplex _let_8 _let_1)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted) (V_u $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_u (tptp.c_NthRoot_Osqrt (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_1))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) _let_4) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y) _let_4) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_NthRoot_Osqrt (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2))) V_u)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y))) (= V_x _let_1))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_w))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint) 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(tptp.class_Groups_Ozero tptp.tc_Int_Oint) (tptp.class_Rings_Oring tptp.tc_Int_Oint) (tptp.class_Rings_Oidom tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Groups_Oone tptp.tc_Int_Oint) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat) (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Power_Opower tptp.tc_Nat_Onat) (tptp.class_Groups_Ozero tptp.tc_Nat_Onat) (tptp.class_Int_Onumber tptp.tc_Nat_Onat) (tptp.class_Groups_Oone tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal) (tptp.class_Power_Opower tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Olinordered__semidom tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Oordered__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ocomm__semiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Ozero__neq__one tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Opreorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Olinorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Omonoid__mult tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Omonoid__add tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring__1 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring__0 tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Omult__zero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Oorder tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Rings_Osemiring tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Orderings_Oord tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Power_Opower tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Ozero tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Int_Onumber tptp.tc_Code__Numeral_Ocode__numeral) (tptp.class_Groups_Oone tptp.tc_Code__Numeral_Ocode__numeral) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.30/3.48  )
% 3.30/3.48  % SZS output end Proof for SWW192+1
% 3.30/3.48  % cvc5---1.0.5 exiting
% 3.30/3.49  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------