%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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 : Thu Aug 31 21:52:45 EDT 2023

% Result   : Unsatisfiable 0.52s 0.73s
% Output   : Proof 0.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15  % Problem    : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.16  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n004.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Tue Aug 29 08:31:37 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.24/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.52  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DxWHogoPUn/cvc5---1.0.5_19988.p...
% 0.24/0.58  ------- get file name : TPTP file name is SWV629-1
% 0.24/0.59  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19988.smt2...
% 0.24/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.52/0.73  % SZS status Unsatisfiable for SWV629-1
% 0.52/0.73  % SZS output start Proof for SWV629-1
% 0.52/0.74  (
% 0.52/0.74  (let ((_let_1 (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_4 (tptp.c_FFT__Mirabelle_Oroot _let_3))) (let ((_let_5 (not (= _let_4 _let_2)))) (let ((_let_6 (tptp.c_HOL_Otimes__class_Otimes _let_3 _let_3 tptp.tc_nat))) (let ((_let_7 (forall ((V_n $$unsorted)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) V_n tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))))) (let ((_let_8 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_9 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))))) (let ((_let_10 (tptp.c_Complex_Ocnj _let_2))) (let ((_let_11 (= _let_10 _let_2))) (let ((_let_12 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_13 (= _let_2 _let_10))) (let ((_let_14 (= _let_2 _let_4))) (let ((_let_15 (tptp.c_Power_Opower__class_Opower _let_4 _let_3 tptp.tc_Complex_Ocomplex))) (let ((_let_16 (= _let_2 _let_15))) (let ((_let_17 (= _let_4 _let_15))) (let ((_let_18 (SYMM (ASSUME :args (_let_11))))) (let ((_let_19 (SYMM (ASSUME :args (_let_5))))) (let ((_let_20 (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) V_n tptp.tc_Complex_Ocomplex))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (not _let_1))) (let ((_let_23 (or _let_22 _let_17))) (let ((_let_24 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= V_a (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (not _let_17))) (let ((_let_27 (not _let_16))) (let ((_let_28 (not _let_13))) (let ((_let_29 (not _let_14))) (let ((_let_30 (SYMM (SYMM _let_18)))) (let ((_let_31 (ASSUME :args (_let_16)))) (let ((_let_32 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_18 _let_31 _let_32 _let_19) :args (_let_13 _let_29 _let_16 _let_17)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_19)) (TRUE_INTRO (TRANS _let_30 (SYMM (TRANS (SYMM (SYMM _let_32)) (SYMM _let_31) _let_30)))))) :args (_let_13 _let_16 _let_17 _let_29)) :args ((not (and _let_13 _let_29 _let_16 _let_17)) SB_LITERAL))) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_14))) (REFL :args (_let_27)) (REFL :args (_let_26)) :args (or))) :args ((or _let_14 _let_28 _let_27 _let_26))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_17 (not _let_23)))) (ASSUME :args (_let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.tc_Complex_Ocomplex _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Power_Opower__class_Opower V_a _let_3 T_a)))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_17 false _let_1 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_FFT__Mirabelle_Oroot V_n)))) :args (_let_20))) _let_21 :args (_let_16 false _let_20)) _let_19 _let_18 :args (false false _let_17 false _let_16 true _let_14 false _let_13)) :args ((forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_x (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) tptp.tc_nat) V_x)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_a tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b tptp.tc_nat)) (= V_a V_b))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_a tptp.tc_nat)) (= V_a V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_m tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) tptp.tc_nat) V_x)) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_x tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) (tptp.c_Divides_Odiv__class_Odiv V_w V_z T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_x V_w T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_w T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_r tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_r tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_r tptp.tc_nat))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_e tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_e tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_e tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_k tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) tptp.tc_nat)) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) tptp.tc_nat)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) tptp.tc_nat)) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_y V_z tptp.tc_nat) V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Olcm _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Olcm V_m _let_1 tptp.tc_nat) _let_1))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Olcm _let_1 V_x tptp.tc_nat) _let_1))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Olcm V_x _let_1 tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_q T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_q T_a) (tptp.c_Power_Opower__class_Opower V_y V_q T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Osgn__class_Osgn V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_x V_z tptp.tc_nat) tptp.tc_nat) tptp.tc_nat)) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_k T_a) (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.c_HOL_Osgn__class_Osgn V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Oabs__class_Oabs V_x T_a) T_a) V_x))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) _let_1)) (= V_x _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) _let_1)) (= V_d _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_b tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_a tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_x) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_y)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) V_m)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) V_m) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) V_n)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) V_n) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Olcm V_y V_x tptp.tc_nat) V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_z tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_z tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_x tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm V_a V_b tptp.tc_nat) V_x tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_k V_n tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_k V_n tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) _let_1)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) _let_1)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_b tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Power_Opower__class_Opower V_x V_p T_a) V_q T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Otimes__class_Otimes V_p V_q tptp.tc_nat) T_a)))) (= (tptp.c_Complex_Ocnj _let_12) _let_12) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Olcm (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_x V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_x (tptp.c_GCD_Ogcd__class_Olcm V_y V_z tptp.tc_nat) tptp.tc_nat) tptp.tc_nat)) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_x V_x tptp.tc_nat) V_x)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat))) (or (not (= V_b (tptp.c_HOL_Otimes__class_Otimes V_b_H _let_1 tptp.tc_nat))) (not (= V_a (tptp.c_HOL_Otimes__class_Otimes V_a_H _let_1 tptp.tc_nat))) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_a_H V_b_H tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) V_a T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (= (tptp.c_Fact_Ofact__class_Ofact _let_8 tptp.tc_nat) _let_3) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_x T_a) V_n T_a) (tptp.c_Power_Opower__class_Opower V_x V_n T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_a T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_Power_Opower__class_Opower V_x V_n tptp.tc_Complex_Ocomplex)) (tptp.c_Power_Opower__class_Opower (tptp.c_Complex_Ocnj V_x) V_n tptp.tc_Complex_Ocomplex))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_y tptp.tc_nat)) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_x tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_a tptp.tc_nat)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_b tptp.tc_nat)) (forall ((V_e $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_e (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_e V_b tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_e V_a tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m tptp.tc_nat)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x tptp.tc_nat) V_x)) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_x)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x V_x tptp.tc_nat) V_x)) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_d (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_nat) tptp.tc_nat) _let_1)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_d V_b tptp.tc_nat) _let_1)))) (forall ((V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_d (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_nat) tptp.tc_nat) _let_1)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_d V_a tptp.tc_nat) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_Complex_Ocnj V_z)) V_z)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_n V_m tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_y V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (tptp.c_Parity_Oeven__odd__class_Oeven _let_8 tptp.tc_nat) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) V_n T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_y (tptp.c_GCD_Ogcd__class_Ogcd V_x V_z tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_GCD_Ogcd__class_Ogcd V_k V_m tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_k (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_z tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_x (tptp.c_GCD_Ogcd__class_Ogcd V_y V_z tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) _let_1))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= V_z (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Int_Oiszero V_z T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m (tptp.c_HOL_Oabs__class_Oabs V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m (tptp.c_HOL_Oabs__class_Oabs V_k T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Olcm V_x _let_1 tptp.tc_nat) _let_1))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_k V_n tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_x (tptp.c_GCD_Ogcd__class_Olcm V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_y (tptp.c_GCD_Ogcd__class_Olcm V_x V_z tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_p $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm (tptp.c_GCD_Ogcd__class_Olcm V_n V_m tptp.tc_nat) V_p tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_n (tptp.c_GCD_Ogcd__class_Olcm V_m V_p tptp.tc_nat) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm (tptp.c_GCD_Ogcd__class_Olcm V_x V_y tptp.tc_nat) V_z tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Olcm V_x (tptp.c_GCD_Ogcd__class_Olcm V_y V_z tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (not (= (tptp.c_Complex_Ocnj V_z) _let_1)) (= V_z _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Complex_Ocnj V_x) (tptp.c_Complex_Ocnj V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (tptp.c_Int_Oiszero (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (not (= tptp.c_Complex_Oii _let_12)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_d V_b tptp.tc_nat) _let_1)) (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_d V_a tptp.tc_nat) _let_1)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_d (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_nat) tptp.tc_nat) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_x) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) V_x)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd _let_8 _let_8 tptp.tc_nat) _let_8) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_n V_m tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat) (tptp.c_GCD_Ogcd__class_Ogcd V_y V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_GCD_Ogcd__class_Ogcd V_x V_y tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x _let_1 tptp.tc_nat) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_Power_Opower__class_Opower V_a V_m T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Osgn__class_Osgn V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Osgn__class_Osgn V_b T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_A V_B tptp.tc_nat) _let_1)) (= V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Ogcd V_A V_B tptp.tc_nat) _let_1)) (= V_B _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_x tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_a tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_x tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_GCD_Ogcd__class_Ogcd V_a V_b tptp.tc_nat) V_x tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_b tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_l T_a) (tptp.c_HOL_Oabs__class_Oabs V_k T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_l V_k T_a))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_n _let_1)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_FFT__Mirabelle_Oroot V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (not (tptp.c_Int_Oiszero (tptp.c_HOL_Oone__class_Oone T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) _let_11 (= (tptp.c_GCD_Ogcd__class_Olcm _let_3 _let_3 tptp.tc_nat) _let_3) _let_9 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (not (= tptp.c_Complex_Oii _let_2)) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_x)) (forall ((V_x $$unsorted)) (= (tptp.c_GCD_Ogcd__class_Olcm (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_x tptp.tc_nat) V_x)) (forall ((V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_A V_B tptp.tc_nat) _let_1)) (= V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_A V_B tptp.tc_nat) _let_1)) (= V_A _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_GCD_Ogcd__class_Olcm V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (= (tptp.c_FFT__Mirabelle_Oroot _let_8) _let_2) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_3 tptp.tc_nat)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd V_x _let_1 tptp.tc_nat) _let_1))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd _let_1 V_x tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (= (tptp.c_GCD_Ogcd__class_Ogcd V_m _let_1 tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (= V_m _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))) (forall ((V_x $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_x tptp.tc_nat)) (= (tptp.c_Fact_Ofact__class_Ofact _let_3 tptp.tc_nat) _let_3) _let_7 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (= _let_3 _let_6) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_3 _let_3 tptp.tc_nat) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1)) (= V_x _let_1)))) (= _let_6 _let_3) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) _let_5 (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Odvd tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) _let_1 (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Nat_Osemiring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odvd tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))))))))))))))))))))))))))))))))))))
% 0.52/0.74  )
% 0.52/0.74  % SZS output end Proof for SWV629-1
% 0.52/0.74  % cvc5---1.0.5 exiting
% 0.52/0.75  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------