TSTP Solution File: NUM926_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 10:49:08 EDT 2023
% Result : Theorem 0.55s 1.06s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.20 % Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.21 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n024.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Fri Aug 25 16:35:09 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.27/0.63 %----Proving TF0_NAR, FOF, or CNF
% 0.55/1.06 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.6YzecfbuTX/cvc5---1.0.5_11076.p...
% 0.55/1.06 ------- get file name : TPTP file name is NUM926_2
% 0.55/1.06 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11076.smt2...
% 0.55/1.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.55/1.06 % SZS status Theorem for NUM926_2
% 0.55/1.06 % SZS output start Proof for NUM926_2
% 0.55/1.06 (
% 0.55/1.06 (let ((_let_1 (not (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_2 (tptp.bit1 tptp.pls))) (let ((_let_3 (tptp.bit0 _let_2))) (let ((_let_4 (tptp.number_number_of_int _let_3))) (let ((_let_5 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_3)) tptp.m) tptp.one_one_int))) (let ((_let_6 (tptp.number_number_of_int tptp.min))) (let ((_let_7 (= (tptp.legendre _let_6 _let_5) tptp.one_one_int))) (let ((_let_8 (tptp.quadRes _let_5 _let_6))) (let ((_let_9 (tptp.number_number_of_nat _let_3))) (let ((_let_10 (tptp.power_power_int tptp.s _let_9))) (let ((_let_11 (tptp.plus_plus_int _let_10 tptp.one_one_int))) (let ((_let_12 (tptp.minus_minus_int _let_10 _let_6))) (let ((_let_13 (forall ((X_3 tptp.int) (Y_3 tptp.int)) (=> (tptp.ord_less_eq_int X_3 Y_3) (=> (not (= X_3 Y_3)) (tptp.ord_less_int X_3 Y_3)))))) (let ((_let_14 (tptp.number_number_of_nat tptp.pls))) (let ((_let_15 (= _let_14 tptp.zero_zero_nat))) (let ((_let_16 (tptp.number_number_of_int tptp.pls))) (let ((_let_17 (= tptp.zero_zero_int _let_16))) (let ((_let_18 (= _let_16 tptp.zero_zero_int))) (let ((_let_19 (tptp.number267125858f_real tptp.pls))) (let ((_let_20 (= _let_19 tptp.zero_zero_real))) (let ((_let_21 (tptp.power_power_int tptp.s1 _let_9))) (let ((_let_22 (tptp.times_times_int _let_5 tptp.t))) (let ((_let_23 (= (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) _let_4))) (let ((_let_24 (= (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat) _let_9))) (let ((_let_25 (= (tptp.plus_plus_real tptp.one_one_real tptp.one_one_real) (tptp.number267125858f_real _let_3)))) (let ((_let_26 (tptp.number_number_of_int _let_2))) (let ((_let_27 (= tptp.one_one_int _let_26))) (let ((_let_28 (tptp.number267125858f_real _let_2))) (let ((_let_29 (= _let_26 tptp.one_one_int))) (let ((_let_30 (= _let_28 tptp.one_one_real))) (let ((_let_31 (tptp.number_number_of_nat _let_2))) (let ((_let_32 (= _let_31 tptp.one_one_nat))) (let ((_let_33 (tptp.ord_less_int tptp.one_one_int tptp.t))) (let ((_let_34 (=> _let_33 (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_35 (=> (= tptp.t tptp.one_one_int) (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_36 (tptp.ord_less_eq_int tptp.one_one_int tptp.t))) (let ((_let_37 (forall ((X_3 tptp.int) (Y_3 tptp.int)) (or (not (tptp.ord_less_eq_int X_3 Y_3)) (= X_3 Y_3) (tptp.ord_less_int X_3 Y_3))))) (let ((_let_38 (= tptp.one_one_int tptp.t))) (let ((_let_39 (not _let_36))) (let ((_let_40 (or _let_39 _let_38 _let_33))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_44 (not _let_38))) (let ((_let_45 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2))))))))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_43 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) _let_45) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_43 false _let_45)))) (let ((_let_47 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2))))))))) (let ((_let_48 (not _let_33))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.one_one_int tptp.t QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ord_less_eq_int X_3 Y_3) false))))) :args (_let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_33 _let_38 _let_39 _let_42))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_47) _let_48))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_43 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) _let_47) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_46 :args (_let_47 false _let_43)) :args (_let_48 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_43) _let_44))) _let_46 :args (_let_44 false _let_43)) (ASSUME :args (_let_36)) :args (_let_42 true _let_33 true _let_38 false _let_36)) _let_41 :args (false true _let_40 false _let_37)) :args (_let_36 _let_35 _let_34 (tptp.ord_less_int tptp.t _let_5) (tptp.zprime _let_5) (= _let_11 _let_22) (tptp.twoSqu512355103sum2sq _let_22) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.plus_plus_int A B_1) _let_2) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int A _let_2) (tptp.times_times_int (tptp.times_times_int (tptp.number_number_of_int _let_1) A) B_1)) (tptp.power_power_int B_1 _let_2)))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_5 (tptp.number_number_of_int _let_2))) (= (tptp.power_power_int (tptp.plus_plus_int A B_1) _let_3) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int A _let_3) (tptp.times_times_int (tptp.times_times_int _let_5 (tptp.power_power_int A _let_4)) B_1)) (tptp.times_times_int (tptp.times_times_int _let_5 A) (tptp.power_power_int B_1 _let_4))) (tptp.power_power_int B_1 _let_3))))))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_real (tptp.plus_plus_real X_2 Y_2) _let_2) (tptp.plus_plus_real (tptp.plus_plus_real (tptp.power_power_real X_2 _let_2) (tptp.power_power_real Y_2 _let_2)) (tptp.times_times_real (tptp.times_times_real (tptp.number267125858f_real _let_1) X_2) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power_nat (tptp.plus_plus_nat X_2 Y_2) _let_1) (tptp.plus_plus_nat (tptp.plus_plus_nat (tptp.power_power_nat X_2 _let_1) (tptp.power_power_nat Y_2 _let_1)) (tptp.times_times_nat (tptp.times_times_nat _let_1 X_2) Y_2))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.plus_plus_int X_2 Y_2) _let_2) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int X_2 _let_2) (tptp.power_power_int Y_2 _let_2)) (tptp.times_times_int (tptp.times_times_int (tptp.number_number_of_int _let_1) X_2) Y_2)))))) (forall ((W_15 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_15))) (= (tptp.power_power_nat _let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_nat _let_1 _let_1)))) (forall ((W_15 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_15))) (= (tptp.power_power_real _let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_real _let_1 _let_1)))) (forall ((W_15 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_15))) (= (tptp.power_power_int _let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_int _let_1 _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (= (tptp.times_times_int A (tptp.power_power_int A (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (tptp.power_power_int A (tptp.number_number_of_nat (tptp.bit1 _let_1)))))) (= (tptp.power_power_real tptp.one_one_real _let_9) tptp.one_one_real) (= (tptp.power_power_nat tptp.one_one_nat _let_9) tptp.one_one_nat) (= (tptp.power_power_int tptp.one_one_int _let_9) tptp.one_one_int) (forall ((X_21 tptp.nat)) (= (tptp.times_times_nat X_21 X_21) (tptp.power_power_nat X_21 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_21 tptp.real)) (= (tptp.times_times_real X_21 X_21) (tptp.power_power_real X_21 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_21 tptp.int)) (= (tptp.times_times_int X_21 X_21) (tptp.power_power_int X_21 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((A_57 tptp.nat)) (= (tptp.power_power_nat A_57 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_nat A_57 A_57))) (forall ((A_57 tptp.real)) (= (tptp.power_power_real A_57 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_real A_57 A_57))) (forall ((A_57 tptp.int)) (= (tptp.power_power_int A_57 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_int A_57 A_57))) (forall ((X_20 tptp.nat) (N_38 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_20 N_38))) (= (tptp.power_power_nat X_20 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_38)) (tptp.times_times_nat _let_1 _let_1)))) (forall ((X_20 tptp.real) (N_38 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_20 N_38))) (= (tptp.power_power_real X_20 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_38)) (tptp.times_times_real _let_1 _let_1)))) (forall ((X_20 tptp.int) (N_38 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_20 N_38))) (= (tptp.power_power_int X_20 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_38)) (tptp.times_times_int _let_1 _let_1)))) (forall ((W_14 tptp.int)) (= (tptp.plus_plus_real tptp.one_one_real (tptp.number267125858f_real W_14)) (tptp.number267125858f_real (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_14)))) (forall ((W_14 tptp.int)) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int W_14)) (tptp.number_number_of_int (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_14)))) (forall ((V_17 tptp.int)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_17) tptp.one_one_real) (tptp.number267125858f_real (tptp.plus_plus_int V_17 (tptp.bit1 tptp.pls))))) (forall ((V_17 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_17) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int V_17 (tptp.bit1 tptp.pls))))) _let_25 _let_23 (not (forall ((T tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus_int (tptp.power_power_int tptp.s (tptp.number_number_of_nat _let_1)) tptp.one_one_int) (tptp.times_times_int (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) T)))))) (forall ((W tptp.int)) (tptp.ord_less_eq_int W W)) (forall ((Z tptp.int) (W tptp.int)) (or (tptp.ord_less_eq_int Z W) (tptp.ord_less_eq_int W Z))) (forall ((Z_1 tptp.int) (W_1 tptp.int)) (= (tptp.ord_less_int Z_1 W_1) (and (tptp.ord_less_eq_int Z_1 W_1) (not (= Z_1 W_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (or (tptp.ord_less_int X_1 Y_1) (= X_1 Y_1) (tptp.ord_less_int Y_1 X_1))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_eq_int I J) (=> (tptp.ord_less_eq_int J K) (tptp.ord_less_eq_int I K)))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.ord_less_eq_int Z W) (=> (tptp.ord_less_eq_int W Z) (= Z W)))) (forall ((X_19 tptp.nat) (P_3 tptp.nat) (Q_4 tptp.nat)) (= (tptp.power_power_nat (tptp.power_power_nat X_19 P_3) Q_4) (tptp.power_power_nat X_19 (tptp.times_times_nat P_3 Q_4)))) (forall ((X_19 tptp.real) (P_3 tptp.nat) (Q_4 tptp.nat)) (= (tptp.power_power_real (tptp.power_power_real X_19 P_3) Q_4) (tptp.power_power_real X_19 (tptp.times_times_nat P_3 Q_4)))) (forall ((X_19 tptp.int) (P_3 tptp.nat) (Q_4 tptp.nat)) (= (tptp.power_power_int (tptp.power_power_int X_19 P_3) Q_4) (tptp.power_power_int X_19 (tptp.times_times_nat P_3 Q_4)))) (forall ((X_18 tptp.nat)) (= (tptp.power_power_nat X_18 tptp.one_one_nat) X_18)) (forall ((X_18 tptp.real)) (= (tptp.power_power_real X_18 tptp.one_one_nat) X_18)) (forall ((X_18 tptp.int)) (= (tptp.power_power_int X_18 tptp.one_one_nat) X_18)) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (= (tptp.power_power_int (tptp.power_power_int X_1 Y_1) Z) (tptp.power_power_int X_1 (tptp.times_times_nat Y_1 Z)))) (forall ((V_3 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_3))) (let ((_let_2 (tptp.number267125858f_real W_1))) (= (tptp.ord_less_eq_real _let_1 _let_2) (not (tptp.ord_less_real _let_2 _let_1)))))) (forall ((V_3 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_3))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.ord_less_eq_nat _let_1 _let_2) (not (tptp.ord_less_nat _let_2 _let_1)))))) (forall ((V_3 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_3))) (let ((_let_2 (tptp.number_number_of_int W_1))) (= (tptp.ord_less_eq_int _let_1 _let_2) (not (tptp.ord_less_int _let_2 _let_1)))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_real (tptp.number267125858f_real X_2) (tptp.number267125858f_real Y_2)) (tptp.ord_less_int X_2 Y_2))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_int (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (tptp.ord_less_int X_2 Y_2))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_eq_real (tptp.number267125858f_real X_2) (tptp.number267125858f_real Y_2)) (tptp.ord_less_eq_int X_2 Y_2))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (tptp.ord_less_eq_int X_2 Y_2))) (forall ((Z_9 tptp.int) (Z tptp.int) (W_13 tptp.int) (W tptp.int)) (=> (tptp.ord_less_int W_13 W) (=> (tptp.ord_less_eq_int Z_9 Z) (tptp.ord_less_int (tptp.plus_plus_int W_13 Z_9) (tptp.plus_plus_int W Z))))) (forall ((X_17 tptp.nat) (P_2 tptp.nat) (Q_3 tptp.nat)) (= (tptp.times_times_nat (tptp.power_power_nat X_17 P_2) (tptp.power_power_nat X_17 Q_3)) (tptp.power_power_nat X_17 (tptp.plus_plus_nat P_2 Q_3)))) (forall ((X_17 tptp.real) (P_2 tptp.nat) (Q_3 tptp.nat)) (= (tptp.times_times_real (tptp.power_power_real X_17 P_2) (tptp.power_power_real X_17 Q_3)) (tptp.power_power_real X_17 (tptp.plus_plus_nat P_2 Q_3)))) (forall ((X_17 tptp.int) (P_2 tptp.nat) (Q_3 tptp.nat)) (= (tptp.times_times_int (tptp.power_power_int X_17 P_2) (tptp.power_power_int X_17 Q_3)) (tptp.power_power_int X_17 (tptp.plus_plus_nat P_2 Q_3)))) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (= (tptp.power_power_int X_1 (tptp.plus_plus_nat Y_1 Z)) (tptp.times_times_int (tptp.power_power_int X_1 Y_1) (tptp.power_power_int X_1 Z)))) (forall ((Z tptp.nat)) (= (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus_nat Z Z))) (forall ((Z tptp.nat)) (= (tptp.times_times_nat Z (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_nat Z Z))) _let_24 (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K_1) (tptp.bit1 L_1)) (tptp.ord_less_int K_1 L_1))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq_int K_1 L_1))) (not (tptp.ord_less_int tptp.pls tptp.pls)) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K_1) (tptp.bit0 L_1)) (tptp.ord_less_int K_1 L_1))) (tptp.ord_less_eq_int tptp.pls tptp.pls) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K_1) (tptp.bit0 L_1)) (tptp.ord_less_eq_int K_1 L_1))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int (tptp.number_number_of_int K_1) (tptp.number_number_of_int L_1)) (tptp.ord_less_int K_1 L_1))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int K_1) (tptp.number_number_of_int L_1)) (tptp.ord_less_eq_int K_1 L_1))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_int I J) (tptp.ord_less_int (tptp.plus_plus_int I K) (tptp.plus_plus_int J K)))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_eq_int I J) (tptp.ord_less_eq_int (tptp.plus_plus_int K I) (tptp.plus_plus_int K J)))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_2))) (let ((_let_2 (tptp.number_number_of_nat V_1))) (let ((_let_3 (tptp.plus_plus_nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less_int V_2 tptp.pls))) (let ((_let_5 (tptp.ord_less_int V_1 tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of_nat (tptp.plus_plus_int V_1 V_2))))))))))))) _let_32 (= tptp.one_one_nat _let_31) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K_1) tptp.pls) (tptp.ord_less_int K_1 tptp.pls))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int tptp.pls (tptp.bit1 K_1)) (tptp.ord_less_eq_int tptp.pls K_1))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K_1) (tptp.bit0 L_1)) (tptp.ord_less_int K_1 L_1))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq_int K_1 L_1))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.ord_less_int W Z) (tptp.ord_less_eq_int (tptp.plus_plus_int W tptp.one_one_int) Z))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.plus_plus_int W_1 tptp.one_one_int) Z_1) (tptp.ord_less_int W_1 Z_1))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_int W_1 (tptp.plus_plus_int Z_1 tptp.one_one_int)) (tptp.ord_less_eq_int W_1 Z_1))) (tptp.zprime _let_4) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.twoSqu512355103sum2sq X_1) (=> (tptp.twoSqu512355103sum2sq Y_1) (tptp.twoSqu512355103sum2sq (tptp.times_times_int X_1 Y_1))))) (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx_6 Ly_4) (tptp.times_times_real Rx_6 Ry_4)) (tptp.times_times_real (tptp.times_times_real Lx_6 Rx_6) (tptp.times_times_real Ly_4 Ry_4)))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_6 Ly_4) (tptp.times_times_nat Rx_6 Ry_4)) (tptp.times_times_nat (tptp.times_times_nat Lx_6 Rx_6) (tptp.times_times_nat Ly_4 Ry_4)))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx_6 Ly_4) (tptp.times_times_int Rx_6 Ry_4)) (tptp.times_times_int (tptp.times_times_int Lx_6 Rx_6) (tptp.times_times_int Ly_4 Ry_4)))) (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_5 Ly_3))) (= (tptp.times_times_real _let_1 (tptp.times_times_real Rx_5 Ry_3)) (tptp.times_times_real Rx_5 (tptp.times_times_real _let_1 Ry_3))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_5 Ly_3))) (= (tptp.times_times_nat _let_1 (tptp.times_times_nat Rx_5 Ry_3)) (tptp.times_times_nat Rx_5 (tptp.times_times_nat _let_1 Ry_3))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_5 Ly_3))) (= (tptp.times_times_int _let_1 (tptp.times_times_int Rx_5 Ry_3)) (tptp.times_times_int Rx_5 (tptp.times_times_int _let_1 Ry_3))))) (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (tptp.times_times_real Rx_4 Ry_2))) (= (tptp.times_times_real (tptp.times_times_real Lx_4 Ly_2) _let_1) (tptp.times_times_real Lx_4 (tptp.times_times_real Ly_2 _let_1))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Rx_4 Ry_2))) (= (tptp.times_times_nat (tptp.times_times_nat Lx_4 Ly_2) _let_1) (tptp.times_times_nat Lx_4 (tptp.times_times_nat Ly_2 _let_1))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.times_times_int Rx_4 Ry_2))) (= (tptp.times_times_int (tptp.times_times_int Lx_4 Ly_2) _let_1) (tptp.times_times_int Lx_4 (tptp.times_times_int Ly_2 _let_1))))) (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx_3 Ly_1) Rx_3) (tptp.times_times_real (tptp.times_times_real Lx_3 Rx_3) Ly_1))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_3 Ly_1) Rx_3) (tptp.times_times_nat (tptp.times_times_nat Lx_3 Rx_3) Ly_1))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx_3 Ly_1) Rx_3) (tptp.times_times_int (tptp.times_times_int Lx_3 Rx_3) Ly_1))) (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx_2 Ly) Rx_2) (tptp.times_times_real Lx_2 (tptp.times_times_real Ly Rx_2)))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_2 Ly) Rx_2) (tptp.times_times_nat Lx_2 (tptp.times_times_nat Ly Rx_2)))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx_2 Ly) Rx_2) (tptp.times_times_int Lx_2 (tptp.times_times_int Ly Rx_2)))) (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (= (tptp.times_times_real Lx_1 (tptp.times_times_real Rx_1 Ry_1)) (tptp.times_times_real (tptp.times_times_real Lx_1 Rx_1) Ry_1))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (= (tptp.times_times_nat Lx_1 (tptp.times_times_nat Rx_1 Ry_1)) (tptp.times_times_nat (tptp.times_times_nat Lx_1 Rx_1) Ry_1))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (= (tptp.times_times_int Lx_1 (tptp.times_times_int Rx_1 Ry_1)) (tptp.times_times_int (tptp.times_times_int Lx_1 Rx_1) Ry_1))) (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (= (tptp.times_times_real Lx (tptp.times_times_real Rx Ry)) (tptp.times_times_real Rx (tptp.times_times_real Lx Ry)))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (= (tptp.times_times_nat Lx (tptp.times_times_nat Rx Ry)) (tptp.times_times_nat Rx (tptp.times_times_nat Lx Ry)))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (= (tptp.times_times_int Lx (tptp.times_times_int Rx Ry)) (tptp.times_times_int Rx (tptp.times_times_int Lx Ry)))) (forall ((A_56 tptp.real) (B_17 tptp.real)) (= (tptp.times_times_real A_56 B_17) (tptp.times_times_real B_17 A_56))) (forall ((A_56 tptp.nat) (B_17 tptp.nat)) (= (tptp.times_times_nat A_56 B_17) (tptp.times_times_nat B_17 A_56))) (forall ((A_56 tptp.int) (B_17 tptp.int)) (= (tptp.times_times_int A_56 B_17) (tptp.times_times_int B_17 A_56))) (forall ((A_55 tptp.real) (B_16 tptp.real) (C_10 tptp.real) (D_5 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_55 B_16) (tptp.plus_plus_real C_10 D_5)) (tptp.plus_plus_real (tptp.plus_plus_real A_55 C_10) (tptp.plus_plus_real B_16 D_5)))) (forall ((A_55 tptp.nat) (B_16 tptp.nat) (C_10 tptp.nat) (D_5 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_55 B_16) (tptp.plus_plus_nat C_10 D_5)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_55 C_10) (tptp.plus_plus_nat B_16 D_5)))) (forall ((A_55 tptp.int) (B_16 tptp.int) (C_10 tptp.int) (D_5 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_55 B_16) (tptp.plus_plus_int C_10 D_5)) (tptp.plus_plus_int (tptp.plus_plus_int A_55 C_10) (tptp.plus_plus_int B_16 D_5)))) (forall ((A_54 tptp.real) (B_15 tptp.real) (C_9 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_54 B_15) C_9) (tptp.plus_plus_real (tptp.plus_plus_real A_54 C_9) B_15))) (forall ((A_54 tptp.nat) (B_15 tptp.nat) (C_9 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_54 B_15) C_9) (tptp.plus_plus_nat (tptp.plus_plus_nat A_54 C_9) B_15))) (forall ((A_54 tptp.int) (B_15 tptp.int) (C_9 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_54 B_15) C_9) (tptp.plus_plus_int (tptp.plus_plus_int A_54 C_9) B_15))) (forall ((A_53 tptp.real) (B_14 tptp.real) (C_8 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_53 B_14) C_8) (tptp.plus_plus_real A_53 (tptp.plus_plus_real B_14 C_8)))) (forall ((A_53 tptp.nat) (B_14 tptp.nat) (C_8 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_53 B_14) C_8) (tptp.plus_plus_nat A_53 (tptp.plus_plus_nat B_14 C_8)))) (forall ((A_53 tptp.int) (B_14 tptp.int) (C_8 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_53 B_14) C_8) (tptp.plus_plus_int A_53 (tptp.plus_plus_int B_14 C_8)))) (forall ((A_52 tptp.real) (C_7 tptp.real) (D_4 tptp.real)) (= (tptp.plus_plus_real A_52 (tptp.plus_plus_real C_7 D_4)) (tptp.plus_plus_real (tptp.plus_plus_real A_52 C_7) D_4))) (forall ((A_52 tptp.nat) (C_7 tptp.nat) (D_4 tptp.nat)) (= (tptp.plus_plus_nat A_52 (tptp.plus_plus_nat C_7 D_4)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_52 C_7) D_4))) (forall ((A_52 tptp.int) (C_7 tptp.int) (D_4 tptp.int)) (= (tptp.plus_plus_int A_52 (tptp.plus_plus_int C_7 D_4)) (tptp.plus_plus_int (tptp.plus_plus_int A_52 C_7) D_4))) (forall ((A_51 tptp.real) (C_6 tptp.real) (D_3 tptp.real)) (= (tptp.plus_plus_real A_51 (tptp.plus_plus_real C_6 D_3)) (tptp.plus_plus_real C_6 (tptp.plus_plus_real A_51 D_3)))) (forall ((A_51 tptp.nat) (C_6 tptp.nat) (D_3 tptp.nat)) (= (tptp.plus_plus_nat A_51 (tptp.plus_plus_nat C_6 D_3)) (tptp.plus_plus_nat C_6 (tptp.plus_plus_nat A_51 D_3)))) (forall ((A_51 tptp.int) (C_6 tptp.int) (D_3 tptp.int)) (= (tptp.plus_plus_int A_51 (tptp.plus_plus_int C_6 D_3)) (tptp.plus_plus_int C_6 (tptp.plus_plus_int A_51 D_3)))) (forall ((A_50 tptp.real) (C_5 tptp.real)) (= (tptp.plus_plus_real A_50 C_5) (tptp.plus_plus_real C_5 A_50))) (forall ((A_50 tptp.nat) (C_5 tptp.nat)) (= (tptp.plus_plus_nat A_50 C_5) (tptp.plus_plus_nat C_5 A_50))) (forall ((A_50 tptp.int) (C_5 tptp.int)) (= (tptp.plus_plus_int A_50 C_5) (tptp.plus_plus_int C_5 A_50))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.number267125858f_real X_2) (tptp.number267125858f_real Y_2)) (= X_2 Y_2))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (= X_2 Y_2))) (forall ((W_1 tptp.int) (X_2 tptp.real)) (let ((_let_1 (tptp.number267125858f_real W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 tptp.int) (X_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 tptp.int) (X_2 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (= (tptp.bit1 K_1) (tptp.bit1 L_1)) (= K_1 L_1))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (= (tptp.bit0 K_1) (tptp.bit0 L_1)) (= K_1 L_1))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Z1 Z2) Z3) (tptp.times_times_int Z1 (tptp.times_times_int Z2 Z3)))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.times_times_int Z W) (tptp.times_times_int W Z))) (forall ((K tptp.int)) (= (tptp.number_number_of_int K) K)) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int Z1 Z2) Z3) (tptp.plus_plus_int Z1 (tptp.plus_plus_int Z2 Z3)))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z tptp.int)) (= (tptp.plus_plus_int X_1 (tptp.plus_plus_int Y_1 Z)) (tptp.plus_plus_int Y_1 (tptp.plus_plus_int X_1 Z)))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.plus_plus_int Z W) (tptp.plus_plus_int W Z))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K_1) tptp.pls) (tptp.ord_less_int K_1 tptp.pls))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K_1) (tptp.bit0 L_1)) (tptp.ord_less_int K_1 L_1))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K_1) tptp.pls) (tptp.ord_less_int K_1 tptp.pls))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int tptp.pls (tptp.bit0 K_1)) (tptp.ord_less_int tptp.pls K_1))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.pls (tptp.bit1 K_1)) (tptp.ord_less_eq_int tptp.pls K_1))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq_int K_1 L_1))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K_1) tptp.pls) (tptp.ord_less_eq_int K_1 tptp.pls))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.pls (tptp.bit0 K_1)) (tptp.ord_less_eq_int tptp.pls K_1))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_int W_1 (tptp.plus_plus_int Z_1 tptp.one_one_int)) (or (tptp.ord_less_int W_1 Z_1) (= W_1 Z_1)))) (forall ((A_49 tptp.nat) (N_37 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power_nat A_49 (tptp.times_times_nat _let_1 N_37)) (tptp.power_power_nat (tptp.power_power_nat A_49 N_37) _let_1)))) (forall ((A_49 tptp.real) (N_37 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power_real A_49 (tptp.times_times_nat _let_1 N_37)) (tptp.power_power_real (tptp.power_power_real A_49 N_37) _let_1)))) (forall ((A_49 tptp.int) (N_37 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power_int A_49 (tptp.times_times_nat _let_1 N_37)) (tptp.power_power_int (tptp.power_power_int A_49 N_37) _let_1)))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_real (tptp.number267125858f_real X_2) tptp.one_one_real) (tptp.ord_less_int X_2 (tptp.bit1 tptp.pls)))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_int (tptp.number_number_of_int X_2) tptp.one_one_int) (tptp.ord_less_int X_2 (tptp.bit1 tptp.pls)))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_real tptp.one_one_real (tptp.number267125858f_real Y_2)) (tptp.ord_less_int (tptp.bit1 tptp.pls) Y_2))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_int tptp.one_one_int (tptp.number_number_of_int Y_2)) (tptp.ord_less_int (tptp.bit1 tptp.pls) Y_2))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_eq_real (tptp.number267125858f_real X_2) tptp.one_one_real) (tptp.ord_less_eq_int X_2 (tptp.bit1 tptp.pls)))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_2) tptp.one_one_int) (tptp.ord_less_eq_int X_2 (tptp.bit1 tptp.pls)))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_eq_real tptp.one_one_real (tptp.number267125858f_real Y_2)) (tptp.ord_less_eq_int (tptp.bit1 tptp.pls) Y_2))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_eq_int tptp.one_one_int (tptp.number_number_of_int Y_2)) (tptp.ord_less_eq_int (tptp.bit1 tptp.pls) Y_2))) (forall ((W_1 tptp.real) (Y_2 tptp.real) (X_2 tptp.real) (Z_1 tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real W_1 Y_2) (tptp.times_times_real X_2 Z_1)) (tptp.plus_plus_real (tptp.times_times_real W_1 Z_1) (tptp.times_times_real X_2 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))) (forall ((W_1 tptp.nat) (Y_2 tptp.nat) (X_2 tptp.nat) (Z_1 tptp.nat)) (= (= (tptp.plus_plus_nat (tptp.times_times_nat W_1 Y_2) (tptp.times_times_nat X_2 Z_1)) (tptp.plus_plus_nat (tptp.times_times_nat W_1 Z_1) (tptp.times_times_nat X_2 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))) (forall ((W_1 tptp.int) (Y_2 tptp.int) (X_2 tptp.int) (Z_1 tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int W_1 Y_2) (tptp.times_times_int X_2 Z_1)) (tptp.plus_plus_int (tptp.times_times_int W_1 Z_1) (tptp.times_times_int X_2 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))) (forall ((A_48 tptp.real) (M_12 tptp.real) (B_13 tptp.real)) (= (tptp.plus_plus_real (tptp.times_times_real A_48 M_12) (tptp.times_times_real B_13 M_12)) (tptp.times_times_real (tptp.plus_plus_real A_48 B_13) M_12))) (forall ((A_48 tptp.nat) (M_12 tptp.nat) (B_13 tptp.nat)) (= (tptp.plus_plus_nat (tptp.times_times_nat A_48 M_12) (tptp.times_times_nat B_13 M_12)) (tptp.times_times_nat (tptp.plus_plus_nat A_48 B_13) M_12))) (forall ((A_48 tptp.int) (M_12 tptp.int) (B_13 tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int A_48 M_12) (tptp.times_times_int B_13 M_12)) (tptp.times_times_int (tptp.plus_plus_int A_48 B_13) M_12))) (forall ((A_47 tptp.real) (B_12 tptp.real) (C_4 tptp.real)) (= (tptp.times_times_real (tptp.plus_plus_real A_47 B_12) C_4) (tptp.plus_plus_real (tptp.times_times_real A_47 C_4) (tptp.times_times_real B_12 C_4)))) (forall ((A_47 tptp.nat) (B_12 tptp.nat) (C_4 tptp.nat)) (= (tptp.times_times_nat (tptp.plus_plus_nat A_47 B_12) C_4) (tptp.plus_plus_nat (tptp.times_times_nat A_47 C_4) (tptp.times_times_nat B_12 C_4)))) (forall ((A_47 tptp.int) (B_12 tptp.int) (C_4 tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int A_47 B_12) C_4) (tptp.plus_plus_int (tptp.times_times_int A_47 C_4) (tptp.times_times_int B_12 C_4)))) (forall ((C tptp.real) (D tptp.real) (A_1 tptp.real) (B_2 tptp.real)) (= (and (not (= A_1 B_2)) (not (= C D))) (not (= (tptp.plus_plus_real (tptp.times_times_real A_1 C) (tptp.times_times_real B_2 D)) (tptp.plus_plus_real (tptp.times_times_real A_1 D) (tptp.times_times_real B_2 C)))))) (forall ((C tptp.nat) (D tptp.nat) (A_1 tptp.nat) (B_2 tptp.nat)) (= (and (not (= A_1 B_2)) (not (= C D))) (not (= (tptp.plus_plus_nat (tptp.times_times_nat A_1 C) (tptp.times_times_nat B_2 D)) (tptp.plus_plus_nat (tptp.times_times_nat A_1 D) (tptp.times_times_nat B_2 C)))))) (forall ((C tptp.int) (D tptp.int) (A_1 tptp.int) (B_2 tptp.int)) (= (and (not (= A_1 B_2)) (not (= C D))) (not (= (tptp.plus_plus_int (tptp.times_times_int A_1 C) (tptp.times_times_int B_2 D)) (tptp.plus_plus_int (tptp.times_times_int A_1 D) (tptp.times_times_int B_2 C)))))) (forall ((X_16 tptp.real) (Y_14 tptp.real) (Z_8 tptp.real)) (= (tptp.times_times_real X_16 (tptp.plus_plus_real Y_14 Z_8)) (tptp.plus_plus_real (tptp.times_times_real X_16 Y_14) (tptp.times_times_real X_16 Z_8)))) (forall ((X_16 tptp.nat) (Y_14 tptp.nat) (Z_8 tptp.nat)) (= (tptp.times_times_nat X_16 (tptp.plus_plus_nat Y_14 Z_8)) (tptp.plus_plus_nat (tptp.times_times_nat X_16 Y_14) (tptp.times_times_nat X_16 Z_8)))) (forall ((X_16 tptp.int) (Y_14 tptp.int) (Z_8 tptp.int)) (= (tptp.times_times_int X_16 (tptp.plus_plus_int Y_14 Z_8)) (tptp.plus_plus_int (tptp.times_times_int X_16 Y_14) (tptp.times_times_int X_16 Z_8)))) (forall ((A_46 tptp.real)) (= (tptp.times_times_real A_46 tptp.one_one_real) A_46)) (forall ((A_46 tptp.nat)) (= (tptp.times_times_nat A_46 tptp.one_one_nat) A_46)) (forall ((A_46 tptp.int)) (= (tptp.times_times_int A_46 tptp.one_one_int) A_46)) (forall ((A_45 tptp.real)) (= (tptp.times_times_real tptp.one_one_real A_45) A_45)) (forall ((A_45 tptp.nat)) (= (tptp.times_times_nat tptp.one_one_nat A_45) A_45)) (forall ((A_45 tptp.int)) (= (tptp.times_times_int tptp.one_one_int A_45) A_45)) (forall ((X_15 tptp.nat) (Y_13 tptp.nat) (Q_2 tptp.nat)) (= (tptp.power_power_nat (tptp.times_times_nat X_15 Y_13) Q_2) (tptp.times_times_nat (tptp.power_power_nat X_15 Q_2) (tptp.power_power_nat Y_13 Q_2)))) (forall ((X_15 tptp.real) (Y_13 tptp.real) (Q_2 tptp.nat)) (= (tptp.power_power_real (tptp.times_times_real X_15 Y_13) Q_2) (tptp.times_times_real (tptp.power_power_real X_15 Q_2) (tptp.power_power_real Y_13 Q_2)))) (forall ((X_15 tptp.int) (Y_13 tptp.int) (Q_2 tptp.nat)) (= (tptp.power_power_int (tptp.times_times_int X_15 Y_13) Q_2) (tptp.times_times_int (tptp.power_power_int X_15 Q_2) (tptp.power_power_int Y_13 Q_2)))) (forall ((K tptp.int)) (not (= (tptp.bit1 K) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (tptp.bit1 K) (tptp.bit0 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (tptp.bit0 K) (tptp.bit1 L)))) (forall ((K_1 tptp.int)) (= (= (tptp.bit0 K_1) tptp.pls) (= K_1 tptp.pls))) (forall ((L_1 tptp.int)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls L_1))) (= (tptp.bit0 tptp.pls) tptp.pls) (forall ((W tptp.int)) (= (tptp.times_times_int tptp.pls W) tptp.pls)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.times_times_int (tptp.bit0 K) L) (tptp.bit0 (tptp.times_times_int K L)))) (forall ((K tptp.int)) (= (tptp.plus_plus_int K tptp.pls) K)) (forall ((K tptp.int)) (= (tptp.plus_plus_int tptp.pls K) K)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit0 K) (tptp.bit0 L)) (tptp.bit0 (tptp.plus_plus_int K L)))) (forall ((K tptp.int)) (= (tptp.bit0 K) (tptp.plus_plus_int K K))) (forall ((Z tptp.int)) (= (tptp.times_times_int Z tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (tptp.times_times_int tptp.one_one_int Z) Z)) (forall ((V_1 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_1) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.times_times_int V_1 W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int Z1 Z2) W) (tptp.plus_plus_int (tptp.times_times_int Z1 W) (tptp.times_times_int Z2 W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (= (tptp.times_times_int W (tptp.plus_plus_int Z1 Z2)) (tptp.plus_plus_int (tptp.times_times_int W Z1) (tptp.times_times_int W Z2)))) (forall ((V_1 tptp.int) (W tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_1) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.plus_plus_int V_1 W)))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_15) (=> (tptp.ord_less_eq_int tptp.pls V_16) (= (tptp.times_times_real (tptp.number267125858f_real V_15) (tptp.number267125858f_real V_16)) (tptp.number267125858f_real (tptp.times_times_int V_15 V_16)))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_15) (=> (tptp.ord_less_eq_int tptp.pls V_16) (= (tptp.times_times_nat (tptp.number_number_of_nat V_15) (tptp.number_number_of_nat V_16)) (tptp.number_number_of_nat (tptp.times_times_int V_15 V_16)))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_15) (=> (tptp.ord_less_eq_int tptp.pls V_16) (= (tptp.times_times_int (tptp.number_number_of_int V_15) (tptp.number_number_of_int V_16)) (tptp.number_number_of_int (tptp.times_times_int V_15 V_16)))))) (forall ((V_14 tptp.int) (V_13 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_13) (=> (tptp.ord_less_eq_int tptp.pls V_14) (= (tptp.plus_plus_real (tptp.number267125858f_real V_13) (tptp.number267125858f_real V_14)) (tptp.number267125858f_real (tptp.plus_plus_int V_13 V_14)))))) (forall ((V_14 tptp.int) (V_13 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_13) (=> (tptp.ord_less_eq_int tptp.pls V_14) (= (tptp.plus_plus_nat (tptp.number_number_of_nat V_13) (tptp.number_number_of_nat V_14)) (tptp.number_number_of_nat (tptp.plus_plus_int V_13 V_14)))))) (forall ((V_14 tptp.int) (V_13 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_13) (=> (tptp.ord_less_eq_int tptp.pls V_14) (= (tptp.plus_plus_int (tptp.number_number_of_int V_13) (tptp.number_number_of_int V_14)) (tptp.number_number_of_int (tptp.plus_plus_int V_13 V_14)))))) (forall ((X_1 tptp.int)) (tptp.ord_less_eq_int X_1 (tptp.power_power_int X_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((A_44 tptp.real) (B_11 tptp.real) (V_12 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_12))) (= (tptp.times_times_real (tptp.plus_plus_real A_44 B_11) _let_1) (tptp.plus_plus_real (tptp.times_times_real A_44 _let_1) (tptp.times_times_real B_11 _let_1))))) (forall ((A_44 tptp.nat) (B_11 tptp.nat) (V_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_12))) (= (tptp.times_times_nat (tptp.plus_plus_nat A_44 B_11) _let_1) (tptp.plus_plus_nat (tptp.times_times_nat A_44 _let_1) (tptp.times_times_nat B_11 _let_1))))) (forall ((A_44 tptp.int) (B_11 tptp.int) (V_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_12))) (= (tptp.times_times_int (tptp.plus_plus_int A_44 B_11) _let_1) (tptp.plus_plus_int (tptp.times_times_int A_44 _let_1) (tptp.times_times_int B_11 _let_1))))) (forall ((V_11 tptp.int) (B_10 tptp.real) (C_3 tptp.real)) (let ((_let_1 (tptp.number267125858f_real V_11))) (= (tptp.times_times_real _let_1 (tptp.plus_plus_real B_10 C_3)) (tptp.plus_plus_real (tptp.times_times_real _let_1 B_10) (tptp.times_times_real _let_1 C_3))))) (forall ((V_11 tptp.int) (B_10 tptp.nat) (C_3 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat V_11))) (= (tptp.times_times_nat _let_1 (tptp.plus_plus_nat B_10 C_3)) (tptp.plus_plus_nat (tptp.times_times_nat _let_1 B_10) (tptp.times_times_nat _let_1 C_3))))) (forall ((V_11 tptp.int) (B_10 tptp.int) (C_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_11))) (= (tptp.times_times_int _let_1 (tptp.plus_plus_int B_10 C_3)) (tptp.plus_plus_int (tptp.times_times_int _let_1 B_10) (tptp.times_times_int _let_1 C_3))))) (forall ((A_43 tptp.real) (M_11 tptp.real)) (= (tptp.plus_plus_real (tptp.times_times_real A_43 M_11) M_11) (tptp.times_times_real (tptp.plus_plus_real A_43 tptp.one_one_real) M_11))) (forall ((A_43 tptp.nat) (M_11 tptp.nat)) (= (tptp.plus_plus_nat (tptp.times_times_nat A_43 M_11) M_11) (tptp.times_times_nat (tptp.plus_plus_nat A_43 tptp.one_one_nat) M_11))) (forall ((A_43 tptp.int) (M_11 tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int A_43 M_11) M_11) (tptp.times_times_int (tptp.plus_plus_int A_43 tptp.one_one_int) M_11))) (forall ((M_10 tptp.real) (A_42 tptp.real)) (= (tptp.plus_plus_real M_10 (tptp.times_times_real A_42 M_10)) (tptp.times_times_real (tptp.plus_plus_real A_42 tptp.one_one_real) M_10))) (forall ((M_10 tptp.nat) (A_42 tptp.nat)) (= (tptp.plus_plus_nat M_10 (tptp.times_times_nat A_42 M_10)) (tptp.times_times_nat (tptp.plus_plus_nat A_42 tptp.one_one_nat) M_10))) (forall ((M_10 tptp.int) (A_42 tptp.int)) (= (tptp.plus_plus_int M_10 (tptp.times_times_int A_42 M_10)) (tptp.times_times_int (tptp.plus_plus_int A_42 tptp.one_one_int) M_10))) (forall ((M_9 tptp.real)) (= (tptp.plus_plus_real M_9 M_9) (tptp.times_times_real (tptp.plus_plus_real tptp.one_one_real tptp.one_one_real) M_9))) (forall ((M_9 tptp.nat)) (= (tptp.plus_plus_nat M_9 M_9) (tptp.times_times_nat (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat) M_9))) (forall ((M_9 tptp.int)) (= (tptp.plus_plus_int M_9 M_9) (tptp.times_times_int (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) M_9))) (forall ((A_41 tptp.real)) (= (tptp.plus_plus_real (tptp.number267125858f_real tptp.pls) A_41) A_41)) (forall ((A_41 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int tptp.pls) A_41) A_41)) (forall ((A_40 tptp.real)) (= (tptp.plus_plus_real A_40 (tptp.number267125858f_real tptp.pls)) A_40)) (forall ((A_40 tptp.int)) (= (tptp.plus_plus_int A_40 (tptp.number_number_of_int tptp.pls)) A_40)) (forall ((V_10 tptp.int) (W_12 tptp.int) (Z_7 tptp.real)) (= (tptp.times_times_real (tptp.number267125858f_real V_10) (tptp.times_times_real (tptp.number267125858f_real W_12) Z_7)) (tptp.times_times_real (tptp.number267125858f_real (tptp.times_times_int V_10 W_12)) Z_7))) (forall ((V_10 tptp.int) (W_12 tptp.int) (Z_7 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_10) (tptp.times_times_int (tptp.number_number_of_int W_12) Z_7)) (tptp.times_times_int (tptp.number_number_of_int (tptp.times_times_int V_10 W_12)) Z_7))) (forall ((V_9 tptp.int) (W_11 tptp.int)) (= (tptp.times_times_real (tptp.number267125858f_real V_9) (tptp.number267125858f_real W_11)) (tptp.number267125858f_real (tptp.times_times_int V_9 W_11)))) (forall ((V_9 tptp.int) (W_11 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_9) (tptp.number_number_of_int W_11)) (tptp.number_number_of_int (tptp.times_times_int V_9 W_11)))) (forall ((V_8 tptp.int) (W_10 tptp.int)) (= (tptp.number267125858f_real (tptp.times_times_int V_8 W_10)) (tptp.times_times_real (tptp.number267125858f_real V_8) (tptp.number267125858f_real W_10)))) (forall ((V_8 tptp.int) (W_10 tptp.int)) (= (tptp.number_number_of_int (tptp.times_times_int V_8 W_10)) (tptp.times_times_int (tptp.number_number_of_int V_8) (tptp.number_number_of_int W_10)))) (forall ((V_7 tptp.int) (W_9 tptp.int) (Z_6 tptp.real)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_7) (tptp.plus_plus_real (tptp.number267125858f_real W_9) Z_6)) (tptp.plus_plus_real (tptp.number267125858f_real (tptp.plus_plus_int V_7 W_9)) Z_6))) (forall ((V_7 tptp.int) (W_9 tptp.int) (Z_6 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_7) (tptp.plus_plus_int (tptp.number_number_of_int W_9) Z_6)) (tptp.plus_plus_int (tptp.number_number_of_int (tptp.plus_plus_int V_7 W_9)) Z_6))) (forall ((V_6 tptp.int) (W_8 tptp.int)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_6) (tptp.number267125858f_real W_8)) (tptp.number267125858f_real (tptp.plus_plus_int V_6 W_8)))) (forall ((V_6 tptp.int) (W_8 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_6) (tptp.number_number_of_int W_8)) (tptp.number_number_of_int (tptp.plus_plus_int V_6 W_8)))) (forall ((V_5 tptp.int) (W_7 tptp.int)) (= (tptp.number267125858f_real (tptp.plus_plus_int V_5 W_7)) (tptp.plus_plus_real (tptp.number267125858f_real V_5) (tptp.number267125858f_real W_7)))) (forall ((V_5 tptp.int) (W_7 tptp.int)) (= (tptp.number_number_of_int (tptp.plus_plus_int V_5 W_7)) (tptp.plus_plus_int (tptp.number_number_of_int V_5) (tptp.number_number_of_int W_7)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit1 K) (tptp.bit0 L)) (tptp.bit1 (tptp.plus_plus_int K L)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit0 K) (tptp.bit1 L)) (tptp.bit1 (tptp.plus_plus_int K L)))) (forall ((K tptp.int)) (= (tptp.bit1 K) (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int K) K))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_6))) (= (tptp.number267125858f_real (tptp.bit1 W_6)) (tptp.plus_plus_real (tptp.plus_plus_real tptp.one_one_real _let_1) _let_1)))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_6))) (= (tptp.number_number_of_int (tptp.bit1 W_6)) (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int _let_1) _let_1)))) (forall ((A_39 tptp.real)) (= (tptp.times_times_real (tptp.number267125858f_real (tptp.bit1 tptp.pls)) A_39) A_39)) (forall ((A_39 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int (tptp.bit1 tptp.pls)) A_39) A_39)) (forall ((A_38 tptp.real)) (= (tptp.times_times_real A_38 (tptp.number267125858f_real (tptp.bit1 tptp.pls))) A_38)) (forall ((A_38 tptp.int)) (= (tptp.times_times_int A_38 (tptp.number_number_of_int (tptp.bit1 tptp.pls))) A_38)) _let_30 _let_32 _let_29 _let_30 _let_29 (= tptp.one_one_real _let_28) _let_27 _let_27 (forall ((K tptp.int) (L tptp.int)) (= (tptp.times_times_int (tptp.bit1 K) L) (tptp.plus_plus_int (tptp.bit0 (tptp.times_times_int K L)) L))) (forall ((W_5 tptp.int)) (= (tptp.times_times_real (tptp.plus_plus_real tptp.one_one_real tptp.one_one_real) (tptp.number267125858f_real W_5)) (tptp.number267125858f_real (tptp.bit0 W_5)))) (forall ((W_5 tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) (tptp.number_number_of_int W_5)) (tptp.number_number_of_int (tptp.bit0 W_5)))) (forall ((A_37 tptp.nat)) (= (tptp.power_power_nat A_37 (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.times_times_nat (tptp.times_times_nat A_37 A_37) A_37))) (forall ((A_37 tptp.real)) (= (tptp.power_power_real A_37 (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.times_times_real (tptp.times_times_real A_37 A_37) A_37))) (forall ((A_37 tptp.int)) (= (tptp.power_power_int A_37 (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.times_times_int (tptp.times_times_int A_37 A_37) A_37))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.power_power_int X_1 _let_2) _let_2) (tptp.power_power_int X_1 (tptp.number_number_of_nat (tptp.bit0 _let_1))))))) (forall ((Z_5 tptp.real)) (= (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls))) Z_5) (tptp.plus_plus_real Z_5 Z_5))) (forall ((Z_5 tptp.nat)) (= (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z_5) (tptp.plus_plus_nat Z_5 Z_5))) (forall ((Z_5 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) Z_5) (tptp.plus_plus_int Z_5 Z_5))) (forall ((Z_4 tptp.real)) (= (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls))) Z_4) (tptp.plus_plus_real Z_4 Z_4))) (forall ((Z_4 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) Z_4) (tptp.plus_plus_int Z_4 Z_4))) (forall ((Z_3 tptp.real)) (= (tptp.times_times_real Z_3 (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_real Z_3 Z_3))) (forall ((Z_3 tptp.nat)) (= (tptp.times_times_nat Z_3 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_nat Z_3 Z_3))) (forall ((Z_3 tptp.int)) (= (tptp.times_times_int Z_3 (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_int Z_3 Z_3))) (forall ((Z_2 tptp.real)) (= (tptp.times_times_real Z_2 (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_real Z_2 Z_2))) (forall ((Z_2 tptp.int)) (= (tptp.times_times_int Z_2 (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_int Z_2 Z_2))) _let_25 _let_24 _let_23 (tptp.ord_less_int tptp.zero_zero_int _let_5) (tptp.dvd_dvd_int _let_5 _let_11) (forall ((P tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (=> (tptp.zprime P) (=> (not (= P (tptp.number_number_of_int _let_2))) (=> (not (= P (tptp.number_number_of_int (tptp.bit1 _let_1)))) (tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 _let_2)) P))))))) (= (tptp.twoSqu2107342101sum2sq (tptp.product_Pair_int_int tptp.s tptp.one_one_int)) _let_22) (forall ((X_1 tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_real (tptp.plus_plus_real X_1 Y_1) _let_2) (tptp.plus_plus_real (tptp.plus_plus_real (tptp.power_power_real X_1 _let_2) (tptp.power_power_real Y_1 _let_2)) (tptp.times_times_real (tptp.times_times_real (tptp.number267125858f_real _let_1) X_1) Y_1)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 _let_1)) (tptp.power_power_real X_1 _let_2)) (tptp.power_power_real (tptp.times_times_real (tptp.number267125858f_real _let_1) X_1) _let_2))))) (forall ((N_36 tptp.nat) (A_36 tptp.real)) (let ((_let_1 (tptp.power_power_real A_36 N_36))) (=> (tptp.ord_less_real tptp.one_one_real A_36) (tptp.ord_less_real _let_1 (tptp.times_times_real A_36 _let_1))))) (forall ((N_36 tptp.nat) (A_36 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_36 N_36))) (=> (tptp.ord_less_nat tptp.one_one_nat A_36) (tptp.ord_less_nat _let_1 (tptp.times_times_nat A_36 _let_1))))) (forall ((N_36 tptp.nat) (A_36 tptp.int)) (let ((_let_1 (tptp.power_power_int A_36 N_36))) (=> (tptp.ord_less_int tptp.one_one_int A_36) (tptp.ord_less_int _let_1 (tptp.times_times_int A_36 _let_1))))) (forall ((N_35 tptp.nat) (A_35 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real A_35) (tptp.ord_less_real tptp.one_one_real (tptp.times_times_real A_35 (tptp.power_power_real A_35 N_35))))) (forall ((N_35 tptp.nat) (A_35 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat A_35) (tptp.ord_less_nat tptp.one_one_nat (tptp.times_times_nat A_35 (tptp.power_power_nat A_35 N_35))))) (forall ((N_35 tptp.nat) (A_35 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int A_35) (tptp.ord_less_int tptp.one_one_int (tptp.times_times_int A_35 (tptp.power_power_int A_35 N_35))))) (forall ((M_8 tptp.nat) (N_34 tptp.nat) (A_34 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real A_34) (=> (tptp.ord_less_eq_real (tptp.power_power_real A_34 M_8) (tptp.power_power_real A_34 N_34)) (tptp.ord_less_eq_nat M_8 N_34)))) (forall ((M_8 tptp.nat) (N_34 tptp.nat) (A_34 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat A_34) (=> (tptp.ord_less_eq_nat (tptp.power_power_nat A_34 M_8) (tptp.power_power_nat A_34 N_34)) (tptp.ord_less_eq_nat M_8 N_34)))) (forall ((M_8 tptp.nat) (N_34 tptp.nat) (A_34 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int A_34) (=> (tptp.ord_less_eq_int (tptp.power_power_int A_34 M_8) (tptp.power_power_int A_34 N_34)) (tptp.ord_less_eq_nat M_8 N_34)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real B_2) (= (tptp.ord_less_eq_real (tptp.power_power_real B_2 X_2) (tptp.power_power_real B_2 Y_2)) (tptp.ord_less_eq_nat X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat B_2) (= (tptp.ord_less_eq_nat (tptp.power_power_nat B_2 X_2) (tptp.power_power_nat B_2 Y_2)) (tptp.ord_less_eq_nat X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int B_2) (= (tptp.ord_less_eq_int (tptp.power_power_int B_2 X_2) (tptp.power_power_int B_2 Y_2)) (tptp.ord_less_eq_nat X_2 Y_2)))) (tptp.zcong _let_10 _let_21 _let_5) (and (tptp.ord_less_eq_int tptp.zero_zero_int tptp.s) (tptp.ord_less_int tptp.s _let_5) (tptp.zcong tptp.s1 tptp.s _let_5)) (exists ((X tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (and (tptp.ord_less_eq_int tptp.zero_zero_int X) (tptp.ord_less_int X _let_1) (tptp.zcong tptp.s1 X _let_1) (forall ((Y tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (=> (and (tptp.ord_less_eq_int tptp.zero_zero_int Y) (tptp.ord_less_int Y _let_1) (tptp.zcong tptp.s1 Y _let_1)) (= Y X))))))) (not (forall ((S tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (not (and (tptp.ord_less_eq_int tptp.zero_zero_int S) (tptp.ord_less_int S _let_1) (tptp.zcong tptp.s1 S _let_1)))))) (tptp.zcong _let_21 _let_6 _let_5) (forall ((A_1 tptp.real) (N_1 tptp.nat)) (= (= (tptp.power_power_real A_1 N_1) tptp.zero_zero_real) (and (= A_1 tptp.zero_zero_real) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A_1 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.power_power_nat A_1 N_1) tptp.zero_zero_nat) (and (= A_1 tptp.zero_zero_nat) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A_1 tptp.int) (N_1 tptp.nat)) (= (= (tptp.power_power_int A_1 N_1) tptp.zero_zero_int) (and (= A_1 tptp.zero_zero_int) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A_33 tptp.nat) (M_7 tptp.nat) (N_33 tptp.nat)) (=> (tptp.ord_less_eq_nat M_7 N_33) (tptp.dvd_dvd_nat (tptp.power_power_nat A_33 M_7) (tptp.power_power_nat A_33 N_33)))) (forall ((A_33 tptp.int) (M_7 tptp.nat) (N_33 tptp.nat)) (=> (tptp.ord_less_eq_nat M_7 N_33) (tptp.dvd_dvd_int (tptp.power_power_int A_33 M_7) (tptp.power_power_int A_33 N_33)))) (forall ((A_33 tptp.real) (M_7 tptp.nat) (N_33 tptp.nat)) (=> (tptp.ord_less_eq_nat M_7 N_33) (tptp.dvd_dvd_real (tptp.power_power_real A_33 M_7) (tptp.power_power_real A_33 N_33)))) (forall ((N_32 tptp.nat) (M_6 tptp.nat) (X_14 tptp.nat) (Y_12 tptp.nat)) (=> (tptp.dvd_dvd_nat X_14 Y_12) (=> (tptp.ord_less_eq_nat N_32 M_6) (tptp.dvd_dvd_nat (tptp.power_power_nat X_14 N_32) (tptp.power_power_nat Y_12 M_6))))) (forall ((N_32 tptp.nat) (M_6 tptp.nat) (X_14 tptp.int) (Y_12 tptp.int)) (=> (tptp.dvd_dvd_int X_14 Y_12) (=> (tptp.ord_less_eq_nat N_32 M_6) (tptp.dvd_dvd_int (tptp.power_power_int X_14 N_32) (tptp.power_power_int Y_12 M_6))))) (forall ((N_32 tptp.nat) (M_6 tptp.nat) (X_14 tptp.real) (Y_12 tptp.real)) (=> (tptp.dvd_dvd_real X_14 Y_12) (=> (tptp.ord_less_eq_nat N_32 M_6) (tptp.dvd_dvd_real (tptp.power_power_real X_14 N_32) (tptp.power_power_real Y_12 M_6))))) (forall ((M_5 tptp.nat) (A_32 tptp.nat) (N_31 tptp.nat) (B_9 tptp.nat)) (=> (tptp.dvd_dvd_nat (tptp.power_power_nat A_32 N_31) B_9) (=> (tptp.ord_less_eq_nat M_5 N_31) (tptp.dvd_dvd_nat (tptp.power_power_nat A_32 M_5) B_9)))) (forall ((M_5 tptp.nat) (A_32 tptp.int) (N_31 tptp.nat) (B_9 tptp.int)) (=> (tptp.dvd_dvd_int (tptp.power_power_int A_32 N_31) B_9) (=> (tptp.ord_less_eq_nat M_5 N_31) (tptp.dvd_dvd_int (tptp.power_power_int A_32 M_5) B_9)))) (forall ((M_5 tptp.nat) (A_32 tptp.real) (N_31 tptp.nat) (B_9 tptp.real)) (=> (tptp.dvd_dvd_real (tptp.power_power_real A_32 N_31) B_9) (=> (tptp.ord_less_eq_nat M_5 N_31) (tptp.dvd_dvd_real (tptp.power_power_real A_32 M_5) B_9)))) (forall ((A_31 tptp.real) (N_30 tptp.nat) (B_8 tptp.real)) (=> (= (tptp.power_power_real A_31 N_30) (tptp.power_power_real B_8 N_30)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real A_31) (=> (tptp.ord_less_eq_real tptp.zero_zero_real B_8) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_30) (= A_31 B_8)))))) (forall ((A_31 tptp.nat) (N_30 tptp.nat) (B_8 tptp.nat)) (=> (= (tptp.power_power_nat A_31 N_30) (tptp.power_power_nat B_8 N_30)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat A_31) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat B_8) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_30) (= A_31 B_8)))))) (forall ((A_31 tptp.int) (N_30 tptp.nat) (B_8 tptp.int)) (=> (= (tptp.power_power_int A_31 N_30) (tptp.power_power_int B_8 N_30)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A_31) (=> (tptp.ord_less_eq_int tptp.zero_zero_int B_8) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_30) (= A_31 B_8)))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int M) (=> (tptp.ord_less_int M N) (not (tptp.dvd_dvd_int N M))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int M) (=> (tptp.ord_less_eq_int tptp.zero_zero_int N) (=> (tptp.dvd_dvd_int M N) (=> (tptp.dvd_dvd_int N M) (= M N)))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (=> (tptp.dvd_dvd_int (tptp.times_times_int K M) (tptp.times_times_int K N)) (=> (not (= K tptp.zero_zero_int)) (tptp.dvd_dvd_int M N)))) (forall ((N_29 tptp.nat) (X_13 tptp.nat) (Y_11 tptp.nat)) (=> (tptp.dvd_dvd_nat X_13 Y_11) (tptp.dvd_dvd_nat (tptp.power_power_nat X_13 N_29) (tptp.power_power_nat Y_11 N_29)))) (forall ((N_29 tptp.nat) (X_13 tptp.int) (Y_11 tptp.int)) (=> (tptp.dvd_dvd_int X_13 Y_11) (tptp.dvd_dvd_int (tptp.power_power_int X_13 N_29) (tptp.power_power_int Y_11 N_29)))) (forall ((N_29 tptp.nat) (X_13 tptp.real) (Y_11 tptp.real)) (=> (tptp.dvd_dvd_real X_13 Y_11) (tptp.dvd_dvd_real (tptp.power_power_real X_13 N_29) (tptp.power_power_real Y_11 N_29)))) (forall ((N_28 tptp.nat) (A_30 tptp.real)) (=> (not (= A_30 tptp.zero_zero_real)) (not (= (tptp.power_power_real A_30 N_28) tptp.zero_zero_real)))) (forall ((N_28 tptp.nat) (A_30 tptp.int)) (=> (not (= A_30 tptp.zero_zero_int)) (not (= (tptp.power_power_int A_30 N_28) tptp.zero_zero_int)))) (forall ((N_27 tptp.nat)) (let ((_let_1 (tptp.power_power_real tptp.zero_zero_real N_27))) (let ((_let_2 (= N_27 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N_27 tptp.nat)) (let ((_let_1 (tptp.power_power_nat tptp.zero_zero_nat N_27))) (let ((_let_2 (= N_27 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_27 tptp.nat)) (let ((_let_1 (tptp.power_power_int tptp.zero_zero_int N_27))) (let ((_let_2 (= N_27 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Z tptp.int) (N tptp.int)) (=> (tptp.dvd_dvd_int Z N) (=> (tptp.ord_less_int tptp.zero_zero_int N) (tptp.ord_less_eq_int Z N)))) (forall ((N_26 tptp.nat) (A_29 tptp.real) (B_7 tptp.real)) (=> (tptp.ord_less_real A_29 B_7) (=> (tptp.ord_less_eq_real tptp.zero_zero_real A_29) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_26) (tptp.ord_less_real (tptp.power_power_real A_29 N_26) (tptp.power_power_real B_7 N_26)))))) (forall ((N_26 tptp.nat) (A_29 tptp.nat) (B_7 tptp.nat)) (=> (tptp.ord_less_nat A_29 B_7) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat A_29) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_26) (tptp.ord_less_nat (tptp.power_power_nat A_29 N_26) (tptp.power_power_nat B_7 N_26)))))) (forall ((N_26 tptp.nat) (A_29 tptp.int) (B_7 tptp.int)) (=> (tptp.ord_less_int A_29 B_7) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A_29) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_26) (tptp.ord_less_int (tptp.power_power_int A_29 N_26) (tptp.power_power_int B_7 N_26)))))) (forall ((A_28 tptp.real)) (= (tptp.times_times_real tptp.zero_zero_real A_28) tptp.zero_zero_real)) (forall ((A_28 tptp.nat)) (= (tptp.times_times_nat tptp.zero_zero_nat A_28) tptp.zero_zero_nat)) (forall ((A_28 tptp.int)) (= (tptp.times_times_int tptp.zero_zero_int A_28) tptp.zero_zero_int)) (forall ((A_27 tptp.real)) (= (tptp.times_times_real A_27 tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_27 tptp.nat)) (= (tptp.times_times_nat A_27 tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_27 tptp.int)) (= (tptp.times_times_int A_27 tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_26 tptp.real)) (= (tptp.plus_plus_real tptp.zero_zero_real A_26) A_26)) (forall ((A_26 tptp.nat)) (= (tptp.plus_plus_nat tptp.zero_zero_nat A_26) A_26)) (forall ((A_26 tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int A_26) A_26)) (forall ((A_25 tptp.real)) (= (tptp.plus_plus_real A_25 tptp.zero_zero_real) A_25)) (forall ((A_25 tptp.nat)) (= (tptp.plus_plus_nat A_25 tptp.zero_zero_nat) A_25)) (forall ((A_25 tptp.int)) (= (tptp.plus_plus_int A_25 tptp.zero_zero_int) A_25)) (forall ((B_2 tptp.real) (A_1 tptp.real)) (= (= B_2 (tptp.plus_plus_real B_2 A_1)) (= A_1 tptp.zero_zero_real))) (forall ((B_2 tptp.nat) (A_1 tptp.nat)) (= (= B_2 (tptp.plus_plus_nat B_2 A_1)) (= A_1 tptp.zero_zero_nat))) (forall ((B_2 tptp.int) (A_1 tptp.int)) (= (= B_2 (tptp.plus_plus_int B_2 A_1)) (= A_1 tptp.zero_zero_int))) (forall ((A_1 tptp.real)) (= (= (tptp.plus_plus_real A_1 A_1) tptp.zero_zero_real) (= A_1 tptp.zero_zero_real))) (forall ((A_1 tptp.int)) (= (= (tptp.plus_plus_int A_1 A_1) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))) (= tptp.pls tptp.zero_zero_int) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((Z tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int Z) Z)) (forall ((Z tptp.int)) (= (tptp.plus_plus_int Z tptp.zero_zero_int) Z)) (forall ((N_25 tptp.nat) (A_24 tptp.real)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real A_24) (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.power_power_real A_24 N_25)))) (forall ((N_25 tptp.nat) (A_24 tptp.nat)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat A_24) (tptp.ord_less_eq_nat tptp.zero_zero_nat (tptp.power_power_nat A_24 N_25)))) (forall ((N_25 tptp.nat) (A_24 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A_24) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.power_power_int A_24 N_25)))) (forall ((N_24 tptp.nat) (A_23 tptp.real) (B_6 tptp.real)) (=> (tptp.ord_less_eq_real A_23 B_6) (=> (tptp.ord_less_eq_real tptp.zero_zero_real A_23) (tptp.ord_less_eq_real (tptp.power_power_real A_23 N_24) (tptp.power_power_real B_6 N_24))))) (forall ((N_24 tptp.nat) (A_23 tptp.nat) (B_6 tptp.nat)) (=> (tptp.ord_less_eq_nat A_23 B_6) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat A_23) (tptp.ord_less_eq_nat (tptp.power_power_nat A_23 N_24) (tptp.power_power_nat B_6 N_24))))) (forall ((N_24 tptp.nat) (A_23 tptp.int) (B_6 tptp.int)) (=> (tptp.ord_less_eq_int A_23 B_6) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A_23) (tptp.ord_less_eq_int (tptp.power_power_int A_23 N_24) (tptp.power_power_int B_6 N_24))))) (forall ((N_23 tptp.nat) (A_22 tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real A_22) (tptp.ord_less_real tptp.zero_zero_real (tptp.power_power_real A_22 N_23)))) (forall ((N_23 tptp.nat) (A_22 tptp.nat)) (=> (tptp.ord_less_nat tptp.zero_zero_nat A_22) (tptp.ord_less_nat tptp.zero_zero_nat (tptp.power_power_nat A_22 N_23)))) (forall ((N_23 tptp.nat) (A_22 tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int A_22) (tptp.ord_less_int tptp.zero_zero_int (tptp.power_power_int A_22 N_23)))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.nat) (P tptp.int)) (=> (tptp.zcong (tptp.power_power_int X_1 Y_1) tptp.one_one_int P) (tptp.zcong (tptp.power_power_int X_1 (tptp.times_times_nat Y_1 Z)) tptp.one_one_int P))) (forall ((K_1 tptp.int) (N_1 tptp.int) (Ma tptp.int)) (= (tptp.dvd_dvd_int K_1 (tptp.plus_plus_int N_1 (tptp.times_times_int K_1 Ma))) (tptp.dvd_dvd_int K_1 N_1))) (forall ((C tptp.int) (X_2 tptp.int) (Ta tptp.int) (A_1 tptp.int) (D tptp.int)) (=> (tptp.dvd_dvd_int A_1 D) (= (tptp.dvd_dvd_int A_1 (tptp.plus_plus_int X_2 Ta)) (tptp.dvd_dvd_int A_1 (tptp.plus_plus_int (tptp.plus_plus_int X_2 (tptp.times_times_int C D)) Ta))))) (forall ((A_21 tptp.real) (N_22 tptp.nat) (B_5 tptp.real)) (=> (tptp.ord_less_real (tptp.power_power_real A_21 N_22) (tptp.power_power_real B_5 N_22)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real B_5) (tptp.ord_less_real A_21 B_5)))) (forall ((A_21 tptp.nat) (N_22 tptp.nat) (B_5 tptp.nat)) (=> (tptp.ord_less_nat (tptp.power_power_nat A_21 N_22) (tptp.power_power_nat B_5 N_22)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat B_5) (tptp.ord_less_nat A_21 B_5)))) (forall ((A_21 tptp.int) (N_22 tptp.nat) (B_5 tptp.int)) (=> (tptp.ord_less_int (tptp.power_power_int A_21 N_22) (tptp.power_power_int B_5 N_22)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int B_5) (tptp.ord_less_int A_21 B_5)))) (forall ((A_20 tptp.real) (N_21 tptp.nat) (N_20 tptp.nat)) (=> (tptp.ord_less_eq_nat N_21 N_20) (=> (tptp.ord_less_eq_real tptp.zero_zero_real A_20) (=> (tptp.ord_less_eq_real A_20 tptp.one_one_real) (tptp.ord_less_eq_real (tptp.power_power_real A_20 N_20) (tptp.power_power_real A_20 N_21)))))) (forall ((A_20 tptp.nat) (N_21 tptp.nat) (N_20 tptp.nat)) (=> (tptp.ord_less_eq_nat N_21 N_20) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat A_20) (=> (tptp.ord_less_eq_nat A_20 tptp.one_one_nat) (tptp.ord_less_eq_nat (tptp.power_power_nat A_20 N_20) (tptp.power_power_nat A_20 N_21)))))) (forall ((A_20 tptp.int) (N_21 tptp.nat) (N_20 tptp.nat)) (=> (tptp.ord_less_eq_nat N_21 N_20) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A_20) (=> (tptp.ord_less_eq_int A_20 tptp.one_one_int) (tptp.ord_less_eq_int (tptp.power_power_int A_20 N_20) (tptp.power_power_int A_20 N_21)))))) (forall ((A_19 tptp.real) (N_19 tptp.nat) (N_18 tptp.nat)) (=> (tptp.ord_less_nat N_19 N_18) (=> (tptp.ord_less_real tptp.zero_zero_real A_19) (=> (tptp.ord_less_real A_19 tptp.one_one_real) (tptp.ord_less_real (tptp.power_power_real A_19 N_18) (tptp.power_power_real A_19 N_19)))))) (forall ((A_19 tptp.nat) (N_19 tptp.nat) (N_18 tptp.nat)) (=> (tptp.ord_less_nat N_19 N_18) (=> (tptp.ord_less_nat tptp.zero_zero_nat A_19) (=> (tptp.ord_less_nat A_19 tptp.one_one_nat) (tptp.ord_less_nat (tptp.power_power_nat A_19 N_18) (tptp.power_power_nat A_19 N_19)))))) (forall ((A_19 tptp.int) (N_19 tptp.nat) (N_18 tptp.nat)) (=> (tptp.ord_less_nat N_19 N_18) (=> (tptp.ord_less_int tptp.zero_zero_int A_19) (=> (tptp.ord_less_int A_19 tptp.one_one_int) (tptp.ord_less_int (tptp.power_power_int A_19 N_18) (tptp.power_power_int A_19 N_19)))))) (forall ((A_1 tptp.real)) (= (tptp.ord_less_real (tptp.plus_plus_real A_1 A_1) tptp.zero_zero_real) (tptp.ord_less_real A_1 tptp.zero_zero_real))) (forall ((A_1 tptp.int)) (= (tptp.ord_less_int (tptp.plus_plus_int A_1 A_1) tptp.zero_zero_int) (tptp.ord_less_int A_1 tptp.zero_zero_int))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real X_2 X_2) (tptp.times_times_real Y_2 Y_2)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int X_2 X_2) (tptp.times_times_int Y_2 Y_2)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((C_2 tptp.real) (D_2 tptp.real) (A_18 tptp.real) (B_4 tptp.real) (R_3 tptp.real)) (=> (not (= R_3 tptp.zero_zero_real)) (=> (and (= A_18 B_4) (not (= C_2 D_2))) (not (= (tptp.plus_plus_real A_18 (tptp.times_times_real R_3 C_2)) (tptp.plus_plus_real B_4 (tptp.times_times_real R_3 D_2))))))) (forall ((C_2 tptp.nat) (D_2 tptp.nat) (A_18 tptp.nat) (B_4 tptp.nat) (R_3 tptp.nat)) (=> (not (= R_3 tptp.zero_zero_nat)) (=> (and (= A_18 B_4) (not (= C_2 D_2))) (not (= (tptp.plus_plus_nat A_18 (tptp.times_times_nat R_3 C_2)) (tptp.plus_plus_nat B_4 (tptp.times_times_nat R_3 D_2))))))) (forall ((C_2 tptp.int) (D_2 tptp.int) (A_18 tptp.int) (B_4 tptp.int) (R_3 tptp.int)) (=> (not (= R_3 tptp.zero_zero_int)) (=> (and (= A_18 B_4) (not (= C_2 D_2))) (not (= (tptp.plus_plus_int A_18 (tptp.times_times_int R_3 C_2)) (tptp.plus_plus_int B_4 (tptp.times_times_int R_3 D_2))))))) (forall ((A tptp.int) (N tptp.nat) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd_int P (tptp.power_power_int A N)) (tptp.dvd_dvd_int P A)))) (= tptp.zero_zero_real _let_19) _let_17 _let_20 _let_18 _let_20 _let_15 _let_18 (forall ((W_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 W_1) tptp.zero_zero_int) (tptp.ord_less_int W_1 tptp.zero_zero_int))) (not (tptp.ord_less_int tptp.pls tptp.zero_zero_int)) (forall ((W_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 W_1) tptp.zero_zero_int) (tptp.ord_less_int W_1 tptp.zero_zero_int))) _let_17 (tptp.ord_less_int tptp.zero_zero_int tptp.one_one_int) (forall ((B_1 tptp.int) (A tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (tptp.ord_less_int tptp.zero_zero_int (tptp.times_times_int A B_1)) (tptp.ord_less_int tptp.zero_zero_int B_1)))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_int I J) (=> (tptp.ord_less_int tptp.zero_zero_int K) (tptp.ord_less_int (tptp.times_times_int K I) (tptp.times_times_int K J))))) (forall ((Z tptp.int)) (not (= (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int Z) Z) tptp.zero_zero_int))) (forall ((N_17 tptp.nat) (A_17 tptp.real)) (let ((_let_1 (tptp.power_power_real A_17 N_17))) (=> (tptp.ord_less_real tptp.zero_zero_real A_17) (=> (tptp.ord_less_real A_17 tptp.one_one_real) (tptp.ord_less_real (tptp.times_times_real A_17 _let_1) _let_1))))) (forall ((N_17 tptp.nat) (A_17 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_17 N_17))) (=> (tptp.ord_less_nat tptp.zero_zero_nat A_17) (=> (tptp.ord_less_nat A_17 tptp.one_one_nat) (tptp.ord_less_nat (tptp.times_times_nat A_17 _let_1) _let_1))))) (forall ((N_17 tptp.nat) (A_17 tptp.int)) (let ((_let_1 (tptp.power_power_int A_17 N_17))) (=> (tptp.ord_less_int tptp.zero_zero_int A_17) (=> (tptp.ord_less_int A_17 tptp.one_one_int) (tptp.ord_less_int (tptp.times_times_int A_17 _let_1) _let_1))))) (forall ((N tptp.nat) (B_1 tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (tptp.power_power_int P N))) (=> (tptp.zprime P) (=> (not (tptp.dvd_dvd_int P A)) (=> (tptp.dvd_dvd_int _let_1 (tptp.times_times_int A B_1)) (tptp.dvd_dvd_int _let_1 B_1)))))) (forall ((N tptp.nat) (A tptp.int) (B_1 tptp.int) (P tptp.int)) (let ((_let_1 (tptp.power_power_int P N))) (=> (tptp.zprime P) (=> (not (tptp.dvd_dvd_int P B_1)) (=> (tptp.dvd_dvd_int _let_1 (tptp.times_times_int A B_1)) (tptp.dvd_dvd_int _let_1 A)))))) (forall ((X_12 tptp.real) (Y_10 tptp.real)) (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.plus_plus_real (tptp.times_times_real X_12 X_12) (tptp.times_times_real Y_10 Y_10)))) (forall ((X_12 tptp.int) (Y_10 tptp.int)) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int X_12 X_12) (tptp.times_times_int Y_10 Y_10)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real X_2 X_2) (tptp.times_times_real Y_2 Y_2)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int X_2 X_2) (tptp.times_times_int Y_2 Y_2)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((V_3 tptp.int) (V_4 tptp.int)) (let ((_let_1 (tptp.ord_less_int V_3 V_4))) (= (tptp.ord_less_nat (tptp.number_number_of_nat V_3) (tptp.number_number_of_nat V_4)) (and (=> _let_1 (tptp.ord_less_int tptp.pls V_4)) _let_1)))) (forall ((X_11 tptp.real) (Y_9 tptp.real)) (not (tptp.ord_less_real (tptp.plus_plus_real (tptp.times_times_real X_11 X_11) (tptp.times_times_real Y_9 Y_9)) tptp.zero_zero_real))) (forall ((X_11 tptp.int) (Y_9 tptp.int)) (not (tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int X_11 X_11) (tptp.times_times_int Y_9 Y_9)) tptp.zero_zero_int))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.ord_less_real tptp.zero_zero_real (tptp.plus_plus_real (tptp.times_times_real X_2 X_2) (tptp.times_times_real Y_2 Y_2))) (or (not (= X_2 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int X_2 X_2) (tptp.times_times_int Y_2 Y_2))) (or (not (= X_2 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int))))) (forall ((V_3 tptp.int) (V_4 tptp.int)) (= (tptp.ord_less_eq_nat (tptp.number_number_of_nat V_3) (tptp.number_number_of_nat V_4)) (=> (not (tptp.ord_less_eq_int V_3 V_4)) (tptp.ord_less_eq_int V_3 tptp.pls)))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_4))) (= (tptp.number267125858f_real (tptp.bit0 W_4)) (tptp.plus_plus_real (tptp.plus_plus_real tptp.zero_zero_real _let_1) _let_1)))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_4))) (= (tptp.number_number_of_int (tptp.bit0 W_4)) (tptp.plus_plus_int (tptp.plus_plus_int tptp.zero_zero_int _let_1) _let_1)))) (forall ((A_16 tptp.nat)) (= (tptp.power_power_nat A_16 tptp.one_one_nat) A_16)) (forall ((A_16 tptp.real)) (= (tptp.power_power_real A_16 tptp.one_one_nat) A_16)) (forall ((A_16 tptp.int)) (= (tptp.power_power_int A_16 tptp.one_one_nat) A_16)) (forall ((Z_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.one_one_int Z_1) (tptp.ord_less_int tptp.zero_zero_int Z_1))) (forall ((N_1 tptp.int) (Ma tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int Ma) (= (= (tptp.times_times_int Ma N_1) tptp.one_one_int) (and (= Ma tptp.one_one_int) (= N_1 tptp.one_one_int))))) (forall ((Z_1 tptp.int)) (= (tptp.ord_less_int (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int Z_1) Z_1) tptp.zero_zero_int) (tptp.ord_less_int Z_1 tptp.zero_zero_int))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_real tptp.zero_zero_real (tptp.number267125858f_real Y_2)) (tptp.ord_less_int tptp.pls Y_2))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.number_number_of_int Y_2)) (tptp.ord_less_int tptp.pls Y_2))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_real (tptp.number267125858f_real X_2) tptp.zero_zero_real) (tptp.ord_less_int X_2 tptp.pls))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_int (tptp.number_number_of_int X_2) tptp.zero_zero_int) (tptp.ord_less_int X_2 tptp.pls))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.number267125858f_real Y_2)) (tptp.ord_less_eq_int tptp.pls Y_2))) (forall ((Y_2 tptp.int)) (= (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.number_number_of_int Y_2)) (tptp.ord_less_eq_int tptp.pls Y_2))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_eq_real (tptp.number267125858f_real X_2) tptp.zero_zero_real) (tptp.ord_less_eq_int X_2 tptp.pls))) (forall ((X_2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_2) tptp.zero_zero_int) (tptp.ord_less_eq_int X_2 tptp.pls))) (forall ((Z tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Z) (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int tptp.one_one_int Z)))) (= (tptp.power_power_real tptp.zero_zero_real _let_9) tptp.zero_zero_real) (= (tptp.power_power_nat tptp.zero_zero_nat _let_9) tptp.zero_zero_nat) (= (tptp.power_power_int tptp.zero_zero_int _let_9) tptp.zero_zero_int) (forall ((A_1 tptp.real)) (= (= (tptp.power_power_real A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_1 tptp.zero_zero_real))) (forall ((A_1 tptp.int)) (= (= (tptp.power_power_int A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))) (forall ((A_15 tptp.real)) (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.power_power_real A_15 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((A_15 tptp.int)) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.power_power_int A_15 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_10 tptp.real) (Y_8 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_eq_real (tptp.power_power_real X_10 _let_1) (tptp.power_power_real Y_8 _let_1)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real Y_8) (tptp.ord_less_eq_real X_10 Y_8))))) (forall ((X_10 tptp.nat) (Y_8 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_eq_nat (tptp.power_power_nat X_10 _let_1) (tptp.power_power_nat Y_8 _let_1)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat Y_8) (tptp.ord_less_eq_nat X_10 Y_8))))) (forall ((X_10 tptp.int) (Y_8 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_eq_int (tptp.power_power_int X_10 _let_1) (tptp.power_power_int Y_8 _let_1)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Y_8) (tptp.ord_less_eq_int X_10 Y_8))))) (forall ((X_9 tptp.real) (Y_7 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.power_power_real X_9 _let_1) (tptp.power_power_real Y_7 _let_1)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real X_9) (=> (tptp.ord_less_eq_real tptp.zero_zero_real Y_7) (= X_9 Y_7)))))) (forall ((X_9 tptp.nat) (Y_7 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.power_power_nat X_9 _let_1) (tptp.power_power_nat Y_7 _let_1)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat X_9) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat Y_7) (= X_9 Y_7)))))) (forall ((X_9 tptp.int) (Y_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.power_power_int X_9 _let_1) (tptp.power_power_int Y_7 _let_1)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_9) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Y_7) (= X_9 Y_7)))))) (forall ((A_14 tptp.real)) (not (tptp.ord_less_real (tptp.power_power_real A_14 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real))) (forall ((A_14 tptp.int)) (not (tptp.ord_less_int (tptp.power_power_int A_14 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int))) (forall ((A_1 tptp.real)) (= (tptp.ord_less_real tptp.zero_zero_real (tptp.power_power_real A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= A_1 tptp.zero_zero_real)))) (forall ((A_1 tptp.int)) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.power_power_int A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= A_1 tptp.zero_zero_int)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus_real (tptp.power_power_real X_2 _let_1) (tptp.power_power_real Y_2 _let_1)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus_int (tptp.power_power_int X_2 _let_1) (tptp.power_power_int Y_2 _let_1)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((A_13 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_13 N_16))) (= (tptp.times_times_nat _let_1 A_13) (tptp.times_times_nat A_13 _let_1)))) (forall ((A_13 tptp.real) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_13 N_16))) (= (tptp.times_times_real _let_1 A_13) (tptp.times_times_real A_13 _let_1)))) (forall ((A_13 tptp.int) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_13 N_16))) (= (tptp.times_times_int _let_1 A_13) (tptp.times_times_int A_13 _let_1)))) (forall ((A_12 tptp.nat) (B_3 tptp.nat) (N_15 tptp.nat)) (= (tptp.power_power_nat (tptp.times_times_nat A_12 B_3) N_15) (tptp.times_times_nat (tptp.power_power_nat A_12 N_15) (tptp.power_power_nat B_3 N_15)))) (forall ((A_12 tptp.real) (B_3 tptp.real) (N_15 tptp.nat)) (= (tptp.power_power_real (tptp.times_times_real A_12 B_3) N_15) (tptp.times_times_real (tptp.power_power_real A_12 N_15) (tptp.power_power_real B_3 N_15)))) (forall ((A_12 tptp.int) (B_3 tptp.int) (N_15 tptp.nat)) (= (tptp.power_power_int (tptp.times_times_int A_12 B_3) N_15) (tptp.times_times_int (tptp.power_power_int A_12 N_15) (tptp.power_power_int B_3 N_15)))) (forall ((A_11 tptp.nat) (M_4 tptp.nat) (N_14 tptp.nat)) (= (tptp.power_power_nat A_11 (tptp.plus_plus_nat M_4 N_14)) (tptp.times_times_nat (tptp.power_power_nat A_11 M_4) (tptp.power_power_nat A_11 N_14)))) (forall ((A_11 tptp.real) (M_4 tptp.nat) (N_14 tptp.nat)) (= (tptp.power_power_real A_11 (tptp.plus_plus_nat M_4 N_14)) (tptp.times_times_real (tptp.power_power_real A_11 M_4) (tptp.power_power_real A_11 N_14)))) (forall ((A_11 tptp.int) (M_4 tptp.nat) (N_14 tptp.nat)) (= (tptp.power_power_int A_11 (tptp.plus_plus_nat M_4 N_14)) (tptp.times_times_int (tptp.power_power_int A_11 M_4) (tptp.power_power_int A_11 N_14)))) (forall ((N_13 tptp.nat)) (= (tptp.power_power_real tptp.one_one_real N_13) tptp.one_one_real)) (forall ((N_13 tptp.nat)) (= (tptp.power_power_nat tptp.one_one_nat N_13) tptp.one_one_nat)) (forall ((N_13 tptp.nat)) (= (tptp.power_power_int tptp.one_one_int N_13) tptp.one_one_int)) (forall ((A_10 tptp.nat) (M_3 tptp.nat) (N_12 tptp.nat)) (= (tptp.power_power_nat A_10 (tptp.times_times_nat M_3 N_12)) (tptp.power_power_nat (tptp.power_power_nat A_10 M_3) N_12))) (forall ((A_10 tptp.real) (M_3 tptp.nat) (N_12 tptp.nat)) (= (tptp.power_power_real A_10 (tptp.times_times_nat M_3 N_12)) (tptp.power_power_real (tptp.power_power_real A_10 M_3) N_12))) (forall ((A_10 tptp.int) (M_3 tptp.nat) (N_12 tptp.nat)) (= (tptp.power_power_int A_10 (tptp.times_times_nat M_3 N_12)) (tptp.power_power_int (tptp.power_power_int A_10 M_3) N_12))) (forall ((X_8 tptp.real) (Y_6 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_real (tptp.power_power_real X_8 _let_1) (tptp.power_power_real Y_6 _let_1)) (=> (tptp.ord_less_eq_real tptp.zero_zero_real Y_6) (tptp.ord_less_real X_8 Y_6))))) (forall ((X_8 tptp.nat) (Y_6 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_nat (tptp.power_power_nat X_8 _let_1) (tptp.power_power_nat Y_6 _let_1)) (=> (tptp.ord_less_eq_nat tptp.zero_zero_nat Y_6) (tptp.ord_less_nat X_8 Y_6))))) (forall ((X_8 tptp.int) (Y_6 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_int (tptp.power_power_int X_8 _let_1) (tptp.power_power_int Y_6 _let_1)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Y_6) (tptp.ord_less_int X_8 Y_6))))) (forall ((X_7 tptp.real) (Y_5 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.plus_plus_real (tptp.power_power_real X_7 _let_1) (tptp.power_power_real Y_5 _let_1))))) (forall ((X_7 tptp.int) (Y_5 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.power_power_int X_7 _let_1) (tptp.power_power_int Y_5 _let_1))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.power_power_real X_2 _let_1) (tptp.power_power_real Y_2 _let_1)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.power_power_int X_2 _let_1) (tptp.power_power_int Y_2 _let_1)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((X_6 tptp.real) (Y_4 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.ord_less_real (tptp.plus_plus_real (tptp.power_power_real X_6 _let_1) (tptp.power_power_real Y_4 _let_1)) tptp.zero_zero_real)))) (forall ((X_6 tptp.int) (Y_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.ord_less_int (tptp.plus_plus_int (tptp.power_power_int X_6 _let_1) (tptp.power_power_int Y_4 _let_1)) tptp.zero_zero_int)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_real tptp.zero_zero_real (tptp.plus_plus_real (tptp.power_power_real X_2 _let_1) (tptp.power_power_real Y_2 _let_1))) (or (not (= X_2 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real)))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.power_power_int X_2 _let_1) (tptp.power_power_int Y_2 _let_1))) (or (not (= X_2 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int)))))) (forall ((A_9 tptp.real) (N_11 tptp.nat)) (tptp.ord_less_eq_real tptp.zero_zero_real (tptp.power_power_real A_9 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_11)))) (forall ((A_9 tptp.int) (N_11 tptp.nat)) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.power_power_int A_9 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_11)))) (forall ((N_10 tptp.nat) (A_8 tptp.real)) (=> (tptp.ord_less_eq_real tptp.one_one_real A_8) (tptp.ord_less_eq_real tptp.one_one_real (tptp.power_power_real A_8 N_10)))) (forall ((N_10 tptp.nat) (A_8 tptp.nat)) (=> (tptp.ord_less_eq_nat tptp.one_one_nat A_8) (tptp.ord_less_eq_nat tptp.one_one_nat (tptp.power_power_nat A_8 N_10)))) (forall ((N_10 tptp.nat) (A_8 tptp.int)) (=> (tptp.ord_less_eq_int tptp.one_one_int A_8) (tptp.ord_less_eq_int tptp.one_one_int (tptp.power_power_int A_8 N_10)))) (forall ((A_7 tptp.real) (N_9 tptp.nat) (N_8 tptp.nat)) (=> (tptp.ord_less_eq_nat N_9 N_8) (=> (tptp.ord_less_eq_real tptp.one_one_real A_7) (tptp.ord_less_eq_real (tptp.power_power_real A_7 N_9) (tptp.power_power_real A_7 N_8))))) (forall ((A_7 tptp.nat) (N_9 tptp.nat) (N_8 tptp.nat)) (=> (tptp.ord_less_eq_nat N_9 N_8) (=> (tptp.ord_less_eq_nat tptp.one_one_nat A_7) (tptp.ord_less_eq_nat (tptp.power_power_nat A_7 N_9) (tptp.power_power_nat A_7 N_8))))) (forall ((A_7 tptp.int) (N_9 tptp.nat) (N_8 tptp.nat)) (=> (tptp.ord_less_eq_nat N_9 N_8) (=> (tptp.ord_less_eq_int tptp.one_one_int A_7) (tptp.ord_less_eq_int (tptp.power_power_int A_7 N_9) (tptp.power_power_int A_7 N_8))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A_1 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real A_1) (= (= (tptp.power_power_real A_1 Ma) (tptp.power_power_real A_1 N_1)) (= Ma N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A_1 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat A_1) (= (= (tptp.power_power_nat A_1 Ma) (tptp.power_power_nat A_1 N_1)) (= Ma N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A_1 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int A_1) (= (= (tptp.power_power_int A_1 Ma) (tptp.power_power_int A_1 N_1)) (= Ma N_1)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real B_2) (= (tptp.ord_less_real (tptp.power_power_real B_2 X_2) (tptp.power_power_real B_2 Y_2)) (tptp.ord_less_nat X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat B_2) (= (tptp.ord_less_nat (tptp.power_power_nat B_2 X_2) (tptp.power_power_nat B_2 Y_2)) (tptp.ord_less_nat X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int B_2) (= (tptp.ord_less_int (tptp.power_power_int B_2 X_2) (tptp.power_power_int B_2 Y_2)) (tptp.ord_less_nat X_2 Y_2)))) (forall ((M_2 tptp.nat) (N_7 tptp.nat) (A_6 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real A_6) (=> (tptp.ord_less_real (tptp.power_power_real A_6 M_2) (tptp.power_power_real A_6 N_7)) (tptp.ord_less_nat M_2 N_7)))) (forall ((M_2 tptp.nat) (N_7 tptp.nat) (A_6 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat A_6) (=> (tptp.ord_less_nat (tptp.power_power_nat A_6 M_2) (tptp.power_power_nat A_6 N_7)) (tptp.ord_less_nat M_2 N_7)))) (forall ((M_2 tptp.nat) (N_7 tptp.nat) (A_6 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int A_6) (=> (tptp.ord_less_int (tptp.power_power_int A_6 M_2) (tptp.power_power_int A_6 N_7)) (tptp.ord_less_nat M_2 N_7)))) (forall ((A_5 tptp.real) (N_6 tptp.nat) (N_5 tptp.nat)) (=> (tptp.ord_less_nat N_6 N_5) (=> (tptp.ord_less_real tptp.one_one_real A_5) (tptp.ord_less_real (tptp.power_power_real A_5 N_6) (tptp.power_power_real A_5 N_5))))) (forall ((A_5 tptp.nat) (N_6 tptp.nat) (N_5 tptp.nat)) (=> (tptp.ord_less_nat N_6 N_5) (=> (tptp.ord_less_nat tptp.one_one_nat A_5) (tptp.ord_less_nat (tptp.power_power_nat A_5 N_6) (tptp.power_power_nat A_5 N_5))))) (forall ((A_5 tptp.int) (N_6 tptp.nat) (N_5 tptp.nat)) (=> (tptp.ord_less_nat N_6 N_5) (=> (tptp.ord_less_int tptp.one_one_int A_5) (tptp.ord_less_int (tptp.power_power_int A_5 N_6) (tptp.power_power_int A_5 N_5))))) (tptp.zcong _let_10 _let_6 _let_5) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (not (tptp.zcong X_1 tptp.zero_zero_int P)) (=> (tptp.zcong (tptp.power_power_int Y_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_1 P) (not (tptp.dvd_dvd_int P Y_1))))) (forall ((X_1 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_int X_1 (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (or (= X_1 tptp.zero_zero_int) (= X_1 tptp.one_one_int))))) (forall ((A_4 tptp.real) (K_3 tptp.nat)) (=> (tptp.ord_less_eq_real (tptp.power_power_real A_4 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) K_3)) tptp.zero_zero_real) (= A_4 tptp.zero_zero_real))) (forall ((A_4 tptp.int) (K_3 tptp.nat)) (=> (tptp.ord_less_eq_int (tptp.power_power_int A_4 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) K_3)) tptp.zero_zero_int) (= A_4 tptp.zero_zero_int))) (forall ((P_1 tptp.int)) (= (tptp.zprime P_1) (and (tptp.ord_less_int tptp.one_one_int P_1) (forall ((M_1 tptp.int)) (=> (and (tptp.ord_less_eq_int tptp.zero_zero_int M_1) (tptp.dvd_dvd_int M_1 P_1)) (or (= M_1 tptp.one_one_int) (= M_1 P_1))))))) (not (forall ((S1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.zcong (tptp.power_power_int S1 (tptp.number_number_of_nat _let_1)) (tptp.number_number_of_int tptp.min) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) _let_7 (forall ((X_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.ord_less_nat tptp.zero_zero_nat (tptp.power_power_nat X_2 N_1)) (or (tptp.ord_less_nat tptp.zero_zero_nat X_2) (= N_1 tptp.zero_zero_nat)))) (forall ((X_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.ord_less_nat tptp.zero_zero_nat (tptp.power_power_nat X_2 N_1)) (or (= N_1 tptp.zero_zero_nat) (tptp.ord_less_nat tptp.zero_zero_nat X_2)))) (forall ((X_2 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (tptp.ord_less_nat tptp.zero_zero_nat (tptp.power_power_nat X_2 _let_1)) (or (= _let_1 tptp.zero_zero_nat) (tptp.ord_less_nat tptp.zero_zero_nat X_2))))) (forall ((M tptp.nat) (N tptp.nat) (I tptp.nat)) (=> (tptp.ord_less_nat tptp.zero_zero_nat I) (=> (tptp.ord_less_nat (tptp.power_power_nat I M) (tptp.power_power_nat I N)) (tptp.ord_less_nat M N)))) (forall ((K_1 tptp.int)) (= (= (tptp.bit1 K_1) tptp.min) (= K_1 tptp.min))) (forall ((L_1 tptp.int)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min L_1))) (= (tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K tptp.int)) (not (= (tptp.bit0 K) tptp.min))) (forall ((L tptp.int)) (not (= tptp.min (tptp.bit0 L)))) (not (tptp.ord_less_int tptp.min tptp.min)) (tptp.ord_less_eq_int tptp.min tptp.min) (forall ((X_2 tptp.real)) (= (not (tptp.ord_less_real tptp.zero_zero_real (tptp.times_times_real X_2 X_2))) (= X_2 tptp.zero_zero_real))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit1 K_1) tptp.min) (tptp.ord_less_int K_1 tptp.min))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int tptp.min (tptp.bit1 K_1)) (tptp.ord_less_int tptp.min K_1))) (not (tptp.ord_less_int tptp.pls tptp.min)) (tptp.ord_less_int tptp.min tptp.pls) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int tptp.min (tptp.bit0 K_1)) (tptp.ord_less_int tptp.min K_1))) (tptp.ord_less_int tptp.min tptp.zero_zero_int) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K_1) tptp.min) (tptp.ord_less_eq_int K_1 tptp.min))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.min (tptp.bit1 K_1)) (tptp.ord_less_eq_int tptp.min K_1))) (not (tptp.ord_less_eq_int tptp.pls tptp.min)) (tptp.ord_less_eq_int tptp.min tptp.pls) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K_1) tptp.min) (tptp.ord_less_eq_int K_1 tptp.min))) (not (= _let_16 _let_6)) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.dvd_dvd_nat (tptp.power_power_nat I M) (tptp.power_power_nat I N)) (=> (tptp.ord_less_nat tptp.one_one_nat I) (tptp.ord_less_eq_nat M N)))) (forall ((X_5 tptp.real)) (= (tptp.power_power_real X_5 tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_5 tptp.nat)) (= (tptp.power_power_nat X_5 tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_5 tptp.int)) (= (tptp.power_power_int X_5 tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_3 tptp.real)) (= (tptp.power_power_real A_3 tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_3 tptp.nat)) (= (tptp.power_power_nat A_3 tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_3 tptp.int)) (= (tptp.power_power_int A_3 tptp.zero_zero_nat) tptp.one_one_int)) _let_15 (= tptp.zero_zero_nat _let_14) (forall ((K_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.min (tptp.bit0 K_1)) (tptp.ord_less_int tptp.min K_1))) (forall ((K_1 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K_1) tptp.min) (tptp.ord_less_eq_int K_1 tptp.min))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.times_times_int M N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.number_number_of_int tptp.min))))) (forall ((Ma tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (= (= (tptp.times_times_int Ma N_1) tptp.one_one_int) (or (and (= Ma tptp.one_one_int) (= N_1 tptp.one_one_int)) (and (= Ma _let_1) (= N_1 _let_1)))))) (forall ((N_4 tptp.nat) (A_2 tptp.real)) (=> (tptp.ord_less_real tptp.one_one_real A_2) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_4) (tptp.ord_less_real tptp.one_one_real (tptp.power_power_real A_2 N_4))))) (forall ((N_4 tptp.nat) (A_2 tptp.nat)) (=> (tptp.ord_less_nat tptp.one_one_nat A_2) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_4) (tptp.ord_less_nat tptp.one_one_nat (tptp.power_power_nat A_2 N_4))))) (forall ((N_4 tptp.nat) (A_2 tptp.int)) (=> (tptp.ord_less_int tptp.one_one_int A_2) (=> (tptp.ord_less_nat tptp.zero_zero_nat N_4) (tptp.ord_less_int tptp.one_one_int (tptp.power_power_int A_2 N_4))))) (forall ((X_4 tptp.nat) (N_3 tptp.nat)) (=> (or (tptp.ord_less_nat tptp.zero_zero_nat N_3) (= X_4 tptp.one_one_nat)) (tptp.dvd_dvd_nat X_4 (tptp.power_power_nat X_4 N_3)))) (forall ((X_4 tptp.int) (N_3 tptp.nat)) (=> (or (tptp.ord_less_nat tptp.zero_zero_nat N_3) (= X_4 tptp.one_one_int)) (tptp.dvd_dvd_int X_4 (tptp.power_power_int X_4 N_3)))) (forall ((X_4 tptp.real) (N_3 tptp.nat)) (=> (or (tptp.ord_less_nat tptp.zero_zero_nat N_3) (= X_4 tptp.one_one_real)) (tptp.dvd_dvd_real X_4 (tptp.power_power_real X_4 N_3)))) (forall ((V_3 tptp.int)) (= (tptp.ord_less_nat tptp.zero_zero_nat (tptp.number_number_of_nat V_3)) (tptp.ord_less_int tptp.pls V_3))) (forall ((V_3 tptp.int)) (= (= (tptp.number_number_of_nat V_3) tptp.zero_zero_nat) (tptp.ord_less_eq_int V_3 tptp.pls))) (forall ((V_3 tptp.int)) (= (= tptp.zero_zero_nat (tptp.number_number_of_nat V_3)) (tptp.ord_less_eq_int V_3 tptp.pls))) (forall ((A_1 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.zcong A_1 B_2 Ma) (tptp.zcong B_2 A_1 Ma))) (forall ((K tptp.int) (M tptp.int)) (tptp.zcong K K M)) (forall ((C_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (=> (tptp.zcong B_1 C_1 M) (tptp.zcong A C_1 M)))) (tptp.ord_less_nat tptp.zero_zero_nat _let_9) (forall ((V_2 tptp.int) (K tptp.nat) (V_1 tptp.int)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_1) (tptp.times_times_nat (tptp.number_number_of_nat V_2) K)))) (let ((_let_2 (tptp.ord_less_int V_1 tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.times_times_int V_1 V_2)) K))))))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_1) (tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.ord_less_int V_1 tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.times_times_int V_1 V_2)))))))) (forall ((X_3 tptp.real) (Y_3 tptp.real)) (=> (tptp.ord_less_eq_real X_3 Y_3) (=> (not (= X_3 Y_3)) (tptp.ord_less_real X_3 Y_3)))) (forall ((X_3 tptp.nat) (Y_3 tptp.nat)) (=> (tptp.ord_less_eq_nat X_3 Y_3) (=> (not (= X_3 Y_3)) (tptp.ord_less_nat X_3 Y_3)))) _let_13 (forall ((B_1 tptp.int) (A tptp.int) (C_1 tptp.int)) (=> (tptp.ord_less_int A C_1) (=> (tptp.ord_less_int B_1 C_1) (or (tptp.ord_less_eq_int A B_1) (tptp.ord_less_eq_int B_1 A))))) (forall ((A_1 tptp.int) (B_2 tptp.int)) (= (tptp.zcong A_1 B_2 tptp.zero_zero_int) (= A_1 B_2))) (forall ((A tptp.int) (B_1 tptp.int)) (tptp.zcong A B_1 tptp.one_one_int)) (forall ((C_1 tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (=> (tptp.zcong C_1 D_1 M) (tptp.zcong (tptp.times_times_int A C_1) (tptp.times_times_int B_1 D_1) M)))) (forall ((K tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (tptp.zcong (tptp.times_times_int K A) (tptp.times_times_int K B_1) M))) (forall ((K tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (tptp.zcong (tptp.times_times_int A K) (tptp.times_times_int B_1 K) M))) (forall ((A tptp.int) (M tptp.int) (B_1 tptp.int)) (tptp.zcong (tptp.times_times_int A M) (tptp.times_times_int B_1 M) M)) (forall ((C_1 tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (=> (tptp.zcong C_1 D_1 M) (tptp.zcong (tptp.plus_plus_int A C_1) (tptp.plus_plus_int B_1 D_1) M)))) (forall ((N_2 tptp.nat)) (= (tptp.power_power_real (tptp.number267125858f_real tptp.min) (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_2)) tptp.one_one_real)) (forall ((N_2 tptp.nat)) (= (tptp.power_power_int (tptp.number_number_of_int tptp.min) (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N_2)) tptp.one_one_int)) (forall ((A_1 tptp.real) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.power_power_real A_1 _let_1) tptp.zero_zero_real) (and (= A_1 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_1 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.power_power_nat A_1 _let_1) tptp.zero_zero_nat) (and (= A_1 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_1 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.power_power_int A_1 _let_1) tptp.zero_zero_int) (and (= A_1 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((B_1 tptp.int) (M tptp.int) (A tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (tptp.ord_less_int A M) (=> (tptp.ord_less_int tptp.zero_zero_int B_1) (=> (tptp.ord_less_int B_1 A) (not (tptp.zcong A B_1 M))))))) (forall ((A_1 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.zcong A_1 B_2 Ma) (exists ((K_2 tptp.int)) (= B_2 (tptp.plus_plus_int A_1 (tptp.times_times_int Ma K_2)))))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_3))) (let ((_let_2 (tptp.power_power_real tptp.zero_zero_real _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_3))) (let ((_let_2 (tptp.power_power_nat tptp.zero_zero_nat _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_nat))))))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_3))) (let ((_let_2 (tptp.power_power_int tptp.zero_zero_int _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 tptp.zero_zero_int))))))) (forall ((B_1 tptp.int) (M tptp.int) (A tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A) (=> (tptp.ord_less_int A M) (=> (tptp.ord_less_eq_int tptp.zero_zero_int B_1) (=> (tptp.ord_less_int B_1 M) (=> (tptp.zcong A B_1 M) (= A B_1))))))) (forall ((M tptp.int) (A tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int A) (=> (tptp.ord_less_int A M) (=> (tptp.zcong A tptp.zero_zero_int M) (= A tptp.zero_zero_int))))) (forall ((N tptp.int) (P tptp.int) (M tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int M) (=> (tptp.zprime P) (=> (tptp.dvd_dvd_int P (tptp.times_times_int M N)) (or (tptp.dvd_dvd_int P M) (tptp.dvd_dvd_int P N)))))) _let_8 (tptp.dvd_dvd_int _let_5 _let_12) (forall ((J tptp.nat) (K tptp.nat) (M tptp.int)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.power_power_int _let_1 K))) (let ((_let_3 (tptp.power_power_int _let_1 J))) (=> (tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) M) (=> (tptp.zcong _let_3 _let_2 M) (= _let_3 _let_2))))))) (= _let_12 _let_11) (=> (not _let_8) (not _let_7)) (forall ((C_1 tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (=> (tptp.zcong C_1 D_1 M) (tptp.zcong (tptp.minus_minus_int A C_1) (tptp.minus_minus_int B_1 D_1) M)))) (forall ((K tptp.int)) (= (tptp.minus_minus_int K tptp.pls) K)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit0 K) (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus_int K L)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.minus_minus_int Z1 Z2) W) (tptp.minus_minus_int (tptp.times_times_int Z1 W) (tptp.times_times_int Z2 W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (= (tptp.times_times_int W (tptp.minus_minus_int Z1 Z2)) (tptp.minus_minus_int (tptp.times_times_int W Z1) (tptp.times_times_int W Z2)))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (=> (tptp.dvd_dvd_int K (tptp.minus_minus_int M N)) (=> (tptp.dvd_dvd_int K N) (tptp.dvd_dvd_int K M)))) (forall ((V tptp.int) (W_2 tptp.int)) (= (tptp.number_number_of_int (tptp.minus_minus_int V W_2)) (tptp.minus_minus_int (tptp.number_number_of_int V) (tptp.number_number_of_int W_2)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit1 K) (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus_int K L)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit1 K) (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus_int K L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.pls (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus_int tptp.pls L)))) (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.ord_less_int K_1 L_1) (tptp.ord_less_int (tptp.minus_minus_int K_1 L_1) tptp.zero_zero_int))) (forall ((A tptp.int) (R_1 tptp.int) (B_1 tptp.int) (M tptp.int) (C_1 tptp.int) (D_1 tptp.int) (N tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int A (tptp.times_times_int R_1 B_1)) M) (tptp.times_times_int (tptp.minus_minus_int C_1 (tptp.times_times_int R_1 D_1)) N)) (tptp.minus_minus_int (tptp.plus_plus_int (tptp.times_times_int A M) (tptp.times_times_int C_1 N)) (tptp.times_times_int R_1 (tptp.plus_plus_int (tptp.times_times_int B_1 M) (tptp.times_times_int D_1 N)))))) (forall ((A_1 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.zcong A_1 B_2 Ma) (tptp.dvd_dvd_int Ma (tptp.minus_minus_int A_1 B_2)))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.minus_minus_int A tptp.one_one_int))) (=> (tptp.ord_less_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_int X_1 A) (=> (not (= X_1 _let_1)) (tptp.ord_less_int X_1 _let_1)))))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_eq_int W_1 (tptp.minus_minus_int Z_1 tptp.one_one_int)) (tptp.ord_less_int W_1 Z_1))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.pls (tptp.bit1 L)) (tptp.bit1 (tptp.minus_minus_int tptp.min L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.min (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus_int tptp.min L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.min (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus_int tptp.min L)))) (forall ((A_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.minus_minus_int P_1 tptp.one_one_int))) (= (tptp.zcong (tptp.times_times_int A_1 _let_1) tptp.one_one_int P_1) (tptp.zcong A_1 _let_1 P_1)))) (forall ((A tptp.int) (B_1 tptp.int) (P tptp.int) (Q tptp.int)) (= (tptp.times_times_int (tptp.twoSqu2107342101sum2sq (tptp.product_Pair_int_int A B_1)) (tptp.twoSqu2107342101sum2sq (tptp.product_Pair_int_int P Q))) (tptp.twoSqu2107342101sum2sq (tptp.product_Pair_int_int (tptp.plus_plus_int (tptp.times_times_int A P) (tptp.times_times_int B_1 Q)) (tptp.minus_minus_int (tptp.times_times_int A Q) (tptp.times_times_int B_1 P)))))) (forall ((A tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (tptp.zcong (tptp.times_times_int A A) tptp.one_one_int P) (or (tptp.zcong A tptp.one_one_int P) (tptp.zcong A (tptp.minus_minus_int P tptp.one_one_int) P)))))) (forall ((A tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (tptp.ord_less_int A P) (=> (tptp.zcong (tptp.times_times_int A A) tptp.one_one_int P) (or (= A tptp.one_one_int) (= A (tptp.minus_minus_int P tptp.one_one_int)))))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.times_times_int (tptp.plus_plus_int A B_1) (tptp.minus_minus_int A B_1)) (tptp.minus_minus_int (tptp.power_power_int A _let_1) (tptp.power_power_int B_1 _let_1))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.minus_minus_int A B_1) _let_2) (tptp.plus_plus_int (tptp.minus_minus_int (tptp.power_power_int A _let_2) (tptp.times_times_int (tptp.times_times_int (tptp.number_number_of_int _let_1) A) B_1)) (tptp.power_power_int B_1 _let_2)))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_5 (tptp.number_number_of_int _let_2))) (= (tptp.power_power_int (tptp.minus_minus_int A B_1) _let_3) (tptp.minus_minus_int (tptp.plus_plus_int (tptp.minus_minus_int (tptp.power_power_int A _let_3) (tptp.times_times_int (tptp.times_times_int _let_5 (tptp.power_power_int A _let_4)) B_1)) (tptp.times_times_int (tptp.times_times_int _let_5 A) (tptp.power_power_int B_1 _let_4))) (tptp.power_power_int B_1 _let_3))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.power_power_int _let_1 N))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((M tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) M) tptp.one_one_int))) (=> (tptp.zprime _let_1) (= (tptp.legendre (tptp.number_number_of_int tptp.min) _let_1) tptp.one_one_int)))) (forall ((M tptp.int)) (=> (tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) M) (not (tptp.zcong tptp.one_one_int (tptp.number_number_of_int tptp.min) M)))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) P) (=> (tptp.zcong X_1 (tptp.number_number_of_int tptp.min) P) (not (tptp.zcong X_1 tptp.one_one_int P))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (tptp.legendre A P))) (let ((_let_2 (tptp.quadRes P A))) (let ((_let_3 (tptp.zcong A tptp.zero_zero_int P))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_int tptp.min)))))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.dvd_dvd_nat N M) (or (= M tptp.zero_zero_nat) (= M N) (tptp.ord_less_eq_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N) M)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (and (tptp.dvd_dvd_nat X_2 Y_2) (tptp.dvd_dvd_nat Y_2 X_2)) (= X_2 Y_2))) (forall ((D_1 tptp.int) (C_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (=> (= B_1 C_1) (=> (tptp.zcong C_1 D_1 M) (tptp.zcong A D_1 M))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.times_times_nat M N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.plus_plus_nat N (tptp.times_times_nat (tptp.minus_minus_nat M tptp.one_one_nat) N)))))))) (forall ((P tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_nat P M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.times_times_nat P (tptp.power_power_nat P (tptp.minus_minus_nat M tptp.one_one_nat))))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.minus_minus_nat (tptp.power_power_nat X_1 _let_1) (tptp.power_power_nat Y_1 _let_1)) (tptp.times_times_nat (tptp.plus_plus_nat X_1 Y_1) (tptp.minus_minus_nat X_1 Y_1))))) (forall ((B_1 tptp.nat) (D_1 tptp.nat) (A tptp.nat)) (=> (tptp.dvd_dvd_nat D_1 A) (=> (tptp.dvd_dvd_nat D_1 (tptp.plus_plus_nat A B_1)) (tptp.dvd_dvd_nat D_1 B_1)))) (forall ((C_1 tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (tptp.dvd_dvd_nat A B_1) (tptp.dvd_dvd_nat (tptp.times_times_nat C_1 A) (tptp.times_times_nat C_1 B_1)))) (forall ((C_1 tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (tptp.dvd_dvd_nat A B_1) (tptp.dvd_dvd_nat (tptp.times_times_nat A C_1) (tptp.times_times_nat B_1 C_1)))) (forall ((M tptp.int)) (tptp.zcong M tptp.zero_zero_int M)) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (= (tptp.times_times_nat N_1 Ma) tptp.one_one_nat) (and (= N_1 tptp.one_one_nat) (= Ma tptp.one_one_nat)))) (forall ((A tptp.int) (B_1 tptp.int) (C_1 tptp.int)) (=> (= (tptp.minus_minus_int A B_1) C_1) (= A (tptp.plus_plus_int C_1 B_1)))) (forall ((C tptp.int) (D tptp.int) (A_1 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.zcong A_1 B_2 Ma) (= (tptp.zcong C (tptp.times_times_int D A_1) Ma) (tptp.zcong C (tptp.times_times_int D B_2) Ma)))) (forall ((C tptp.int) (D tptp.int) (A_1 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.zcong A_1 B_2 Ma) (= (tptp.zcong C (tptp.times_times_int A_1 D) Ma) (tptp.zcong C (tptp.times_times_int B_2 D) Ma)))) (forall ((C_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.zcong A B_1 M) (tptp.zcong (tptp.plus_plus_int A C_1) (tptp.plus_plus_int B_1 C_1) M))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.power_power_nat Ma N_1) tptp.zero_zero_nat) (and (not (= N_1 tptp.zero_zero_nat)) (= Ma tptp.zero_zero_nat)))) (forall ((N tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.dvd_dvd_nat X_1 Y_1) (tptp.dvd_dvd_nat (tptp.power_power_nat X_1 N) (tptp.power_power_nat Y_1 N)))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (=> (tptp.zcong X_1 Y_1 M) (tptp.zcong (tptp.power_power_int X_1 Z) (tptp.power_power_int Y_1 Z) M))) (forall ((A tptp.nat) (B_1 tptp.nat)) (=> (tptp.dvd_dvd_nat A B_1) (or (= B_1 tptp.zero_zero_nat) (tptp.ord_less_eq_nat A B_1)))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.dvd_dvd_nat (tptp.times_times_nat Ma K_1) (tptp.times_times_nat N_1 K_1)) (or (= K_1 tptp.zero_zero_nat) (tptp.dvd_dvd_nat Ma N_1)))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_int X_1 M) (not (tptp.zcong X_1 tptp.zero_zero_int M))))) (forall ((M tptp.int) (Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_int tptp.zero_zero_int Y_1) (=> (tptp.ord_less_int tptp.zero_zero_int M) (=> (tptp.zcong X_1 Y_1 M) (=> (tptp.ord_less_int X_1 M) (=> (tptp.ord_less_int Y_1 M) (= X_1 Y_1)))))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.dvd_dvd_int N M) (or (tptp.ord_less_eq_int M tptp.zero_zero_int) (tptp.ord_less_eq_int N M)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (tptp.dvd_dvd_nat (tptp.power_power_nat X_1 N) Y_1) (tptp.dvd_dvd_nat X_1 Y_1)))) (forall ((A tptp.nat) (N tptp.nat) (B_1 tptp.nat)) (=> (tptp.dvd_dvd_nat (tptp.power_power_nat A N) (tptp.power_power_nat B_1 N)) (=> (not (= N tptp.zero_zero_nat)) (tptp.dvd_dvd_nat A B_1)))) (forall ((A_1 tptp.int) (Ma tptp.int)) (= (tptp.zcong A_1 tptp.zero_zero_int Ma) (tptp.dvd_dvd_int Ma A_1))) (forall ((X_2 tptp.int) (P_1 tptp.int)) (= (tptp.zcong X_2 tptp.zero_zero_int P_1) (tptp.dvd_dvd_int P_1 X_2))) (forall ((X_2 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.power_power_nat X_2 N_1) tptp.one_one_nat) (or (= X_2 tptp.one_one_nat) (= N_1 tptp.zero_zero_nat)))) (forall ((M tptp.int) (N tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd_int P (tptp.times_times_int M N)) (or (tptp.dvd_dvd_int P M) (tptp.dvd_dvd_int P N))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_int X_1 M) (=> (tptp.zcong X_1 tptp.zero_zero_int M) (= X_1 tptp.zero_zero_int))))) (forall ((P tptp.int) (Y_1 tptp.int) (N tptp.nat)) (=> (tptp.ord_less_nat tptp.zero_zero_nat N) (=> (tptp.dvd_dvd_int P Y_1) (tptp.dvd_dvd_int P (tptp.power_power_int Y_1 N))))) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (not (tptp.zcong X_1 tptp.zero_zero_int P)) (=> (not (tptp.zcong Y_1 tptp.zero_zero_int P)) (not (tptp.zcong (tptp.times_times_int X_1 Y_1) tptp.zero_zero_int P)))))) (forall ((X_1 tptp.nat) (Q tptp.nat) (N tptp.nat) (R_1 tptp.nat)) (=> (= X_1 (tptp.plus_plus_nat (tptp.times_times_nat Q N) R_1)) (=> (tptp.ord_less_nat tptp.zero_zero_nat R_1) (=> (tptp.ord_less_nat R_1 N) (not (tptp.dvd_dvd_nat N X_1)))))) (forall ((B_1 tptp.int) (A tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (and (not (tptp.zcong A tptp.zero_zero_int P)) (not (tptp.zcong B_1 tptp.zero_zero_int P))) (not (tptp.zcong (tptp.times_times_int A B_1) tptp.zero_zero_int P)))))) (forall ((B_1 tptp.int) (A tptp.int) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (tptp.zcong (tptp.times_times_int A B_1) tptp.zero_zero_int P) (or (tptp.zcong A tptp.zero_zero_int P) (tptp.zcong B_1 tptp.zero_zero_int P)))))) (forall ((Y_1 tptp.int) (N tptp.nat) (P tptp.int)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd_int P (tptp.power_power_int Y_1 N)) (=> (tptp.ord_less_nat tptp.zero_zero_nat N) (tptp.dvd_dvd_int P Y_1))))) (forall ((Ma tptp.int) (X_2 tptp.int)) (= (tptp.quadRes Ma X_2) (exists ((Y tptp.int)) (tptp.zcong (tptp.power_power_int Y (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_2 Ma)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus_real (tptp.power_power_real X_2 _let_1) (tptp.power_power_real Y_2 _let_1)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (= A (tptp.plus_plus_int R_1 (tptp.times_times_int A Q))) (=> (tptp.ord_less_int R_1 A) (tptp.ord_less_eq_int tptp.one_one_int Q))))) (not (= tptp.zero_zero_real tptp.one_one_real)) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.ord_less_eq_real X_2 Y_2) (tptp.ord_less_eq_real (tptp.minus_minus_real X_2 Y_2) tptp.zero_zero_real))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.ord_less_real X_2 Y_2) (and (tptp.ord_less_eq_real X_2 Y_2) (not (= X_2 Y_2))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.ord_less_eq_real X_2 Y_2) (or (tptp.ord_less_real X_2 Y_2) (= X_2 Y_2)))) (forall ((Z tptp.real)) (= (tptp.times_times_real tptp.one_one_real Z) Z)) (forall ((Z tptp.real) (W tptp.real)) (= (tptp.times_times_real Z W) (tptp.times_times_real W Z))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Z1 Z2) Z3) (tptp.times_times_real Z1 (tptp.times_times_real Z2 Z3)))) (forall ((Z tptp.real) (X_1 tptp.real) (Y_1 tptp.real)) (=> (tptp.ord_less_eq_real X_1 Y_1) (tptp.ord_less_eq_real (tptp.plus_plus_real Z X_1) (tptp.plus_plus_real Z Y_1)))) (forall ((A_1 tptp.real) (B_2 tptp.real) (C tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.times_times_real C A_1) (tptp.times_times_real C B_2)) (= A_1 B_2)))) (forall ((A_1 tptp.real) (B_2 tptp.real) (C tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.times_times_real A_1 C) (tptp.times_times_real B_2 C)) (= A_1 B_2)))) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (tptp.times_times_real (tptp.plus_plus_real Z1 Z2) W) (tptp.plus_plus_real (tptp.times_times_real Z1 W) (tptp.times_times_real Z2 W)))) (forall ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real Z) (=> (tptp.ord_less_real X_1 Y_1) (tptp.ord_less_real (tptp.times_times_real Z X_1) (tptp.times_times_real Z Y_1))))) (forall ((Y_1 tptp.real) (X_1 tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real X_1) (=> (tptp.ord_less_real tptp.zero_zero_real Y_1) (tptp.ord_less_real tptp.zero_zero_real (tptp.times_times_real X_1 Y_1))))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real Z_1) (= (tptp.ord_less_eq_real (tptp.times_times_real Z_1 X_2) (tptp.times_times_real Z_1 Y_2)) (tptp.ord_less_eq_real X_2 Y_2)))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real Z_1) (= (tptp.ord_less_eq_real (tptp.times_times_real X_2 Z_1) (tptp.times_times_real Y_2 Z_1)) (tptp.ord_less_eq_real X_2 Y_2)))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (=> (tptp.ord_less_real tptp.zero_zero_real Z_1) (= (tptp.ord_less_real (tptp.times_times_real X_2 Z_1) (tptp.times_times_real Y_2 Z_1)) (tptp.ord_less_real X_2 Y_2)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real X_2 X_2) (tptp.times_times_real Y_2 Y_2)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((N tptp.nat)) (tptp.ord_less_eq_real tptp.one_one_real (tptp.power_power_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls))) N))) (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int B Q_1) R_2)) (=> (tptp.ord_less_int R_2 B) (=> (tptp.ord_less_int tptp.zero_zero_int B) (tptp.ord_less_eq_int tptp.zero_zero_int Q_1))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (=> (tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int B Q_1) R_2) tptp.zero_zero_int) (=> (tptp.ord_less_eq_int tptp.zero_zero_int R_2) (=> (tptp.ord_less_int tptp.zero_zero_int B) (tptp.ord_less_eq_int Q_1 tptp.zero_zero_int))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (=> (tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int B_1 Q_1) R_2) (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int R_2) (=> (tptp.ord_less_int R_2 B_1) (=> (tptp.ord_less_int R_1 B_1) (tptp.ord_less_eq_int Q_1 Q)))))) (forall ((B_1 tptp.int) (Q tptp.int) (R_1 tptp.int) (B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int B Q_1) R_2))) (=> (= (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1) _let_1) (=> (tptp.ord_less_eq_int tptp.zero_zero_int _let_1) (=> (tptp.ord_less_int R_2 B) (=> (tptp.ord_less_eq_int tptp.zero_zero_int R_1) (=> (tptp.ord_less_int tptp.zero_zero_int B) (=> (tptp.ord_less_eq_int B B_1) (tptp.ord_less_eq_int Q Q_1))))))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (=> (tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int B_1 Q_1) R_2) (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1)) (=> (tptp.ord_less_eq_int R_1 tptp.zero_zero_int) (=> (tptp.ord_less_int B_1 R_1) (=> (tptp.ord_less_int B_1 R_2) (tptp.ord_less_eq_int Q Q_1)))))) (forall ((B_1 tptp.int) (Q tptp.int) (R_1 tptp.int) (B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int B Q_1) R_2))) (=> (= (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1) _let_1) (=> (tptp.ord_less_int _let_1 tptp.zero_zero_int) (=> (tptp.ord_less_int R_1 B_1) (=> (tptp.ord_less_eq_int tptp.zero_zero_int R_2) (=> (tptp.ord_less_int tptp.zero_zero_int B) (=> (tptp.ord_less_eq_int B B_1) (tptp.ord_less_eq_int Q_1 Q))))))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (tptp.ord_less_int tptp.zero_zero_int A) (=> (= A (tptp.plus_plus_int R_1 (tptp.times_times_int A Q))) (=> (tptp.ord_less_eq_int tptp.zero_zero_int R_1) (tptp.ord_less_eq_int Q tptp.one_one_int))))) (tptp.ord_less_eq_int tptp.zero_zero_int _let_4) (forall ((Z tptp.real) (W tptp.real)) (=> (tptp.ord_less_eq_real Z W) (=> (tptp.ord_less_eq_real W Z) (= Z W)))) (forall ((K tptp.real) (I tptp.real) (J tptp.real)) (=> (tptp.ord_less_eq_real I J) (=> (tptp.ord_less_eq_real J K) (tptp.ord_less_eq_real I K)))) (forall ((Z tptp.real) (W tptp.real)) (or (tptp.ord_less_eq_real Z W) (tptp.ord_less_eq_real W Z))) (forall ((W tptp.real)) (tptp.ord_less_eq_real W W)) (tptp.ord_less_eq_int tptp.zero_zero_int tptp.zero_zero_int) (tptp.ord_less_eq_int tptp.zero_zero_int tptp.one_one_int) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Y_1) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.times_times_int X_1 Y_1))))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_1) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Y_1) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int X_1 Y_1))))) (forall ((N tptp.nat) (X_1 tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int X_1) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.power_power_int X_1 N)))) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.number_number_of_int (tptp.bit1 _let_2))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.ord_less_nat tptp.zero_zero_nat N) (=> (tptp.ord_less_real tptp.zero_zero_real A) (exists ((R tptp.real)) (and (tptp.ord_less_real tptp.zero_zero_real R) (= (tptp.power_power_real R N) A)))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.55/1.06 )
% 0.55/1.06 % SZS output end Proof for NUM926_2
% 0.55/1.07 % cvc5---1.0.5 exiting
% 0.92/1.07 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------