%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM925+7 : 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 10:49:06 EDT 2023

% Result   : Theorem 2.02s 2.23s
% Output   : Proof 2.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.28  % Problem    : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.29  % Command    : do_cvc5 %s %d
% 0.28/0.50  % Computer : n024.cluster.edu
% 0.28/0.50  % Model    : x86_64 x86_64
% 0.28/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.50  % Memory   : 8042.1875MB
% 0.28/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.28/0.50  % CPULimit   : 300
% 0.28/0.50  % WCLimit    : 300
% 0.28/0.50  % DateTime   : Fri Aug 25 14:54:39 EDT 2023
% 0.28/0.50  % CPUTime    : 
% 0.55/0.77  %----Proving TF0_NAR, FOF, or CNF
% 2.02/2.23  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.s00nr5imEk/cvc5---1.0.5_7699.p...
% 2.02/2.23  ------- get file name : TPTP file name is NUM925+7
% 2.02/2.23  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7699.smt2...
% 2.02/2.23  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.02/2.23  % SZS status Theorem for NUM925+7
% 2.02/2.23  % SZS output start Proof for NUM925+7
% 2.02/2.23  (
% 2.02/2.23  (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.bit1 tptp.pls))) (let ((_let_3 (tptp.bit0 _let_2))) (let ((_let_4 (tptp.number_number_of tptp.nat _let_3))) (let ((_let_5 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_6 (tptp.one_one tptp.int))) (let ((_let_7 (tptp.plus_plus tptp.int _let_6 (tptp.hAPP tptp.nat tptp.int _let_5 tptp.n)))) (let ((_let_8 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int _let_7) _let_4))) (let ((_let_9 (not (not (= _let_8 _let_1))))) (let ((_let_10 (tptp.linordered_idom tptp.int))) (let ((_let_11 (tptp.linordered_semidom tptp.int))) (let ((_let_12 (tptp.ring_11004092258visors tptp.int))) (let ((_let_13 (tptp.number_number_of tptp.int tptp.pls))) (let ((_let_14 (tptp.ord_less_eq tptp.int))) (let ((_let_15 (tptp.fun tptp.int tptp.bool))) (let ((_let_16 (tptp.hAPP tptp.int _let_15 _let_14 _let_1))) (let ((_let_17 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_3)) tptp.m) _let_6))) (let ((_let_18 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s1) _let_4))) (let ((_let_19 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s) _let_4))) (let ((_let_20 (tptp.ord_less tptp.int))) (let ((_let_21 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_22 (= (tptp.legendre _let_21 _let_17) _let_6))) (let ((_let_23 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes _let_17) _let_21)))) (let ((_let_24 (tptp.hAPP tptp.int _let_15 _let_20 tptp.min))) (let ((_let_25 (tptp.hAPP tptp.int _let_15 _let_14 tptp.pls))) (let ((_let_26 (tptp.hAPP tptp.int _let_15 _let_14 tptp.min))) (let ((_let_27 (tptp.hAPP tptp.int _let_15 _let_20 tptp.pls))) (let ((_let_28 (tptp.minus_minus tptp.int _let_19 _let_21))) (let ((_let_29 (tptp.hAPP tptp.int _let_15 (tptp.dvd_dvd tptp.int) _let_17))) (let ((_let_30 (tptp.plus_plus tptp.int _let_19 _let_6))) (let ((_let_31 (tptp.number_number_of tptp.int _let_3))) (let ((_let_32 (tptp.times_times tptp.int _let_17 _let_7))) (let ((_let_33 (tptp.times_times tptp.int _let_17 tptp.t))) (let ((_let_34 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq _let_32)))) (let ((_let_35 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_20 _let_7) _let_17)))) (let ((_let_36 (tptp.hAPP tptp.int _let_15 _let_20 _let_1))) (let ((_let_37 (tptp.zero_zero tptp.nat))) (let ((_let_38 (tptp.hAPP tptp.nat tptp.int _let_5 _let_37))) (let ((_let_39 (tptp.bit1 _let_2))) (let ((_let_40 (tptp.number_number_of tptp.int _let_39))) (let ((_let_41 (tptp.number_number_of tptp.nat _let_39))) (let ((_let_42 (tptp.one_one tptp.nat))) (let ((_let_43 (tptp.nat_1 _let_1))) (let ((_let_44 (tptp.minus_minus tptp.nat (tptp.nat_1 tptp.t) _let_42))) (let ((_let_45 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_37))) (let ((_let_46 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)))))))))) (let ((_let_47 (tptp.hAPP tptp.nat tptp.int _let_5 _let_42))) (let ((_let_48 (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (not (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N) _let_1))))))))) (let ((_let_49 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_2) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= (tptp.ti X_a A_2) _let_1))))))))) (let ((_let_50 (tptp.number_number_of tptp.nat _let_2))) (let ((_let_51 (tptp.number_number_of tptp.nat tptp.pls))) (let ((_let_52 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_36 _let_7)))) (let ((_let_53 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_36 _let_8)))) (let ((_let_54 (= _let_1 (tptp.ti tptp.int _let_7)))) (let ((_let_55 (not _let_54))) (let ((_let_56 (= _let_53 _let_55))) (let ((_let_57 (not _let_52))) (let ((_let_58 (not _let_11))) (let ((_let_59 (or _let_58 _let_57 _let_53))) (let ((_let_60 (forall ((X_a $$unsorted) (BOUND_VARIABLE_18397 $$unsorted) (BOUND_VARIABLE_18395 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (or (not (tptp.linordered_semidom X_a)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 BOUND_VARIABLE_18397))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a BOUND_VARIABLE_18397) BOUND_VARIABLE_18395)))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (not _let_10))) (let ((_let_63 (or _let_62 _let_56))) (let ((_let_64 (forall ((X_a $$unsorted) (BOUND_VARIABLE_17618 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (or (not (tptp.linordered_idom X_a)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a BOUND_VARIABLE_17618) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= _let_1 (tptp.ti X_a BOUND_VARIABLE_17618))))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (= _let_1 _let_8))) (let ((_let_67 (not _let_66))) (let ((_let_68 (not _let_12))) (let ((_let_69 (or _let_68 _let_54 _let_67))) (let ((_let_70 (forall ((X_a $$unsorted) (BOUND_VARIABLE_18201 $$unsorted) (BOUND_VARIABLE_18199 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (or (not (tptp.ring_11004092258visors X_a)) (= _let_1 (tptp.ti X_a BOUND_VARIABLE_18201)) (not (= _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a BOUND_VARIABLE_18201) BOUND_VARIABLE_18199)))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or _let_55 (not _let_53) (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_67 _let_54 (not _let_69)))) (ASSUME :args (_let_12)) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.int _let_7 _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP tptp.nat X_a (tptp.power_power X_a BOUND_VARIABLE_18201) BOUND_VARIABLE_18199)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_54 false _let_12 false _let_66 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_62 _let_56 (not _let_63)))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.int _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_power X_a BOUND_VARIABLE_17618)))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_56 false _let_10 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_57 _let_58 _let_53 (not _let_59)))) (ASSUME :args (_let_52)) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.int _let_7 _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP tptp.nat X_a (tptp.power_power X_a BOUND_VARIABLE_18397) BOUND_VARIABLE_18395)))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_53 false _let_52 false _let_11 false _let_59)) :args (false false _let_54 false _let_56 false _let_53)) :args ((forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.abs_abs X_a (tptp.ti X_a B_1_1)) (tptp.abs_abs X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a B_1_1))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.group_add X_a) (= (tptp.minus_minus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.minus_minus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.group_add X_a) (= (tptp.minus_minus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.minus_minus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a B_1_1 B_2_1))) (=> (tptp.group_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.ti tptp.nat B_1_1) B_2_1) (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.minus_minus tptp.nat B_1_1 (tptp.ti tptp.nat B_2_1)) (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (= (tptp.ti tptp.nat _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.one X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.monoid_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.monoid_add X_a) (= (tptp.plus_plus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1 B_2_1))) (=> (tptp.monoid_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (= (tptp.plus_plus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1 B_2_1))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.plus_plus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1 B_2_1))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.dvd X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.power X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.semiring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.mult_zero X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.mult_zero X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.mult_zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (= (tptp.if X_a (tptp.ti tptp.bool B_1_1) B_2_1 B_3) (tptp.if X_a B_1_1 B_2_1 B_3))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (= (tptp.if X_a B_1_1 (tptp.ti X_a B_2_1) B_3) (tptp.if X_a B_1_1 B_2_1 B_3))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (= (tptp.if X_a B_1_1 B_2_1 (tptp.ti X_a B_3)) (tptp.if X_a B_1_1 B_2_1 B_3))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.if X_a B_1_1 B_2_1 B_3))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.zcong (tptp.ti tptp.int B_1_1) B_2_1) (tptp.zcong B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.zcong B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.zcong B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.zcong B_1_1 B_2_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (= (tptp.ti _let_15 tptp.zprime) tptp.zprime) (forall ((B_1_1 $$unsorted)) (= (tptp.bit0 (tptp.ti tptp.int B_1_1)) (tptp.bit0 B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.bit0 B_1_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.bit1 (tptp.ti tptp.int B_1_1)) (tptp.bit1 B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.bit1 B_1_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (= (tptp.ti tptp.int tptp.min) tptp.min) (= (tptp.ti tptp.int tptp.pls) tptp.pls) (forall ((B_1_1 $$unsorted)) (= (tptp.nat_1 (tptp.ti tptp.int B_1_1)) (tptp.nat_1 B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.nat_1 B_1_1))) (= (tptp.ti tptp.nat _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number X_a) (= (tptp.number_number_of X_a (tptp.ti tptp.int B_1_1)) (tptp.number_number_of X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a B_1_1))) (=> (tptp.number X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted)) (= (tptp.succ (tptp.ti tptp.int B_1_1)) (tptp.succ B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.succ B_1_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun tptp.nat X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.power_power X_a (tptp.ti X_a B_1_1)) (tptp.power_power X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.power_power X_a B_1_1))) (=> (tptp.power X_a) (= (tptp.ti (tptp.fun tptp.nat X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.legendre (tptp.ti tptp.int B_1_1) B_2_1) (tptp.legendre B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.legendre B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.legendre B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.legendre B_1_1 B_2_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.quadRes (tptp.ti tptp.int B_1_1)) (tptp.quadRes B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.quadRes B_1_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (=> (tptp.dvd X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (= (tptp.ti _let_15 tptp.twoSqu658283162sum2sq) tptp.twoSqu658283162sum2sq) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.order X_a) (= (tptp.hAPP X_a _let_1 (tptp.ti (tptp.fun X_a _let_1) B_1_1) B_2_1) (tptp.hAPP X_a _let_1 B_1_1 B_2_1))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.order X_a) (= (tptp.hAPP X_a _let_1 B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a _let_1 B_1_1 B_2_1))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 B_1_1 B_2_1))) (=> (tptp.order X_a) (= (tptp.ti _let_1 _let_2) _let_2))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.hAPP X_a tptp.bool (tptp.ti (tptp.fun X_a tptp.bool) B_1_1) B_2_1) (tptp.hAPP X_a tptp.bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.hAPP X_a tptp.bool B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a tptp.bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.bool B_1_1 B_2_1))) (=> (tptp.order X_a) (= (tptp.ti tptp.bool _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.dvd X_a) (= (tptp.hAPP X_a _let_1 (tptp.ti (tptp.fun X_a _let_1) B_1_1) B_2_1) (tptp.hAPP X_a _let_1 B_1_1 B_2_1))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.dvd X_a) (= (tptp.hAPP X_a _let_1 B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a _let_1 B_1_1 B_2_1))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 B_1_1 B_2_1))) (=> (tptp.dvd X_a) (= (tptp.ti _let_1 _let_2) _let_2))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.hAPP X_a tptp.bool (tptp.ti (tptp.fun X_a tptp.bool) B_1_1) B_2_1) (tptp.hAPP X_a tptp.bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.hAPP X_a tptp.bool B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a tptp.bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.bool B_1_1 B_2_1))) (=> (tptp.dvd X_a) (= (tptp.ti tptp.bool _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.hAPP tptp.nat X_a (tptp.ti (tptp.fun tptp.nat X_a) B_1_1) B_2_1) (tptp.hAPP tptp.nat X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.hAPP tptp.nat X_a B_1_1 (tptp.ti tptp.nat B_2_1)) (tptp.hAPP tptp.nat X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a B_1_1 B_2_1))) (=> (tptp.power X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (= (tptp.ti tptp.int tptp.m) tptp.m) (= (tptp.ti tptp.int tptp.m1) tptp.m1) (= (tptp.ti tptp.nat tptp.n) tptp.n) (= (tptp.ti tptp.int tptp.s1) tptp.s1) (= (tptp.ti tptp.int tptp.s) tptp.s) (= (tptp.ti tptp.int tptp.t) tptp.t) (= (tptp.ti tptp.nat tptp.tn) tptp.tn) (= (tptp.ti tptp.int tptp.x) tptp.x) (= (tptp.ti tptp.int tptp.y) tptp.y) _let_52 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_20 _let_6) tptp.t)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Xa) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Ya) _let_2)) _let_1) (and (= (tptp.ti X_a Xa) _let_1) (= (tptp.ti X_a Ya) _let_1)))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_2) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int (tptp.bit1 tptp.pls) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_ring X_a) (= (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_semiring X_a) (= (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power tptp.int X))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_2 _let_3)) _let_3) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat W))) (let ((_let_3 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) _let_2))) (let ((_let_4 (= _let_2 (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 (tptp.one_one X_a))) (=> (not _let_4) (= _let_3 _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.number_number_of X_a (tptp.bit1 tptp.pls))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_45 tptp.n)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) (= (tptp.ti tptp.int X) (tptp.ti tptp.int Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) X)))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.number_number_of tptp.int K)) (tptp.number_number_of tptp.int L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.number_number_of tptp.int V_1) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.plus_plus tptp.int V_1 W)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a Xa)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Xa) Ya)))))) (= _let_1 _let_13) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M)) N) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat M) N)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M)) N)))) (forall ((M $$unsorted) (N $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 N) Z)) (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.plus_plus tptp.nat M N)) Z)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.plus_plus tptp.nat M N))))) (= _let_47 _let_6) (= _let_51 _let_37) (= _let_37 _let_51) (forall ((Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na) (tptp.zero_zero tptp.int)) (= Na (tptp.zero_zero tptp.nat)))) (= _let_38 _let_1) (= (tptp.plus_plus tptp.nat _let_42 _let_42) _let_4) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 tptp.pls))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.plus_plus tptp.int I_2 K_1)) (tptp.plus_plus tptp.int J_1 K_1))))))) (forall ((V_2 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat V_2))) (let ((_let_2 (tptp.number_number_of tptp.nat V_1))) (let ((_let_3 (tptp.plus_plus tptp.nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 V_2) tptp.pls)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 V_1) tptp.pls)))) (and (=> _let_7 (= _let_3 _let_1)) (=> (not _let_7) (and (=> _let_6 (= _let_3 _let_2)) (=> (not _let_6) (= _let_3 (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int V_1 V_2))))))))))))))) (= _let_6 (tptp.number_number_of tptp.int _let_2)) (= _let_50 _let_42) (= _let_42 _let_50) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= (tptp.number_number_of X_a Xa) (tptp.number_number_of X_a Ya)) (= (tptp.ti tptp.int Xa) (tptp.ti tptp.int Ya)))))) (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((Wa $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a Wa))) (let ((_let_2 (tptp.ti X_a Xa))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit1 K) (tptp.bit1 L_1)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L_1)))) (forall ((K $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit0 K) (tptp.bit0 L_1)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_2 A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int Z1 Z2) Z3) (tptp.plus_plus tptp.int Z1 (tptp.plus_plus tptp.int Z2 Z3)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.int X (tptp.plus_plus tptp.int Y Z)) (tptp.plus_plus tptp.int Y (tptp.plus_plus tptp.int X Z)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int Z W) (tptp.plus_plus tptp.int W Z))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 Ma) (tptp.hAPP tptp.nat tptp.int _let_1 Na)) (= Ma Na)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a Xa)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Xa) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) Ya)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((Wa $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.bit1 Wa)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Wa) _let_1))))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 _let_1))) (forall ((Wa $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.bit0 Wa)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Wa) _let_1))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_36 _let_6)) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Wa))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int)))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_1)) (= (tptp.ti tptp.int Wa) (tptp.ti tptp.int Z_1)))))) (forall ((K_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_1)) (tptp.zero_zero tptp.int))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a Xa)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Xa) (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.bit1 tptp.pls)) Ya)))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z_1) Z_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Z_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.plus_plus X_a A_2 A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((K_1 $$unsorted)) (not (= (tptp.bit1 K_1) tptp.pls))) (forall ((L $$unsorted)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (not (= (tptp.bit1 K_1) (tptp.bit0 L)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (not (= (tptp.bit0 K_1) (tptp.bit1 L)))) (forall ((K $$unsorted)) (= (= (tptp.bit0 K) tptp.pls) (= (tptp.ti tptp.int K) tptp.pls))) (forall ((L_1 $$unsorted)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls (tptp.ti tptp.int L_1)))) (= (tptp.bit0 tptp.pls) tptp.pls) (= tptp.pls _let_1) (not (= _let_1 _let_6)) (forall ((K_1 $$unsorted)) (= (tptp.plus_plus tptp.int K_1 tptp.pls) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted)) (= (tptp.plus_plus tptp.int tptp.pls K_1) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K_1) (tptp.bit0 L)) (tptp.bit0 (tptp.plus_plus tptp.int K_1 L)))) (forall ((K_1 $$unsorted)) (= (tptp.bit0 K_1) (tptp.plus_plus tptp.int K_1 K_1))) (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int Z (tptp.zero_zero tptp.int)) (tptp.ti tptp.int Z))) (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.zero_zero tptp.int) Z) (tptp.ti tptp.int Z))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.zero_zero X_a) (tptp.number_number_of X_a tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a tptp.pls) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.number_number_of X_a tptp.pls)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat Wa))) (let ((_let_2 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_2) _let_1) _let_2) (and (= (tptp.ti X_a A_2) _let_2) (not (= _let_1 (tptp.zero_zero tptp.nat)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.plus_plus X_a (tptp.number_number_of X_a W) Z)) (tptp.plus_plus X_a (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 W)) Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 W)) (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a W)))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit1 K_1) (tptp.bit0 L)) (tptp.bit1 (tptp.plus_plus tptp.int K_1 L)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K_1) (tptp.bit1 L)) (tptp.bit1 (tptp.plus_plus tptp.int K_1 L)))) (forall ((K_1 $$unsorted)) (= (tptp.bit1 K_1) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) K_1) K_1))) (forall ((Z $$unsorted)) (not (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z) Z) (tptp.zero_zero tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((N $$unsorted)) (= (tptp.number_number_of X_a (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))))) _let_49 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Xa) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Ya) _let_2)))) (or (not (= (tptp.ti X_a Xa) _let_1)) (not (= (tptp.ti X_a Ya) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_1))) (tptp.zero_zero X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit0 W)) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.zero_zero X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit1 W)) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.one_one X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_20 tptp.m1) _let_7)) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) N)))))) (= _let_31 (tptp.hAPP tptp.nat tptp.int _let_5 _let_4)) (= _let_40 (tptp.hAPP tptp.nat tptp.int _let_5 _let_41)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus tptp.real (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Xa) _let_2) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Ya) _let_2)) _let_1) (and (= Xa _let_1) (= Ya _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) N))) (let ((_let_3 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_2)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.plus_plus X_a _let_1 _let_1)))))) (forall ((P_1 $$unsorted) (K $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.plus_plus tptp.int K (tptp.one_one tptp.int)))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.plus_plus tptp.int I (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_1)))))) (= _let_1 _let_38) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_45 tptp.tn)) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (not (= (tptp.zero_zero tptp.real) (tptp.one_one tptp.real))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.plus_plus tptp.nat I_2 J_1)) I_2)))) (forall ((J_1 $$unsorted) (I_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.plus_plus tptp.nat J_1 I_2)) I_2)))) (forall ((K_1 $$unsorted)) (= (tptp.number_number_of tptp.int K_1) (tptp.ti tptp.int K_1))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= Ma Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) Ma))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.plus_plus tptp.nat M N) (tptp.plus_plus tptp.nat N M))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.nat X (tptp.plus_plus tptp.nat Y Z)) (tptp.plus_plus tptp.nat Y (tptp.plus_plus tptp.nat X Z)))) (forall ((M $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (= (tptp.plus_plus tptp.nat (tptp.plus_plus tptp.nat M N) K_1) (tptp.plus_plus tptp.nat M (tptp.plus_plus tptp.nat N K_1)))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (= (= (tptp.plus_plus tptp.nat K Ma) (tptp.plus_plus tptp.nat K Na)) (= Ma Na))) (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (= (= (tptp.plus_plus tptp.nat Ma K) (tptp.plus_plus tptp.nat Na K)) (= Ma Na))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat K Ma)) (tptp.plus_plus tptp.nat K Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M)) (not (= M N)))) (forall ((S_1 $$unsorted) (T_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S_1) T_2)) (not (= S_1 T_2)))) (forall ((M $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat J_1 M)))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat M J_1)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_2 K_1)) (tptp.plus_plus tptp.nat J_1 K_1))))))) (forall ((K_1 $$unsorted) (L $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_2 K_1)) (tptp.plus_plus tptp.nat J_1 L)))))))) (forall ((M $$unsorted) (N $$unsorted) (K_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L)) (=> (= (tptp.plus_plus tptp.nat M L) (tptp.plus_plus tptp.nat K_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((I_2 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_2 J_1)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)))))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 Na) Ma)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Ma) Na)) _let_2) (=> (=> (= Ma Na) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Na) Ma)) _let_2) _let_2))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (not (= N (tptp.zero_zero tptp.nat))))) (forall ((M $$unsorted) (N $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.power_power tptp.nat I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Xa) Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Xa)) (= Na _let_1)))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat Ma Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= Na _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) Na))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Xa) Na))) (or (= Na _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Xa))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Xa)) (tptp.hAPP tptp.nat tptp.int _let_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Xa) Ya))))) (forall ((Xa $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat Wa))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Xa) _let_3))) (or (= _let_3 _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Xa)))))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Ma)) (tptp.hAPP tptp.nat tptp.int _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) Na))))) (forall ((Va $$unsorted) (V_3 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Va) V_3)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.number_number_of tptp.nat Va)) (tptp.number_number_of tptp.nat V_3))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 tptp.pls) V_3))) _let_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (tptp.plus_plus tptp.nat M N) M) (= N (tptp.zero_zero tptp.nat)))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.plus_plus tptp.nat Ma Na) _let_1) (and (= Ma _let_1) (= Na _let_1))))) (forall ((M $$unsorted)) (= (tptp.plus_plus tptp.nat M (tptp.zero_zero tptp.nat)) M)) (forall ((N $$unsorted)) (= (tptp.plus_plus tptp.nat (tptp.zero_zero tptp.nat) N) N)) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.one_one tptp.nat)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_char_0 X_a) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (= (tptp.hAPP tptp.nat X_a _let_1 Ma) (tptp.hAPP tptp.nat X_a _let_1 Na)) (= Ma Na)))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 Xa) (tptp.hAPP tptp.nat tptp.int _let_1 Ya)) (= Xa Ya)))) (forall ((Xa $$unsorted) (Ya $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.if tptp.nat P_1 Xa Ya)))) (let ((_let_3 (tptp.hBOOL P_1))) (and (=> _let_3 (= (tptp.hAPP tptp.nat tptp.int _let_1 Xa) _let_2)) (=> (not _let_3) (= (tptp.hAPP tptp.nat tptp.int _let_1 Ya) _let_2))))))) (forall ((Va $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.number_number_of tptp.nat Va))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) Va)))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) _let_48 (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) N) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 Ma)) (tptp.hAPP tptp.nat X_a _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) Na))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.plus_plus tptp.nat M N)) (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a _let_1 M) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.one_one tptp.nat)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat M) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_1 M)) N)))))) (= _let_6 _let_47) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 X) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.plus_plus tptp.nat X Y))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 X)) N) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) N))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.plus_plus X_a A_1 C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) _let_46 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.plus_plus X_a A_1 (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (Na $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) A_2)) (= (= (tptp.hAPP tptp.nat X_a _let_1 Ma) (tptp.hAPP tptp.nat X_a _let_1 Na)) (= Ma Na))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a B))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) B)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 Xa)) (tptp.hAPP tptp.nat X_a _let_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Xa) Ya)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) (tptp.hAPP tptp.nat X_a _let_1 N_2))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_2) Na) _let_1) (and (= (tptp.ti X_a A_2) _let_1) (not (= Na (tptp.zero_zero tptp.nat))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.zero_zero tptp.nat)) (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_45 _let_4)) (forall ((K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) K_1)) (exists ((N_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.ti tptp.int K_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)))))) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_2)) (= (tptp.plus_plus tptp.nat I_2 K_2) J_1))))) (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Xa) Na) _let_1) (or (= Xa _let_1) (= Na (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a A_2 A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_2 A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a A_1 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a Xa))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.plus_plus X_a B_1 A_1) (tptp.plus_plus X_a C A_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.plus_plus X_a A_1 B_1) (tptp.plus_plus X_a A_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.plus_plus X_a A_1 B_1) (tptp.plus_plus X_a A_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B_1) (tptp.plus_plus X_a C D_1)) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a B_1 D_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (= (= (tptp.plus_plus X_a B A_2) (tptp.plus_plus X_a C_1 A_2)) (= (tptp.ti X_a B) (tptp.ti X_a C_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (= (tptp.plus_plus X_a A_2 B) (tptp.plus_plus X_a A_2 C_1)) (= (tptp.ti X_a B) (tptp.ti X_a C_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B_1) C) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) B_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B_1) C) (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a B_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B_1) C) (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a B_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a C D_1)) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) D_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a C D_1)) (tptp.plus_plus X_a C (tptp.plus_plus X_a A_1 D_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a C A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.one X_a) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a Xa))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((B $$unsorted) (A_2 $$unsorted)) (= (= (tptp.ti X_a B) (tptp.plus_plus X_a B A_2)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.plus_plus X_a A_2 A_2)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.zero_zero X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.zero_zero X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.zero_zero X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C A_1)) (tptp.plus_plus X_a C B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C A_1)) (tptp.plus_plus X_a C B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C_1 A_2)) (tptp.plus_plus X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_2 C_1)) (tptp.plus_plus X_a B C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) (tptp.one_one tptp.nat)) (tptp.ti X_a X))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Ma) Na) _let_1) (and (not (= Na _let_1)) (= Ma _let_1))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X_1) N) A_1) (forall ((Y_1 $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y_1)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Y_1) N) A_1)) (= Y_1 X_1)))))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (exists ((R $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real R) N) A_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 _let_6) tptp.t)) (forall ((V_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat (tptp.number_number_of tptp.nat V_1) _let_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V_1) tptp.pls)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.number_number_of tptp.nat (tptp.succ V_1))))))))) (forall ((V_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat _let_1 (tptp.number_number_of tptp.nat V_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V_1) tptp.pls)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.number_number_of tptp.nat (tptp.succ V_1))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_2))) (let ((_let_4 (tptp.power_power tptp.int B_1))) (let ((_let_5 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.number_number_of tptp.int _let_2))) (let ((_let_7 (tptp.power_power tptp.int A_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.plus_plus tptp.int A_1 B_1)) _let_3) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_7 _let_3) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_6 (tptp.hAPP tptp.nat tptp.int _let_7 _let_5)) B_1)) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_6 A_1) (tptp.hAPP tptp.nat tptp.int _let_4 _let_5))) (tptp.hAPP tptp.nat tptp.int _let_4 _let_3))))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.plus_plus tptp.int A_1 B_1)) _let_2) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_2) (tptp.times_times tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1) A_1) B_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B_1) _let_2)))))) (= tptp.tn _let_44) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_45 _let_44)) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.minus_minus X_a A_2 B)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.times_times X_a A_1 B_1) (tptp.times_times X_a B_1 A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a Lx (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a Rx (tptp.times_times X_a Lx Ry)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a Lx (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) Ry))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a A_1 B_1) C) (tptp.times_times X_a A_1 (tptp.times_times X_a B_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) Rx) (tptp.times_times X_a Lx (tptp.times_times X_a Ly Rx)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) Rx) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) Ly))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Rx Ry))) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) _let_1) (tptp.times_times X_a Lx (tptp.times_times X_a Ly _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Lx Ly))) (= (tptp.times_times X_a _let_1 (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a Rx (tptp.times_times X_a _let_1 Ry))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) (tptp.times_times X_a Ly Ry)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (=> (= (tptp.minus_minus X_a A_2 B) (tptp.minus_minus X_a C_1 D)) (= (= (tptp.ti X_a A_2) (tptp.ti X_a B)) (= (tptp.ti X_a C_1) (tptp.ti X_a D))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.minus_minus X_a A_2 B) (tptp.minus_minus X_a C_1 D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_2 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_2)) (= (tptp.times_times X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a V_2)) (tptp.number_number_of X_a (tptp.times_times tptp.int V_1 V_2))))))))) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W) W))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int Z W) (tptp.times_times tptp.int W Z))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times tptp.int (tptp.times_times tptp.int Z1 Z2) Z3) (tptp.times_times tptp.int Z1 (tptp.times_times tptp.int Z2 Z3)))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 K_1)))))))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z)) (= (tptp.ti tptp.int Z) (tptp.ti tptp.int W))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.number_number_of X_a Xa)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Xa) Ya)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.times_times tptp.int V_1 W)) (tptp.times_times X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.times_times tptp.int V_1 W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a V_1) (tptp.times_times X_a (tptp.number_number_of X_a W) Z)) (tptp.times_times X_a (tptp.number_number_of X_a (tptp.times_times tptp.int V_1 W)) Z))))) (forall ((Z_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_3)) (= (= (tptp.nat_1 Z_1) (tptp.nat_1 Z_3)) (= (tptp.ti tptp.int Z_1) (tptp.ti tptp.int Z_3))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((V_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V_1))) (= (tptp.times_times X_b _let_1 (tptp.minus_minus X_b B_1 C)) (tptp.minus_minus X_b (tptp.times_times X_b _let_1 B_1) (tptp.times_times X_b _let_1 C))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V_1))) (= (tptp.times_times X_b (tptp.minus_minus X_b A_1 B_1) _let_1) (tptp.minus_minus X_b (tptp.times_times X_b A_1 _let_1) (tptp.times_times X_b B_1 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.minus_minus tptp.int V_1 W)) (tptp.minus_minus X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.times_times tptp.nat M N)) (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 M) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 Ma)) (tptp.hAPP tptp.nat X_a _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) Na))))))) (forall ((I_2 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.minus_minus tptp.nat I_2 J_1) K_1) (tptp.minus_minus tptp.nat (tptp.minus_minus tptp.nat I_2 K_1) J_1))) (forall ((Xa $$unsorted) (Ya $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.nat_1 (tptp.if tptp.int P_1 Xa Ya)))) (let ((_let_2 (tptp.hBOOL P_1))) (and (=> _let_2 (= (tptp.nat_1 Xa) _let_1)) (=> (not _let_2) (= (tptp.nat_1 Ya) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.times_times X_a A_1 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere1490568538miring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.times_times X_a A_1 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a B_1 A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 B_1)) _let_1)))))))))) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Xa)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Ya)) (= (= (tptp.nat_1 Xa) (tptp.nat_1 Ya)) (= (tptp.ti tptp.int Xa) (tptp.ti tptp.int Ya))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.times_times tptp.int X Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a A_1 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1)) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a A_2 B) E_1) C_1)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D)) (= (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a A_2 B) E_1) C_1) (tptp.ti X_a D)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1)) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a B A_2) E_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D)) (= (tptp.ti X_a C_1) (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a B A_2) E_1) D)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.minus_minus X_a (tptp.times_times X_a X Y) (tptp.times_times X_a A_1 B_1)) (tptp.plus_plus X_a (tptp.times_times X_a X (tptp.minus_minus X_a Y B_1)) (tptp.times_times X_a (tptp.minus_minus X_a X A_1) B_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_2 B)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.times_times X_a A_2 B))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)))))))))))) (forall ((P_1 $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X1))) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.nat_1 X_1))))))) (forall ((P_1 $$unsorted)) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.nat_1 X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.times_times X_a A_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1)) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a A_2 B) E_1) C_1)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a A_2 E_1) C_1)) (tptp.plus_plus X_a (tptp.times_times X_a B E_1) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.plus_plus X_a (tptp.times_times X_a (tptp.minus_minus X_a B A_2) E_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.minus_minus X_a (tptp.times_times X_a X X) _let_1) (tptp.times_times X_a (tptp.plus_plus X_a X _let_1) (tptp.minus_minus X_a X _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 _let_3) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_3) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.plus_plus X_a (tptp.times_times X_a X X) (tptp.times_times X_a Y Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.plus_plus X_a (tptp.times_times X_a Xa Xa) (tptp.times_times X_a Ya Ya))) _let_1)) (and (= (tptp.ti X_a Xa) _let_1) (= (tptp.ti X_a Ya) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a X Y)) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a Y X)) X))))))))))) (forall ((Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z) (tptp.zero_zero tptp.int))) (= (tptp.nat_1 Z) (tptp.zero_zero tptp.nat)))) (forall ((I_1 $$unsorted)) (= (= (tptp.nat_1 I_1) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_1) (tptp.zero_zero tptp.int))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) (tptp.hAPP tptp.nat X_a _let_1 N_2))))))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.nat_1 Z)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_1) Z)))) (and (=> _let_3 (= _let_2 (tptp.ti tptp.int Z))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Ma $$unsorted) (Z_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma) (tptp.ti tptp.int Z_1)) (and (= Ma (tptp.nat_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1))))) (forall ((Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.nat_1 Z)) (tptp.ti tptp.int Z)))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (= (tptp.minus_minus X_a A_2 B) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.ti X_a B)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (= (tptp.ti X_a A_2) (tptp.ti X_a B)) (= (tptp.minus_minus X_a A_2 B) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.minus_minus X_a A_1 A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.minus_minus X_a A_1 (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.minus_minus X_a A_2 B) (tptp.minus_minus X_a C_1 D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (= (tptp.minus_minus X_a (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a B_1 D_1)) (tptp.plus_plus X_a (tptp.minus_minus X_a A_1 B_1) (tptp.minus_minus X_a C D_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.minus_minus X_a (tptp.plus_plus X_a A_1 B_1) B_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.minus_minus X_a A_1 B_1) B_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a _let_1 A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a A_1 _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_n68954251visors X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.times_times X_a A_2 B) _let_1) (or (= (tptp.ti X_a A_2) _let_1) (= (tptp.ti X_a B) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (=> (not (= (tptp.ti X_a B_1) _let_1)) (not (= (tptp.times_times X_a A_1 B_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.times_times X_a A_1 B_1) _let_1) (or (= (tptp.ti X_a A_1) _let_1) (= (tptp.ti X_a B_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a A_1 _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a _let_1 A_1) _let_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (= (tptp.minus_minus tptp.nat M N) _let_1) (=> (= (tptp.minus_minus tptp.nat N M) _let_1) (= M N))))) (forall ((M $$unsorted)) (= (tptp.minus_minus tptp.nat M M) (tptp.zero_zero tptp.nat))) (forall ((M $$unsorted)) (= (tptp.minus_minus tptp.nat M (tptp.zero_zero tptp.nat)) M)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.minus_minus tptp.nat _let_1 N) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.times_times X_a (tptp.plus_plus X_a A_1 B_1) C) (tptp.plus_plus X_a (tptp.times_times X_a A_1 C) (tptp.times_times X_a B_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring X_a) (forall ((A_1 $$unsorted) (E $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 E) (tptp.plus_plus X_a (tptp.times_times X_a B_1 E) C)) (tptp.plus_plus X_a (tptp.times_times X_a (tptp.plus_plus X_a A_1 B_1) E) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((Wa $$unsorted) (Ya $$unsorted) (Xa $$unsorted) (Z_1 $$unsorted)) (= (= (tptp.plus_plus X_a (tptp.times_times X_a Wa Ya) (tptp.times_times X_a Xa Z_1)) (tptp.plus_plus X_a (tptp.times_times X_a Wa Z_1) (tptp.times_times X_a Xa Ya))) (or (= (tptp.ti X_a Wa) (tptp.ti X_a Xa)) (= (tptp.ti X_a Ya) (tptp.ti X_a Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (B_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 M) (tptp.times_times X_a B_1 M)) (tptp.times_times X_a (tptp.plus_plus X_a A_1 B_1) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.times_times X_a (tptp.plus_plus X_a A_1 B_1) C) (tptp.plus_plus X_a (tptp.times_times X_a A_1 C) (tptp.times_times X_a B_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C_1 $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (and (not (= (tptp.ti X_a A_2) (tptp.ti X_a B))) (not (= (tptp.ti X_a C_1) (tptp.ti X_a D)))) (not (= (tptp.plus_plus X_a (tptp.times_times X_a A_2 C_1) (tptp.times_times X_a B D)) (tptp.plus_plus X_a (tptp.times_times X_a A_2 D) (tptp.times_times X_a B C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.times_times X_a X (tptp.plus_plus X_a Y Z)) (tptp.plus_plus X_a (tptp.times_times X_a X Y) (tptp.times_times X_a X Z)))))) (forall ((N $$unsorted)) (= (tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) N)) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.one_one X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.one_one X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.one_one X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C A_1)) (tptp.plus_plus X_a C B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C A_1)) (tptp.plus_plus X_a C B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a C_1 A_2)) (tptp.plus_plus X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_2 C_1)) (tptp.plus_plus X_a B C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)))))))) (forall ((N $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat J_1 N)) K_1)))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat L N)) (tptp.minus_minus tptp.nat L M))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N))) (= (tptp.times_times X_a _let_1 A_1) (tptp.times_times X_a A_1 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.times_times X_a A_1 B_1)) N) (tptp.times_times X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B_1) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Q $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.times_times X_a X Y)) Q) (tptp.times_times X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) Q) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) Q)))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat M N) N) M)) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat N M) N) M)) (forall ((I_2 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.minus_minus tptp.nat I_2 J_1) K_1) (tptp.minus_minus tptp.nat I_2 (tptp.plus_plus tptp.nat J_1 K_1)))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat K_1 M) (tptp.plus_plus tptp.nat K_1 N)) (tptp.minus_minus tptp.nat M N))) (forall ((M $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat M K_1) (tptp.plus_plus tptp.nat N K_1)) (tptp.minus_minus tptp.nat M N))) (forall ((W $$unsorted)) (= (tptp.times_times tptp.int tptp.pls W) tptp.pls)) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.times_times tptp.int (tptp.bit0 K_1) L) (tptp.bit0 (tptp.times_times tptp.int K_1 L)))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_25 tptp.pls)) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 _let_1)) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int (tptp.one_one tptp.int) Z) (tptp.ti tptp.int Z))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int Z (tptp.one_one tptp.int)) (tptp.ti tptp.int Z))) (forall ((Z_1 $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Z_1) Wa)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_1) Wa)) (not (= (tptp.ti tptp.int Z_1) (tptp.ti tptp.int Wa))))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (= (tptp.times_times tptp.int W (tptp.plus_plus tptp.int Z1 Z2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int W Z1) (tptp.times_times tptp.int W Z2)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.plus_plus tptp.int Z1 Z2) W) (tptp.plus_plus tptp.int (tptp.times_times tptp.int Z1 W) (tptp.times_times tptp.int Z2 W)))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.plus_plus tptp.int K_1 I_2)) (tptp.plus_plus tptp.int K_1 J_1))))))) (forall ((V_1 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.number_number_of tptp.int V_1) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.times_times tptp.int V_1 W)))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.number_number_of tptp.int K)) (tptp.number_number_of tptp.int L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1278240602ring_1 X_a) (forall ((V_1 $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 U_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 V_1)) (=> (= (tptp.plus_plus X_a U_1 V_1) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a U_1 X) (tptp.times_times X_a V_1 Y))) A_1))))))))))))) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Xa)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Ya)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Xa) Ya)))))))) (forall ((Z_1 $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Wa)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Wa) Z_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) Ya)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.number_number_of X_a Xa)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Xa) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_2)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a B))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.one_one X_a)) B)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 Xa)) (tptp.hAPP tptp.nat X_a _let_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Xa) Ya))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N))))))))) (forall ((Ma $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Wa)))) (= (= Ma (tptp.nat_1 Wa)) (and (=> _let_1 (= (tptp.ti tptp.int Wa) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (=> (not _let_1) (= Ma (tptp.zero_zero tptp.nat))))))) (forall ((Wa $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Wa)))) (= (= (tptp.nat_1 Wa) Ma) (and (=> _let_1 (= (tptp.ti tptp.int Wa) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (=> (not _let_1) (= Ma (tptp.zero_zero tptp.nat))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.plus_plus tptp.nat (tptp.nat_1 X) (tptp.nat_1 Y)) (tptp.nat_1 (tptp.plus_plus tptp.int X Y))))))) (forall ((Z_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_2)) (= (tptp.nat_1 (tptp.plus_plus tptp.int Z Z_2)) (tptp.plus_plus tptp.nat (tptp.nat_1 Z) (tptp.nat_1 Z_2))))))) (forall ((Ma $$unsorted) (Va $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int Va))) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma) _let_1) (and (= Ma (tptp.nat_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_1)))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat (tptp.nat_1 X)) N) (tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) N))))) (forall ((N $$unsorted) (Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)) (= (tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Z) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat (tptp.nat_1 Z)) N)))) (forall ((X_a $$unsorted)) (=> (tptp.linord626643107strict X_a) (forall ((V_1 $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 U_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 V_1)) (=> (= (tptp.plus_plus X_a U_1 V_1) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a (tptp.times_times X_a U_1 X) (tptp.times_times X_a V_1 Y))) A_1))))))))))))) (forall ((Ma $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Wa)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.nat_1 Wa)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Wa) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.bit1 tptp.pls)) Ya)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.number_number_of X_a Xa)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Xa) (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 (tptp.minus_minus tptp.nat N (tptp.one_one tptp.nat))) X) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.minus_minus X_a A_2 B)) (tptp.zero_zero X_a))))))))) (= _let_37 _let_43) (= _let_43 _let_37) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.times_times X_a A_1 A_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_2 C_1)) (tptp.times_times X_a B C_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a A_1 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a B_1 A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a A_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a B_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.times_times X_a A_1 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord893533164strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C A_1)) (tptp.times_times X_a C B_1)))))))))) (forall ((W $$unsorted)) (= (tptp.nat_1 (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.nat W))) (forall ((V_1 $$unsorted)) (= (tptp.number_number_of tptp.nat V_1) (tptp.nat_1 (tptp.number_number_of tptp.int V_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.plus_plus X_a (tptp.times_times X_a Xa Xa) (tptp.times_times X_a Ya Ya)) _let_1) (and (= (tptp.ti X_a Xa) _let_1) (= (tptp.ti X_a Ya) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (R_1 $$unsorted)) (=> (not (= (tptp.ti X_a R_1) (tptp.zero_zero X_a))) (=> (and (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)) (not (= (tptp.ti X_a C) (tptp.ti X_a D_1)))) (not (= (tptp.plus_plus X_a A_1 (tptp.times_times X_a R_1 C)) (tptp.plus_plus X_a B_1 (tptp.times_times X_a R_1 D_1))))))))) (= _let_42 (tptp.nat_1 _let_6)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a M N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a A_2 A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_2 A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a A_1 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Xa)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Ya)) (= (= (tptp.plus_plus X_a Xa Ya) _let_1) (and (= (tptp.ti X_a Xa) _let_1) (= (tptp.ti X_a Ya) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.plus_plus X_a A_1 C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.plus_plus X_a A_1 C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.plus_plus X_a A_1 C)) (tptp.plus_plus X_a B_1 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V_1))) (= (tptp.times_times X_b _let_1 (tptp.plus_plus X_b B_1 C)) (tptp.plus_plus X_b (tptp.times_times X_b _let_1 B_1) (tptp.times_times X_b _let_1 C))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V_1))) (= (tptp.times_times X_b (tptp.plus_plus X_b A_1 B_1) _let_1) (tptp.plus_plus X_b (tptp.times_times X_b A_1 _let_1) (tptp.times_times X_b B_1 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.plus_plus X_a M M) (tptp.times_times X_a (tptp.plus_plus X_a _let_1 _let_1) M)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted)) (= (tptp.plus_plus X_a M (tptp.times_times X_a A_1 M)) (tptp.times_times X_a (tptp.plus_plus X_a A_1 (tptp.one_one X_a)) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 M) M) (tptp.times_times X_a (tptp.plus_plus X_a A_1 (tptp.one_one X_a)) M))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (forall ((Va $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a Va))) (let ((_let_2 (tptp.number_number_of X_a Wa))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) _let_2) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B_1) N)))))))))) (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.minus_minus tptp.nat Na Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat M N)) M)))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.minus_minus tptp.nat N (tptp.plus_plus tptp.nat N M)) (tptp.zero_zero tptp.nat))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)))))))) (forall ((I_1 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) (tptp.minus_minus tptp.nat J K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_1 K)) J)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= (tptp.plus_plus tptp.nat N (tptp.minus_minus tptp.nat M N)) M))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.plus_plus tptp.nat M N)) (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 M) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_2 $$unsorted) (Q $$unsorted)) (let ((_let_1 (tptp.power_power X_a X))) (= (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 P_2) (tptp.hAPP tptp.nat X_a _let_1 Q)) (tptp.hAPP tptp.nat X_a _let_1 (tptp.plus_plus tptp.nat P_2 Q))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.times_times tptp.int A_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B_1)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.times_times tptp.int K_1 I_2)) (tptp.times_times tptp.int K_1 J_1)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 _let_6)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.plus_plus tptp.int X Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 (tptp.nat_1 X)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.nat_1 (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) X))) (tptp.plus_plus X_a _let_2 _let_2)))))))) (forall ((Z_2 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_2) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) Z_2) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.plus_plus tptp.int W_2 Z_2)) (tptp.plus_plus tptp.int W Z)))))))) (forall ((Z $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Z)))) (forall ((P_1 $$unsorted)) (= (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)))) (exists ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_1)))))) (forall ((P_1 $$unsorted)) (= (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_1)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) N)))))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Wa) Z_1)) (exists ((N_1 $$unsorted)) (= (tptp.ti tptp.int Z_1) (tptp.plus_plus tptp.int Wa (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int X))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.plus_plus tptp.nat Y Z)) (tptp.times_times tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 Y) (tptp.hAPP tptp.nat tptp.int _let_1 Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) V_1)) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.succ V_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) V_1)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.succ V_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a X))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.times_times X_a _let_2 _let_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted) (W $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.minus_minus X_a (tptp.number_number_of X_a W) C)) (tptp.minus_minus X_a (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 W)) C))))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Wa) Z_1))))))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Wa) Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.plus_plus X_a (tptp.times_times X_a X X) (tptp.times_times X_a Y Y))) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.plus_plus X_a (tptp.times_times X_a Xa Xa) (tptp.times_times X_a Ya Ya)))) (or (not (= (tptp.ti X_a Xa) _let_1)) (not (= (tptp.ti X_a Ya) _let_1)))))))) (forall ((Ma $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)) Z_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.plus_plus X_a A_1 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.plus_plus X_a A_1 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) (tptp.plus_plus X_a A_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.plus_plus X_a A_1 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.plus_plus X_a A_1 B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B_1) N))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a A_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.times_times X_a A_1 _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.number_number_of X_a (tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) A_1) (tptp.ti X_a A_1))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.minus_minus tptp.nat A_2 B))) (not (or (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))) (exists ((D_3 $$unsorted)) (and (= A_2 (tptp.plus_plus tptp.nat B D_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_3))))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.minus_minus tptp.nat A_2 B))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (forall ((D_3 $$unsorted)) (=> (= A_2 (tptp.plus_plus tptp.nat B D_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_3))))))) (forall ((Va $$unsorted)) (= (= (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat Va)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Va) tptp.pls)))) (forall ((Va $$unsorted)) (= (= (tptp.number_number_of tptp.nat Va) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Va) tptp.pls)))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) tptp.pls) (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) tptp.pls) K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) tptp.pls))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) L_1))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K1) K2))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) L_1))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K1) K2))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.times_times tptp.int (tptp.bit1 K_1) L) (tptp.plus_plus tptp.int (tptp.bit0 (tptp.times_times tptp.int K_1 L)) L))) (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (= (tptp.times_times tptp.int Ma Na) _let_1) (and (= (tptp.ti tptp.int Ma) _let_1) (= (tptp.ti tptp.int Na) _let_1)))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z_1))))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na)) (tptp.zero_zero tptp.int))) (= Na (tptp.zero_zero tptp.nat)))) (= (tptp.succ tptp.pls) _let_2) (forall ((K_1 $$unsorted)) (= (tptp.succ (tptp.bit0 K_1)) (tptp.bit1 K_1))) (forall ((K_1 $$unsorted)) (= (tptp.succ (tptp.bit1 K_1)) (tptp.bit0 (tptp.succ K_1)))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Wa) (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Wa) Z_1))))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.plus_plus tptp.int Wa (tptp.one_one tptp.int))) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Wa) Z_1))))) (forall ((W $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.plus_plus tptp.int W (tptp.one_one tptp.int))) Z))))) (forall ((K_1 $$unsorted)) (= (tptp.succ K_1) (tptp.plus_plus tptp.int K_1 (tptp.one_one tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.minus_minus X_a X Y)) _let_2) (tptp.minus_minus X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2)) (tptp.times_times X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1) X) Y)))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z_1)))) (= _let_41 (tptp.nat_1 _let_40)) (forall ((P_1 $$unsorted) (I_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.nat_1 I_1))) (and (forall ((N_1 $$unsorted)) (=> (= (tptp.ti tptp.int I_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_1) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.times_times X_a A_1 _let_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.times_times X_a (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.bit0 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B_1) N)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.times_times X_a (tptp.times_times X_a A_1 A_1) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_2 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_2)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V_1) (tptp.number_number_of X_a V_2)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V_1 V_2))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 _let_40)) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_1))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.times_times tptp.int _let_1 I_2)) (tptp.times_times tptp.int _let_1 J_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((K_1 $$unsorted)) (= (tptp.number_number_of X_a (tptp.succ K_1)) (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a K_1)))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit1 K_1) (tptp.bit1 L)) (tptp.bit0 (tptp.plus_plus tptp.int K_1 (tptp.succ L))))) (= _let_4 (tptp.nat_1 _let_31)) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a Z (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a Z (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B_1) N))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times X_a A_1 A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.times_times X_a X X) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 _let_31)) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.power_power tptp.int A_1))) (= (tptp.times_times tptp.int A_1 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.number_number_of tptp.nat (tptp.bit1 _let_1))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.monoid_mult X_b) (tptp.number X_b)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b W))) (= (tptp.hAPP tptp.nat X_b (tptp.power_power X_b _let_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times X_b _let_1 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.number_number_of tptp.nat V_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.number_number_of tptp.int V_1))))) (and (=> _let_2 (= _let_1 (tptp.number_number_of X_a V_1))) (=> (not _let_2) (= _let_1 (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.plus_plus X_a X Y)) _let_2) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2)) (tptp.times_times X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Xa) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Ya) _let_2))) _let_1)) (and (= (tptp.ti X_a Xa) _let_1) (= (tptp.ti X_a Ya) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ti tptp.int X))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_2) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) X) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))))) (or (= _let_1 _let_2) (= _let_1 (tptp.one_one tptp.int))))))))) (forall ((A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.nat_1 P_2))) (let ((_let_2 (tptp.power_power tptp.int A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) P_2)) (= (tptp.hAPP tptp.nat tptp.int _let_2 _let_1) (tptp.times_times tptp.int A_1 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.minus_minus tptp.nat _let_1 (tptp.one_one tptp.nat))))))))) (forall ((R_1 $$unsorted) (Q $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) A_1)) (=> (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int R_1 (tptp.times_times tptp.int A_1 Q))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q) (tptp.one_one tptp.int)))))))))) (forall ((R_1 $$unsorted) (Q $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) A_1)) (=> (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int R_1 (tptp.times_times tptp.int A_1 Q))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 R_1) A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Q)))))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a M))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N))) (let ((_let_3 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 (tptp.times_times X_a M (tptp.hAPP tptp.nat X_a _let_1 (tptp.minus_minus tptp.nat N (tptp.one_one tptp.nat))))))))))))) (not (=> _let_35 (not _let_34))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) B_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Q_1)))))))))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) B_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Q_1) _let_1)))))))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq (tptp.times_times tptp.int _let_17 (tptp.plus_plus tptp.int _let_6 _let_38))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_36 _let_17)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_20 tptp.t) _let_17)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq _let_33)) (and _let_35 _let_34) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_2))) (not (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) _let_3) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y_1) _let_3)) (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_2)) tptp.m) _let_1) (tptp.plus_plus tptp.int _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) tptp.n)))))))))) (= _let_30 _let_33) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_17)) (=> (= tptp.t _let_6) (exists ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) _let_2) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y_1) _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.times_times tptp.nat M M)))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.times_times tptp.nat M (tptp.times_times tptp.nat M M))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.times_times tptp.nat M N) (tptp.times_times tptp.nat N M))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)))))) (forall ((M $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (= (tptp.times_times tptp.nat (tptp.times_times tptp.nat M N) K_1) (tptp.times_times tptp.nat M (tptp.times_times tptp.nat N K_1)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat I_2 K_1)) (tptp.times_times tptp.nat J_1 K_1))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K_1 I_2)) (tptp.times_times tptp.nat K_1 J_1))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_1)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((K_1 $$unsorted) (L $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat I_2 K_1)) (tptp.times_times tptp.nat J_1 L)))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Xa) Ya)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.minus_minus tptp.real Xa Ya)) (tptp.zero_zero tptp.real))))))) (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat Ma K)) (tptp.times_times tptp.nat Na K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((Xa $$unsorted) (Ya $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Z_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.times_times tptp.real Xa Z_1)) (tptp.times_times tptp.real Ya Z_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Xa) Ya))))))) (forall ((Xa $$unsorted) (Ya $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Z_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.times_times tptp.real Z_1 Xa)) (tptp.times_times tptp.real Z_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Xa) Ya))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.minus_minus tptp.nat M N)))))) (forall ((K_1 $$unsorted)) (= (tptp.minus_minus tptp.int K_1 tptp.pls) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit0 K_1) (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus tptp.int K_1 L)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.minus_minus tptp.int Z1 Z2) W) (tptp.minus_minus tptp.int (tptp.times_times tptp.int Z1 W) (tptp.times_times tptp.int Z2 W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (= (tptp.times_times tptp.int W (tptp.minus_minus tptp.int Z1 Z2)) (tptp.minus_minus tptp.int (tptp.times_times tptp.int W Z1) (tptp.times_times tptp.int W Z2)))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.times_times tptp.nat _let_1 N) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.times_times tptp.nat M _let_1) _let_1))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.times_times tptp.nat Ma Na) _let_1) (or (= Ma _let_1) (= Na _let_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (= (= (tptp.times_times tptp.nat K Ma) (tptp.times_times tptp.nat K Na)) (or (= Ma Na) (= K (tptp.zero_zero tptp.nat))))) (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (= (= (tptp.times_times tptp.nat Ma K) (tptp.times_times tptp.nat Na K)) (or (= Ma Na) (= K (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_2 $$unsorted) (Q $$unsorted)) (let ((_let_1 (tptp.power_power X_a X))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_1 P_2)) Q) (tptp.hAPP tptp.nat X_a _let_1 (tptp.times_times tptp.nat P_2 Q))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.times_times tptp.nat M N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_1 M)) N)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) _let_1)) (= Na _let_1)))) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.times_times tptp.real C_1 A_2) (tptp.times_times tptp.real C_1 B)) (= A_2 B)))) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.times_times tptp.real A_2 C_1) (tptp.times_times tptp.real B C_1)) (= A_2 B)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) Na)) (= Ma Na))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) Na)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) Na)) (not (= Ma Na)))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) Xa) Ya)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) Xa) Ya)) (not (= Xa Ya)))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) Xa) Ya)) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) Xa) Ya)) (= Xa Ya))))) (forall ((M $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (= (tptp.times_times tptp.nat (tptp.plus_plus tptp.nat M N) K_1) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat M K_1) (tptp.times_times tptp.nat N K_1)))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.times_times tptp.nat K_1 (tptp.plus_plus tptp.nat M N)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat K_1 M) (tptp.times_times tptp.nat K_1 N)))) (forall ((M $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat M K_1)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N))))))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat M K_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat M K_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N)))))) (forall ((K_1 $$unsorted) (L $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_2 K_1)) (tptp.plus_plus tptp.nat J_1 L)))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_2 K_1)) (tptp.plus_plus tptp.nat J_1 K_1))))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat M J_1)))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat J_1 M)))))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat K Ma)) (tptp.plus_plus tptp.nat K Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na)))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) Na)) (exists ((K_2 $$unsorted)) (= Na (tptp.plus_plus tptp.nat Ma K_2))))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.plus_plus tptp.nat N M)))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.plus_plus tptp.nat M N)))) (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.times_times tptp.nat Na Ma) _let_1) (and (= Na _let_1) (= Ma _let_1))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.times_times tptp.nat Ma Na) _let_1) (and (= Ma _let_1) (= Na _let_1))))) (forall ((N $$unsorted)) (= (tptp.times_times tptp.nat N (tptp.one_one tptp.nat)) N)) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= _let_1 (tptp.times_times tptp.nat Ma Na)) (and (= Ma _let_1) (= Na _let_1))))) (forall ((N $$unsorted)) (= (tptp.times_times tptp.nat (tptp.one_one tptp.nat) N) N)) (forall ((M $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (= (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat M N) K_1) (tptp.minus_minus tptp.nat (tptp.times_times tptp.nat M K_1) (tptp.times_times tptp.nat N K_1)))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.times_times tptp.nat K_1 (tptp.minus_minus tptp.nat M N)) (tptp.minus_minus tptp.nat (tptp.times_times tptp.nat K_1 M) (tptp.times_times tptp.nat K_1 N)))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.real (tptp.one_one tptp.real) Z) Z)) (forall ((Na $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat Ma K)) (tptp.minus_minus tptp.nat Na K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (= (tptp.minus_minus tptp.nat (tptp.minus_minus tptp.nat M K_1) (tptp.minus_minus tptp.nat N K_1)) (tptp.minus_minus tptp.nat M N)))))) (forall ((Na $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)) (= (= (tptp.minus_minus tptp.nat Ma K) (tptp.minus_minus tptp.nat Na K)) (= Ma Na)))))) (forall ((I_2 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) N)) (= (tptp.minus_minus tptp.nat N (tptp.minus_minus tptp.nat N I_2)) I_2))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat M L)) (tptp.minus_minus tptp.nat N L))))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat L N)) (tptp.minus_minus tptp.nat L M))))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.minus_minus tptp.nat M N)) M))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.real (tptp.plus_plus tptp.real Z1 Z2) W) (tptp.plus_plus tptp.real (tptp.times_times tptp.real Z1 W) (tptp.times_times tptp.real Z2 W)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int X))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 Y)) Z) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.times_times tptp.nat Y Z))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.plus_plus tptp.real Z X)) (tptp.plus_plus tptp.real Z Y))))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit1 K_1) (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus tptp.int K_1 L)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit1 K_1) (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus tptp.int K_1 L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.pls (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus tptp.int tptp.pls L)))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int A_1 (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 _let_2 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti tptp.int X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 _let_1)))))))))) (forall ((K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.minus_minus tptp.int K L_1)) (tptp.zero_zero tptp.int))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K_1 I_2)) (tptp.times_times tptp.nat K_1 J_1)))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat I_2 K_1)) (tptp.times_times tptp.nat J_1 K_1)))))))) (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat Ma K)) (tptp.times_times tptp.nat Na K))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.times_times tptp.nat Ma Na))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) (tptp.times_times tptp.real Xa Xa)))) (= Xa _let_1)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Z)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.times_times tptp.real Z X)) (tptp.times_times tptp.real Z Y)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.times_times tptp.real X Y))))))) (forall ((Xa $$unsorted) (Ya $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Z_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.times_times tptp.real Xa Z_1)) (tptp.times_times tptp.real Ya Z_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Xa) Ya))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M (tptp.times_times tptp.nat M N)) (or (= N (tptp.one_one tptp.nat)) (= M (tptp.zero_zero tptp.nat))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (= (= (tptp.minus_minus tptp.nat Ma Na) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) Na)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.minus_minus tptp.nat M N) (tptp.zero_zero tptp.nat)))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (= (tptp.plus_plus tptp.real (tptp.times_times tptp.real Xa Xa) (tptp.times_times tptp.real Ya Ya)) _let_1) (and (= Xa _let_1) (= Ya _let_1))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat A_1 C)) (tptp.minus_minus tptp.nat B_1 C)))))))) (forall ((Na $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat Ma K)) (tptp.minus_minus tptp.nat Na K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.times_times tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 X) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.times_times tptp.nat X Y))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.times_times tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.times_times tptp.nat M N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.times_times tptp.nat M N)) (tptp.times_times tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.hAPP tptp.nat tptp.int _let_1 N))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.minus_minus tptp.nat I_2 (tptp.minus_minus tptp.nat J_1 K_1)) (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat I_2 K_1) J_1)))) (forall ((J $$unsorted) (K $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.minus_minus tptp.nat J K)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) (tptp.plus_plus tptp.nat I_1 K))))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat N M) K_1))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.plus_plus tptp.nat N (tptp.minus_minus tptp.nat M N)) M))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.plus_plus tptp.nat I_2 (tptp.minus_minus tptp.nat J_1 K_1)) (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat I_2 J_1) K_1)))) (forall ((I_1 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) (tptp.minus_minus tptp.nat J K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat I_1 K)) J))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.plus_plus tptp.nat (tptp.minus_minus tptp.nat M N) N) M))) (forall ((K $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J)) (= (= (tptp.minus_minus tptp.nat J I_1) K) (= J (tptp.plus_plus tptp.nat K I_1))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat I_2 J_1) K_1) (tptp.plus_plus tptp.nat I_2 (tptp.minus_minus tptp.nat J_1 K_1))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.plus_plus tptp.nat (tptp.minus_minus tptp.nat J_1 K_1) I_2) (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat J_1 I_2) K_1)))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat J_1 I_2) K_1) (tptp.plus_plus tptp.nat (tptp.minus_minus tptp.nat J_1 K_1) I_2)))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Xa)) (tptp.hAPP tptp.nat tptp.int _let_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Xa) Ya))))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Ma)) (tptp.hAPP tptp.nat tptp.int _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) Na))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq (tptp.times_times tptp.int X Y)))))) (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Wa) (tptp.minus_minus tptp.int Z_1 (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Wa) Z_1))))) (forall ((Va $$unsorted) (V_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Va))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.number_number_of tptp.nat Va)) (tptp.number_number_of tptp.nat V_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.minus_minus tptp.nat M N)) (tptp.minus_minus X_a (tptp.hAPP tptp.nat X_a _let_1 M) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Xa)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Ya)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Xa) Ya))))))))) (forall ((Z $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z_2) Z)) (= (tptp.nat_1 (tptp.minus_minus tptp.int Z Z_2)) (tptp.minus_minus tptp.nat (tptp.nat_1 Z) (tptp.nat_1 Z_2)))))))) (forall ((Z_2 $$unsorted) (Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)) (= (tptp.nat_1 (tptp.times_times tptp.int Z Z_2)) (tptp.times_times tptp.nat (tptp.nat_1 Z) (tptp.nat_1 Z_2))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.times_times tptp.nat (tptp.nat_1 X) (tptp.nat_1 Y)) (tptp.nat_1 (tptp.times_times tptp.int X Y))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat M N))) (let ((_let_2 (tptp.zero_zero tptp.nat))) (let ((_let_3 (= M _let_2))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.plus_plus tptp.nat N (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat M (tptp.one_one tptp.nat)) N))))))))) (forall ((Z_1 $$unsorted) (Wa $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) Wa)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) Z_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Wa) Z_1)))))))) (forall ((P_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.power_power tptp.nat P_2))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M))) (let ((_let_4 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.times_times tptp.nat P_2 (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.minus_minus tptp.nat M _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_2 (tptp.times_times tptp.nat _let_1 N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_2 N)) _let_1))))))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus tptp.nat Z Z))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.nat Z (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus tptp.nat Z Z))) (forall ((V_2 $$unsorted) (K_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V_1) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V_2) K_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.times_times tptp.int V_1 V_2)) K_1))))))) (forall ((V_2 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V_1) (tptp.number_number_of tptp.nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.number_number_of tptp.nat (tptp.times_times tptp.int V_1 V_2)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.times_times tptp.real (tptp.number_number_of tptp.real (tptp.bit0 _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1) X)) _let_2))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real (tptp.number_number_of tptp.real (tptp.bit0 (tptp.bit1 tptp.pls)))) N)))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 B_1) C)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_1) A_1))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.times_times tptp.int (tptp.plus_plus tptp.int A_1 B_1) (tptp.minus_minus tptp.int A_1 B_1)) (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_1) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) K_1))) _let_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Y) _let_1)) (tptp.times_times tptp.nat (tptp.plus_plus tptp.nat X Y) (tptp.minus_minus tptp.nat X Y))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_2))) (let ((_let_4 (tptp.power_power tptp.int B_1))) (let ((_let_5 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.number_number_of tptp.int _let_2))) (let ((_let_7 (tptp.power_power tptp.int A_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.minus_minus tptp.int A_1 B_1)) _let_3) (tptp.minus_minus tptp.int (tptp.plus_plus tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int _let_7 _let_3) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_6 (tptp.hAPP tptp.nat tptp.int _let_7 _let_5)) B_1)) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_6 A_1) (tptp.hAPP tptp.nat tptp.int _let_4 _let_5))) (tptp.hAPP tptp.nat tptp.int _let_4 _let_3))))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.minus_minus tptp.int A_1 B_1)) _let_2) (tptp.plus_plus tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_2) (tptp.times_times tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1) A_1) B_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B_1) _let_2)))))) (forall ((B_1 $$unsorted) (Q $$unsorted) (R_1 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q) R_1) _let_5) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_5) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_2) B_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q)))))))))))))) (forall ((B_1 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q_1) R_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q) R_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 R_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q) Q_1)))))))))) (forall ((B_1 $$unsorted) (Q $$unsorted) (R_1 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_2 _let_1 _let_3))) (let ((_let_6 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q) R_1) _let_6) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 _let_6)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_2) B_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q) Q_1))))))))))))))) (forall ((B_1 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q_1) R_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 Q) R_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_1) B_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q)))))))))) (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.x) _let_4) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.y) _let_4)) _let_32) (forall ((P_2 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.int _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_2) P_2)) (= (tptp.minus_minus tptp.nat (tptp.nat_1 P_2) (tptp.number_number_of tptp.nat _let_1)) (tptp.nat_1 (tptp.minus_minus tptp.int P_2 _let_2))))))) (forall ((P_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) P_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.nat_1 (tptp.minus_minus tptp.int P_2 _let_1))))))) (not (forall ((T_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s) (tptp.number_number_of tptp.nat _let_2)) _let_1) (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_2)) tptp.m) _let_1) T_1))))))) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) W) W))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.real Z W) (tptp.times_times tptp.real W Z))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Z) W)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times tptp.real (tptp.times_times tptp.real Z1 Z2) Z3) (tptp.times_times tptp.real Z1 (tptp.times_times tptp.real Z2 Z3)))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 K_1)))))))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Z) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z)) (= Z W)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_31)) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.minus_minus tptp.int A_1 B_1) (tptp.ti tptp.int C)) (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int C B_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_29 _let_30)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real (tptp.plus_plus tptp.real X Y)) _let_2) (tptp.plus_plus tptp.real (tptp.plus_plus tptp.real (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X) _let_2) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Y) _let_2)) (tptp.times_times tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1) X) Y)))))) (= _let_28 _let_30) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.zero_zero X_a)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_29 _let_28)) _let_22 (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.minus_minus tptp.int M N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)))))) (forall ((M $$unsorted) (N $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.times_times tptp.int M N))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 B_1)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 B_1)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.dvd X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (K_1 $$unsorted)) (=> (= A_1 (tptp.times_times X_a B_1 K_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) B_1) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_1 C)) (tptp.times_times X_a B_1 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a B_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.times_times X_a B_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.times_times X_a B_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.times_times X_a A_1 B_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.minus_minus X_a Y Z))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 tptp.min)) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) N) M)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N) M))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a C_1 A_2)) (tptp.times_times X_a C_1 B))) (or (= (tptp.ti X_a C_1) (tptp.zero_zero X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.times_times X_a A_2 C_1)) (tptp.times_times X_a B C_1))) (or (= (tptp.ti X_a C_1) (tptp.zero_zero X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (M $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) M)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted) (N $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.dvd_dvd X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 M)) B_1)))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) N) M)))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.times_times tptp.int K_1 M)) (tptp.times_times tptp.int K_1 N))) (=> (not (= (tptp.ti tptp.int K_1) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N) M)) (= (tptp.ti tptp.int M) (tptp.ti tptp.int N)))))))))) (forall ((K $$unsorted) (Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.plus_plus tptp.int Na (tptp.times_times tptp.int K Ma)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Na))))) (forall ((C_1 $$unsorted) (Xa $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 D)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.plus_plus tptp.int Xa Ta))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int Xa (tptp.times_times tptp.int C_1 D)) Ta))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.min))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_24 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 tptp.min))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.min))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.min))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_24 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_25 tptp.min))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min)))))) (not (= _let_13 _let_21)) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) A_1))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_24 tptp.min))) (forall ((L $$unsorted)) (not (= tptp.min (tptp.bit0 L)))) (forall ((K_1 $$unsorted)) (not (= (tptp.bit0 K_1) tptp.min))) (not (= tptp.min tptp.pls)) (not (= tptp.pls tptp.min)) (= (tptp.bit1 tptp.min) tptp.min) (forall ((L_1 $$unsorted)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min (tptp.ti tptp.int L_1)))) (forall ((K $$unsorted)) (= (= (tptp.bit1 K) tptp.min) (= (tptp.ti tptp.int K) tptp.min))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) (tptp.one_one X_a)) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a B_1 C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) _let_1) A_1)) (= (tptp.ti X_a A_1) _let_1)))))) (= (tptp.succ tptp.min) tptp.pls) (forall ((K_1 $$unsorted)) (= (tptp.minus_minus tptp.int K_1 tptp.min) (tptp.succ K_1))) (forall ((Z $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Z) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z) N)))))) (forall ((P_2 $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) N))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) tptp.min) (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) tptp.min) K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) tptp.min))))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.pls (tptp.bit1 L)) (tptp.bit1 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.min (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.min (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.ti tptp.int Na))) (let ((_let_3 (tptp.ti tptp.int Ma))) (let ((_let_4 (tptp.one_one tptp.int))) (= (= (tptp.times_times tptp.int Ma Na) _let_4) (or (and (= _let_3 _let_4) (= _let_2 _let_4)) (and (= _let_3 _let_1) (= _let_2 _let_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M))) (let ((_let_2 (tptp.one_one tptp.int))) (=> (= (tptp.times_times tptp.int M N) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.number_number_of tptp.int tptp.min))))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int P_2) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_2) B_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.times_times tptp.int A_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1))))))))) (forall ((N $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int P_2) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_2) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.times_times tptp.int A_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.ti X_a X) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) N))))))) (forall ((Y $$unsorted) (N $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.number_number_of X_a tptp.min)) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.one_one X_a))))) _let_23 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_19 _let_21) _let_17)) (=> (not _let_23) (not _let_22)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_18 _let_21) _let_17)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 tptp.s)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_20 tptp.s) _let_17)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 tptp.s) _let_17))) (not (forall ((S1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int S1) (tptp.number_number_of tptp.nat _let_1)) (tptp.number_number_of tptp.int tptp.min)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int)))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat A_1 C)) (tptp.times_times tptp.nat B_1 C))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat C A_1)) (tptp.times_times tptp.nat C B_1))))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.minus_minus tptp.nat M N))))))) (forall ((Xa $$unsorted) (P_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong Xa (tptp.zero_zero tptp.int)) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3) Xa)))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 (tptp.zero_zero tptp.int)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Ma) A_2)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) M)))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) A_1) B_1)) (or (= B_1 (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) A_1) B_1)))))) (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat Ma K)) (tptp.times_times tptp.nat Na K))) (or (= K (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.minus_minus tptp.nat M N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.minus_minus tptp.nat M N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat A_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat B_1) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= N (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) N)) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Xa)) (tptp.hAPP tptp.nat tptp.int _let_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Xa) Ya))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Xa) Ya)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Xa)) (tptp.hAPP tptp.nat tptp.int _let_1 Ya)))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Y) N))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) _let_1)) (= Ma _let_1)))) (forall ((K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat Na K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.plus_plus tptp.nat A_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1)))))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong M (tptp.zero_zero tptp.int)) M))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.plus_plus tptp.int A_1 C) (tptp.plus_plus tptp.int B_1 C)) M)))) (forall ((D_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (=> (= (tptp.ti tptp.int B_1) (tptp.ti tptp.int C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 D_1) M)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X Y) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) Z) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) Z)) M)))) (forall ((M $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X Y) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) M)) (= (tptp.ti tptp.int X) (tptp.ti tptp.int Y)))))))))))) (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 X) M)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X _let_1) M))))))))) (forall ((C_1 $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B $$unsorted) (Ma $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.times_times tptp.int A_2 D)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.times_times tptp.int B D)) Ma))))) (forall ((C_1 $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B $$unsorted) (Ma $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.times_times tptp.int D A_2)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.times_times tptp.int D B)) Ma))))) (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) X) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X _let_1) M)) (= (tptp.ti tptp.int X) _let_1))))))) (forall ((Y $$unsorted) (X $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X _let_1) P_2))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong Y _let_1) P_2))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int X Y) _let_1) P_2)))))))) (forall ((K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_1) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) K_1) N)))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K_1 M)) (tptp.times_times tptp.nat K_1 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 B_1) _let_1) P_2)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B_1 _let_1) P_2)))))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) A_1)) (=> (and (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_2))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B_1 _let_1) P_2)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 B_1) _let_1) P_2)))))))) (forall ((X $$unsorted) (Q $$unsorted) (N $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (= X (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat Q N) R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 R_1) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) X))))))))) (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.times_times tptp.nat Ma Na)) Ma)) (= Na (tptp.one_one tptp.nat)))))) (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.times_times tptp.nat Na Ma)) Ma)) (= Na (tptp.one_one tptp.nat)))))) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Xa)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Ya)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Xa) Ya)))))))) (forall ((I_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.power_power tptp.nat I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))))) (forall ((Z_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.nat_1 Z_1)) Ma)) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Z_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)))) (=> (not _let_2) (= Ma (tptp.zero_zero tptp.nat)))))))) (forall ((X $$unsorted) (P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X (tptp.number_number_of tptp.int tptp.min)) P_2)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X (tptp.one_one tptp.int)) P_2)))))) (forall ((Y $$unsorted) (X $$unsorted) (P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X (tptp.zero_zero tptp.int)) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X) P_2)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2) Y)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) M)) (or (= M (tptp.zero_zero tptp.nat)) (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) M)))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) M) _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_2)) (= (tptp.legendre (tptp.number_number_of tptp.int tptp.min) _let_2) _let_1))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_19 _let_18) _let_17)) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) X_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 X_1) _let_1)) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) Y_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 Y_1) _let_1))) (= (tptp.ti tptp.int Y_1) (tptp.ti tptp.int X_1)))))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) X))) (not (forall ((S $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) S)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) S) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 S) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 Z))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 X)))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Z)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X)))))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) A_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 X)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Z) X))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) A_1)))) (=> (= B_1 C) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 C) A_1)))))))))) (forall ((P_1 $$unsorted) (Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa)))) (=> (and _let_3 (not _let_4)) (=> (and _let_4 (not _let_3)) (tptp.hBOOL P_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= Y X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= X Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (=> (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) _let_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= X Y)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 Z))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Y)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 C))) (=> (= A_1 B_1) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B_1)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 A_1)))))))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)) (= X Y)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 C)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)))) (=> _let_3 (=> (not (= A_1 B_1)) (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) A_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (=> _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (= X Y))))))) (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)) (= Xa Ya)))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) Y)))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B_1)))) (=> (not (= A_1 B_1)) (=> _let_3 (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B_1) A_1)))))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa)))))) (= _let_3 _let_3))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)))) (= (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa)))) (and _let_3 (not (= Xa Ya)))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)))) (= _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa)))) (= Xa Ya))))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (= Xa Ya) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) X)))) (not (and _let_1 (not _let_1))))) (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Xa) Ya)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ya) Xa))) (= Xa Ya))))) (forall ((J_1 $$unsorted) (K_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int (tptp.number_number_of tptp.int tptp.min)))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int _let_1 K_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_1 J_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_3 _let_2) M)) (= _let_3 _let_2))))))) (forall ((M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.one_one tptp.int) (tptp.number_number_of tptp.int tptp.min)) M))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int _let_1) N))) (or (= _let_2 (tptp.one_one tptp.int)) (= _let_2 _let_1))))) (forall ((A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.legendre A_1 P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes P_2) A_1)))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_3) P_2)))) (and (=> _let_4 (= _let_1 _let_3)) (=> (not _let_4) (and (=> _let_2 (= _let_1 (tptp.one_one tptp.int))) (=> (not _let_2) (= _let_1 (tptp.number_number_of tptp.int tptp.min))))))))))) (forall ((Ma $$unsorted) (Xa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes Ma) Xa)) (exists ((Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Xa) Ma))))) (forall ((X $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2) X))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) (tptp.nat_1 (tptp.minus_minus tptp.int P_2 _let_1))) _let_1) P_2)))))) (forall ((A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ti tptp.int A_1))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 A_1) _let_1) P_2)) (or (= _let_2 _let_1) (= _let_2 (tptp.minus_minus tptp.int P_2 _let_1)))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B_1 C) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 C) M))))) (forall ((K_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 K_1) M))) (forall ((A_2 $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B A_2) Ma)))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int A_2) (tptp.ti tptp.int B)))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) (tptp.one_one tptp.int)))) (forall ((A_1 $$unsorted) (M $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 M) (tptp.times_times tptp.int B_1 M)) M))) (forall ((K_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 K_1) (tptp.times_times tptp.int B_1 K_1)) M)))) (forall ((K_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int K_1 A_1) (tptp.times_times tptp.int K_1 B_1)) M)))) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 C) (tptp.times_times tptp.int B_1 D_1)) M))))) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.plus_plus tptp.int A_1 C) (tptp.plus_plus tptp.int B_1 D_1)) M))))) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.minus_minus tptp.int A_1 C) (tptp.minus_minus tptp.int B_1 D_1)) M))))) (forall ((B_1 $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_1) A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M))))))))))) (forall ((A_1 $$unsorted) (R_1 $$unsorted) (B_1 $$unsorted) (M $$unsorted) (C $$unsorted) (D_1 $$unsorted) (N $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.minus_minus tptp.int A_1 (tptp.times_times tptp.int R_1 B_1)) M) (tptp.times_times tptp.int (tptp.minus_minus tptp.int C (tptp.times_times tptp.int R_1 D_1)) N)) (tptp.minus_minus tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int A_1 M) (tptp.times_times tptp.int C N)) (tptp.times_times tptp.int R_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_1 M) (tptp.times_times tptp.int D_1 N)))))) (forall ((A_2 $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) Ma)) (exists ((K_2 $$unsorted)) (= (tptp.ti tptp.int B) (tptp.plus_plus tptp.int A_2 (tptp.times_times tptp.int Ma K_2)))))) (forall ((A_2 $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 B) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Ma) (tptp.minus_minus tptp.int A_2 B))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_1) (tptp.minus_minus tptp.int B_1 (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_1) B_1))))) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) M)) (= (tptp.ti tptp.int A_1) _let_1))))))) (forall ((B_1 $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B_1) M)) (= (tptp.ti tptp.int A_1) (tptp.ti tptp.int B_1))))))))))) (forall ((N $$unsorted) (P_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.times_times tptp.int M N))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 N))))))))) (forall ((P_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) P_3)) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M_1))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) M_1) P_3))) (or (= _let_1 (tptp.one_one tptp.int)) (= _let_1 (tptp.ti tptp.int P_3)))))))))) (forall ((A_1 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_1 A_1) _let_1) P_2)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 (tptp.minus_minus tptp.int P_2 _let_1)) P_2)))))))) (forall ((P_1 $$unsorted) (Xa $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.minus_minus tptp.nat Xa Ya)))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ya) Xa)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int _let_2 Xa) (tptp.hAPP tptp.nat tptp.int _let_2 Ya))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Xa) Ya)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.zero_zero tptp.int))))))))) (forall ((P_2 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (let ((_let_3 (tptp.ti tptp.int P_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (not (= _let_3 (tptp.number_number_of tptp.int _let_2))) (=> (not (= _let_3 (tptp.number_number_of tptp.int (tptp.bit1 _let_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.number_number_of tptp.int (tptp.bit1 _let_2))) P_2))))))))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Xa)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Xa)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((Ma $$unsorted) (Ta $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (not (= (tptp.ti tptp.int K) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Ma) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.times_times tptp.int K Ma)) (tptp.times_times tptp.int K Ta)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.dvd X_a) (tptp.semiring_0 X_a)) (forall ((P_1 $$unsorted) (L_1 $$unsorted)) (= (exists ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.times_times X_a L_1 X_1)))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) L_1) (tptp.plus_plus X_a X_1 (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D) D_2)) (forall ((X_1 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a X_1 Ta))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a (tptp.minus_minus X_a X_1 (tptp.times_times X_a K_2 D_2)) Ta)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D) D_2)) (forall ((X_1 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a X_1 Ta)))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.plus_plus X_a (tptp.minus_minus X_a X_1 (tptp.times_times X_a K_2 D_2)) Ta))))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_16 _let_13)) (forall ((A_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.minus_minus tptp.int P_3 _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.times_times tptp.int A_2 _let_2) _let_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_2 _let_2) P_3)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.power_power tptp.int X))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 Y) _let_1) P_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.times_times tptp.nat Y Z)) _let_1) P_2)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.number_number_of tptp.int N))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.number_number_of tptp.int (tptp.bit0 N)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.number_number_of tptp.int (tptp.bit1 N)))))))) (not (forall ((S $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) tptp.n)))) (not (and (= (tptp.ti tptp.int W_1) (tptp.minus_minus tptp.int tptp.y (tptp.times_times tptp.int S _let_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs tptp.int W_1))) _let_1))))))) (not (forall ((R $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) tptp.n)))) (not (and (= (tptp.ti tptp.int V) (tptp.minus_minus tptp.int tptp.x (tptp.times_times tptp.int R _let_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs tptp.int V))) _let_1))))))) (forall ((D_1 $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (not (= (tptp.ti tptp.int I_2) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) D_1) I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.abs_abs tptp.int D_1)) (tptp.abs_abs tptp.int I_2))))))) (forall ((W $$unsorted) (Z $$unsorted)) (= (tptp.nat_1 (tptp.abs_abs tptp.int (tptp.times_times tptp.int W Z))) (tptp.times_times tptp.nat (tptp.nat_1 (tptp.abs_abs tptp.int W)) (tptp.nat_1 (tptp.abs_abs tptp.int Z))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((L $$unsorted) (K_1 $$unsorted)) (=> (= (tptp.abs_abs X_a L) (tptp.abs_abs X_a K_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) L) K_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Ma $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.abs_abs X_a Ma)) K)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ma) K)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Ma $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Ma))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.abs_abs X_a K))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 K))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_1) A_1)) (= (tptp.abs_abs tptp.int A_1) (tptp.abs_abs tptp.int B_1))))))) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Xa) _let_1)) (= (tptp.abs_abs tptp.int Xa) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) X)) (= (tptp.times_times X_a (tptp.abs_abs X_a Y) X) (tptp.abs_abs X_a (tptp.times_times X_a Y X))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring_abs X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (and (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)))) (= (tptp.abs_abs X_a (tptp.times_times X_a A_1 B_1)) (tptp.times_times X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.abs_abs X_a A_1)) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.abs_abs X_a (tptp.minus_minus X_a (tptp.plus_plus X_a A_1 B_1) (tptp.plus_plus X_a C D_1)))) (tptp.plus_plus X_a (tptp.abs_abs X_a (tptp.minus_minus X_a A_1 C)) (tptp.abs_abs X_a (tptp.minus_minus X_a B_1 D_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.abs_abs X_a (tptp.minus_minus X_a A_1 B_1))) (tptp.plus_plus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (= (tptp.abs_abs X_a (tptp.number_number_of X_a tptp.min)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.abs_abs X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.abs_abs X_a A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1)))) (= (tptp.abs_abs X_a _let_1) _let_1))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_idom X_a) (= (tptp.abs_abs X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (= (tptp.abs_abs X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.abs_abs X_a A_1)) N))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))) (= (tptp.abs_abs X_a _let_1) _let_1))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) M))) (= (tptp.abs_abs tptp.int _let_1) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a A_1))) (= (tptp.abs_abs X_a _let_1) _let_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (= (tptp.abs_abs tptp.int (tptp.times_times tptp.int M N)) _let_1) (= (tptp.abs_abs tptp.int M) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.minus_minus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1))) (tptp.abs_abs X_a (tptp.minus_minus X_a B_1 A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.minus_minus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1))) (tptp.abs_abs X_a (tptp.minus_minus X_a A_1 B_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.abs_abs X_a (tptp.minus_minus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1)))) (tptp.abs_abs X_a (tptp.minus_minus X_a A_1 B_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.abs_abs X_a (tptp.plus_plus X_a A_1 B_1))) (tptp.plus_plus X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a B_1))) (let ((_let_2 (tptp.abs_abs X_a A_1))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_2) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_1) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.times_times X_a _let_2 _let_1)) (tptp.times_times X_a C D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.abs_abs X_a A_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.abs_abs X_a A_2))) (not (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.abs_abs X_a A_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.abs_abs X_a A_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.abs_abs X_a A_2)) _let_1)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.abs_abs X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.abs_abs X_a (tptp.minus_minus X_a A_1 B_1)) (tptp.abs_abs X_a (tptp.minus_minus X_a B_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.abs_abs X_a (tptp.times_times X_a A_1 B_1)) (tptp.times_times X_a (tptp.abs_abs X_a A_1) (tptp.abs_abs X_a B_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a A_1))) (= (tptp.times_times X_a _let_1 _let_1) (tptp.times_times X_a A_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.abs_abs X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.abs_abs X_a A_1)) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))) (forall ((X $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.abs_abs tptp.int X)) N)))) (forall ((Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.abs_abs tptp.int Z_1)) (tptp.one_one tptp.int))) (= (tptp.ti tptp.int Z_1) (tptp.zero_zero tptp.int)))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Z_1))) (let ((_let_2 (tptp.one_one tptp.int))) (= (= (tptp.abs_abs tptp.int Z_1) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.number_number_of tptp.int tptp.min))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((N $$unsorted)) (= (tptp.abs_abs X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.number_number_of X_a tptp.min)) N)) (tptp.one_one X_a))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit1 (tptp.bit1 tptp.pls))))) (= (tptp.abs_abs tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.abs_abs tptp.int X)) _let_1)))) (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.abs_abs tptp.int Xa)) Na))) (or (not (= (tptp.ti tptp.int Xa) _let_1)) (= Na (tptp.zero_zero tptp.nat)))))) (forall ((Na $$unsorted) (Ma $$unsorted)) (=> (not (= (tptp.ti tptp.int Ma) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.times_times tptp.int Ma Na)) Ma)) (= (tptp.abs_abs tptp.int Na) (tptp.one_one tptp.int))))) (forall ((Ma $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) (tptp.nat_1 (tptp.abs_abs tptp.int Z_1)))))) (forall ((Z_1 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Z_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.nat_1 (tptp.abs_abs tptp.int Z_1))) Ma)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (tptp.abs_abs X_a _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.abs_abs X_a A_1)) _let_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) _let_1)))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.abs_abs tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.abs_abs tptp.int A_1)) _let_1)))) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_2) _let_1) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B) _let_1)) (= (tptp.abs_abs tptp.int A_2) (tptp.abs_abs tptp.int B))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1) (= (tptp.abs_abs tptp.int A_1) _let_1)))) (forall ((Z $$unsorted) (X $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) D_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) (tptp.plus_plus tptp.int X (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.abs_abs tptp.int (tptp.minus_minus tptp.int X Z)) (tptp.one_one tptp.int)) D_1)))))))) (forall ((X $$unsorted) (Z $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) D_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.minus_minus tptp.int X (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.abs_abs tptp.int (tptp.minus_minus tptp.int X Z)) (tptp.one_one tptp.int)) D_1))) Z)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) X)) (exists ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs tptp.int (tptp.minus_minus tptp.int Y (tptp.times_times tptp.int N_1 X))))) X))))) (forall ((K $$unsorted) (P_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.minus_minus tptp.int X_1 D))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.minus_minus tptp.int X_1 (tptp.times_times tptp.int K D)))))))))))) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.plus_plus tptp.real (tptp.abs_abs tptp.real X) (tptp.one_one tptp.real))) X)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.plus_plus tptp.real (tptp.one_one tptp.real) (tptp.abs_abs tptp.real X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.abs_abs tptp.real X)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) _let_1))))))) (forall ((Na $$unsorted) (P_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 Na)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K_2) Na)) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.plus_plus tptp.nat K_2 (tptp.one_one tptp.nat))))))))) (forall ((K $$unsorted) (P_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.plus_plus tptp.int X_1 D))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.plus_plus tptp.int X_1 (tptp.times_times tptp.int K D)))))))))))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) J) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat I_1 J) U) Ma)) Na))))))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) I_1) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat J I_1) U) Na)))))))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (= (= (tptp.times_times tptp.nat K Ma) (tptp.times_times tptp.nat K Na)) (or (= K (tptp.zero_zero tptp.nat)) (= Ma Na)))) (forall ((I_2 $$unsorted) (U_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_2 U_1) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J_1 U_1) K_1)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.plus_plus tptp.nat I_2 J_1) U_1) K_1))) (forall ((Ma $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((Ma $$unsorted) (Na $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (= (tptp.times_times tptp.nat K Ma) (tptp.times_times tptp.nat K Na)) (= Ma Na)))) (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (or (= K (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((Ma $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((Ma $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.times_times tptp.nat K Ma)) (tptp.times_times tptp.nat K Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) Na))))))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat I_1 J) U) Ma)) Na))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N $$unsorted) (J_1 $$unsorted) (I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_1) I_2)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_2 U_1) M) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J_1 U_1) N)) (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat I_2 J_1) U_1) M) N)))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J) I_1)) (= (= (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na)) (= (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat I_1 J) U) Ma) Na)))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma)) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat J I_1) U) Na)))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N $$unsorted) (I_2 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) J_1)) (= (tptp.minus_minus tptp.nat (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_2 U_1) M) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J_1 U_1) N)) (tptp.minus_minus tptp.nat M (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat J_1 I_2) U_1) N))))) (forall ((U $$unsorted) (Ma $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J)) (= (= (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat I_1 U) Ma) (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat J U) Na)) (= Ma (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat J I_1) U) Na))))) (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) Na)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.abs_abs tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int F (tptp.plus_plus tptp.nat I (tptp.one_one tptp.nat))) (tptp.hAPP tptp.nat tptp.int F I)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F Na))) (exists ((I $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) Na)) (= (tptp.hAPP tptp.nat tptp.int F I) (tptp.ti tptp.int K)))))))))) (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) Na)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.abs_abs tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int F (tptp.plus_plus tptp.nat I (tptp.one_one tptp.nat))) (tptp.hAPP tptp.nat tptp.int F I)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F Na))) (exists ((I $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) Na)) (= (tptp.hAPP tptp.nat tptp.int F I) (tptp.ti tptp.int K)))))))))) (tptp.semiri456707255roduct tptp.int) (tptp.ordere223160158up_add tptp.int) (tptp.ordere236663937imp_le tptp.int) (tptp.linord893533164strict tptp.int) (tptp.linord626643107strict tptp.int) (tptp.linord20386208strict tptp.int) (tptp.ordere779506340up_add tptp.int) (tptp.ordere142940540dd_abs tptp.int) (tptp.ordere216010020id_add tptp.int) (tptp.linord219039673up_add tptp.int) (tptp.cancel146912293up_add tptp.int) _let_12 (tptp.ordere453448008miring tptp.int) (tptp.linord581940658strict tptp.int) (tptp.ring_n68954251visors tptp.int) (tptp.ordere1490568538miring tptp.int) (tptp.linord1278240602ring_1 tptp.int) (tptp.ordered_ab_group_add tptp.int) (tptp.cancel_semigroup_add tptp.int) (tptp.linordered_semiring tptp.int) _let_11 (tptp.ab_semigroup_mult tptp.int) (tptp.comm_monoid_mult tptp.int) (tptp.ab_semigroup_add tptp.int) (tptp.ordered_semiring tptp.int) (tptp.ordered_ring_abs tptp.int) (tptp.no_zero_divisors tptp.int) (tptp.comm_monoid_add tptp.int) (tptp.linordered_ring tptp.int) _let_10 (tptp.comm_semiring_1 tptp.int) (tptp.comm_semiring tptp.int) (tptp.semiring_char_0 tptp.int) (tptp.number_semiring tptp.int) (tptp.ab_group_add tptp.int) (tptp.zero_neq_one tptp.int) (tptp.ordered_ring tptp.int) (tptp.linorder tptp.int) (tptp.monoid_mult tptp.int) (tptp.comm_ring_1 tptp.int) (tptp.monoid_add tptp.int) (tptp.semiring_1 tptp.int) (tptp.semiring_0 tptp.int) (tptp.group_add tptp.int) (tptp.mult_zero tptp.int) (tptp.comm_ring tptp.int) (tptp.order tptp.int) (tptp.ring_char_0 tptp.int) (tptp.number_ring tptp.int) (tptp.semiring tptp.int) (tptp.ring_1 tptp.int) (tptp.power tptp.int) (tptp.zero tptp.int) (tptp.ring tptp.int) (tptp.idom tptp.int) (tptp.number tptp.int) (tptp.one tptp.int) (tptp.dvd tptp.int) (tptp.semiri456707255roduct tptp.nat) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.linord893533164strict tptp.nat) (tptp.linord20386208strict tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.ordere453448008miring tptp.nat) (tptp.ordere1490568538miring tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semiring tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_mult tptp.nat) (tptp.comm_monoid_mult tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.ordered_semiring tptp.nat) (tptp.no_zero_divisors tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.comm_semiring_1 tptp.nat) (tptp.comm_semiring tptp.nat) (tptp.semiring_char_0 tptp.nat) (tptp.number_semiring tptp.nat) (tptp.zero_neq_one tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_mult tptp.nat) (tptp.monoid_add tptp.nat) (tptp.semiring_1 tptp.nat) (tptp.semiring_0 tptp.nat) (tptp.mult_zero tptp.nat) (tptp.order tptp.nat) (tptp.semiring tptp.nat) (tptp.power tptp.nat) (tptp.zero tptp.nat) (tptp.number tptp.nat) (tptp.one tptp.nat) (tptp.dvd tptp.nat) (tptp.order tptp.bool) (tptp.semiri456707255roduct tptp.real) (tptp.ordere223160158up_add tptp.real) (tptp.ordere236663937imp_le tptp.real) (tptp.linord893533164strict tptp.real) (tptp.linord626643107strict tptp.real) (tptp.linord20386208strict tptp.real) (tptp.ordere779506340up_add tptp.real) (tptp.ordere142940540dd_abs tptp.real) (tptp.ordere216010020id_add tptp.real) (tptp.linord219039673up_add tptp.real) (tptp.cancel146912293up_add tptp.real) (tptp.ring_11004092258visors tptp.real) (tptp.ordere453448008miring tptp.real) (tptp.linord581940658strict tptp.real) (tptp.ring_n68954251visors tptp.real) (tptp.ordere1490568538miring tptp.real) (tptp.linord1278240602ring_1 tptp.real) (tptp.ordered_ab_group_add tptp.real) (tptp.cancel_semigroup_add tptp.real) (tptp.linordered_semiring tptp.real) (tptp.linordered_semidom tptp.real) (tptp.ab_semigroup_mult tptp.real) (tptp.comm_monoid_mult tptp.real) (tptp.ab_semigroup_add tptp.real) (tptp.ordered_semiring tptp.real) (tptp.ordered_ring_abs tptp.real) (tptp.no_zero_divisors tptp.real) (tptp.comm_monoid_add tptp.real) (tptp.linordered_ring tptp.real) (tptp.linordered_idom tptp.real) (tptp.comm_semiring_1 tptp.real) (tptp.comm_semiring tptp.real) (tptp.semiring_char_0 tptp.real) (tptp.number_semiring tptp.real) (tptp.ab_group_add tptp.real) (tptp.zero_neq_one tptp.real) (tptp.ordered_ring tptp.real) (tptp.linorder tptp.real) (tptp.monoid_mult tptp.real) (tptp.comm_ring_1 tptp.real) (tptp.monoid_add tptp.real) (tptp.semiring_1 tptp.real) (tptp.semiring_0 tptp.real) (tptp.group_add tptp.real) (tptp.mult_zero tptp.real) (tptp.comm_ring tptp.real) (tptp.order tptp.real) (tptp.ring_char_0 tptp.real) (tptp.number_ring tptp.real) (tptp.semiring tptp.real) (tptp.ring_1 tptp.real) (tptp.power tptp.real) (tptp.zero tptp.real) (tptp.ring tptp.real) (tptp.idom tptp.real) (tptp.number tptp.real) (tptp.one tptp.real) (tptp.dvd tptp.real) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.if X_a tptp.fTrue X Y) (tptp.ti X_a X))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.if X_a tptp.fFalse X Y) (tptp.ti X_a Y))) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) _let_9 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.02/2.23  )
% 2.02/2.23  % SZS output end Proof for NUM925+7
% 2.02/2.23  % cvc5---1.0.5 exiting
% 2.02/2.24  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------