TSTP Solution File: NUM924+7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 10:48:58 EDT 2023
% Result : Theorem 1.96s 2.16s
% Output : Proof 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.27 % Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.28 % Command : do_cvc5 %s %d
% 0.27/0.48 % Computer : n001.cluster.edu
% 0.27/0.48 % Model : x86_64 x86_64
% 0.27/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.48 % Memory : 8042.1875MB
% 0.27/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.48 % CPULimit : 300
% 0.27/0.48 % WCLimit : 300
% 0.27/0.48 % DateTime : Fri Aug 25 10:07:13 EDT 2023
% 0.27/0.48 % CPUTime :
% 0.33/0.76 %----Proving TF0_NAR, FOF, or CNF
% 1.96/2.16 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Y91Cx1GRPp/cvc5---1.0.5_14989.p...
% 1.96/2.16 ------- get file name : TPTP file name is NUM924+7
% 1.96/2.16 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14989.smt2...
% 1.96/2.16 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.96/2.16 % SZS status Theorem for NUM924+7
% 1.96/2.16 % SZS output start Proof for NUM924+7
% 1.96/2.16 (
% 1.96/2.16 (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.bit1 tptp.pls))) (let ((_let_4 (tptp.bit0 _let_3))) (let ((_let_5 (tptp.number_number_of tptp.nat _let_4))) (let ((_let_6 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s) _let_5))) (let ((_let_7 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int _let_6) _let_2))) (let ((_let_8 (tptp.ord_less tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_7) _let_1)))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.comm_semiring_1 tptp.int))) (let ((_let_13 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_4))) tptp.m)) _let_2))) (let ((_let_14 (tptp.times_times tptp.int _let_13))) (let ((_let_15 (tptp.hAPP tptp.int tptp.int _let_14 tptp.t))) (let ((_let_16 (tptp.number_number_of tptp.int tptp.pls))) (let ((_let_17 (tptp.ord_less_eq tptp.int))) (let ((_let_18 (tptp.hAPP tptp.int _let_9 _let_17 _let_1))) (let ((_let_19 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_20 (= (tptp.legendre _let_19 _let_13) _let_2))) (let ((_let_21 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes _let_13) _let_19)))) (let ((_let_22 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int _let_6) _let_19))) (let ((_let_23 (tptp.hAPP tptp.int _let_9 (tptp.dvd_dvd tptp.int) _let_13))) (let ((_let_24 (tptp.hAPP tptp.int _let_9 _let_17 tptp.pls))) (let ((_let_25 (tptp.hAPP tptp.int _let_9 _let_17 tptp.min))) (let ((_let_26 (tptp.hAPP tptp.int _let_9 _let_8 tptp.min))) (let ((_let_27 (tptp.hAPP tptp.int _let_9 _let_8 tptp.pls))) (let ((_let_28 (tptp.zero_zero tptp.nat))) (let ((_let_29 (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1) _let_1))))))) (let ((_let_30 (tptp.number_number_of tptp.int _let_4))) (let ((_let_31 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s1) _let_5))) (let ((_let_32 (tptp.hAPP tptp.int _let_9 _let_8 _let_1))) (let ((_let_33 (tptp.number_number_of tptp.nat _let_3))) (let ((_let_34 (tptp.one_one tptp.nat))) (let ((_let_35 (tptp.number_number_of tptp.nat tptp.pls))) (let ((_let_36 (forall ((T_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int tptp.s) (tptp.number_number_of tptp.nat _let_2))) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_2))) tptp.m)) _let_1)) T_4)))))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.hAPP tptp.int _let_9 _let_8 tptp.t))) (let ((_let_39 (= _let_7 _let_15))) (let ((_let_40 (tptp.hAPP tptp.int tptp.int _let_14 _let_1))) (let ((_let_41 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_15) _let_40)))) (let ((_let_42 (= _let_15 _let_7))) (let ((_let_43 (= _let_7 (tptp.hAPP tptp.int tptp.int _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_44 (= _let_1 _let_40))) (let ((_let_45 (ASSUME :args (_let_41)))) (let ((_let_46 (SYMM (ASSUME :args (_let_39))))) (let ((_let_47 (ASSUME :args (_let_11)))) (let ((_let_48 (_let_37))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (or))) (let ((_let_51 (_let_43))) (let ((_let_52 (not _let_43))) (let ((_let_53 (not _let_12))) (let ((_let_54 (or _let_53 _let_44))) (let ((_let_55 (forall ((X_a $$unsorted) (BOUND_VARIABLE_21056 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (or (not (tptp.comm_semiring_1 X_a)) (= _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a BOUND_VARIABLE_21056) _let_1))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (not _let_44))) (let ((_let_58 (not _let_42))) (let ((_let_59 (not _let_41))) (let ((_let_60 (APPLY_UF tptp.hBOOL))) (let ((_let_61 (APPLY_UF tptp.hAPP))) (let ((_let_62 (ASSUME :args (_let_44)))) (let ((_let_63 (SYMM _let_46))) (let ((_let_64 (REFL :args (_let_8)))) (let ((_let_65 (REFL :args (_let_9)))) (let ((_let_66 (REFL :args (tptp.int)))) (let ((_let_67 (ASSUME :args _let_51))) (let ((_let_68 (CONG _let_66 _let_65 _let_64 (TRANS (SYMM _let_67) _let_63) :args _let_61))) (let ((_let_69 (REFL :args (tptp.bool)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_47 _let_46 _let_67 _let_62 _let_45) :args (_let_41 _let_11 _let_42 _let_43 _let_44)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_45)) (CONG (CONG _let_66 _let_69 (SYMM _let_68) (REFL :args (_let_40)) :args _let_61) :args _let_60) (CONG (CONG _let_66 _let_69 (TRANS _let_68 (CONG _let_66 _let_65 _let_64 (SYMM _let_63) :args _let_61)) (SYMM _let_62) :args _let_61) :args _let_60) (FALSE_INTRO _let_47))) :args (_let_11 _let_42 _let_43 _let_44 _let_41)) :args ((not (and _let_41 _let_11 _let_42 _let_43 _let_44)) SB_LITERAL))) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) (REFL :args (_let_58)) (REFL :args (_let_52)) (REFL :args (_let_57)) :args _let_50)) :args ((or _let_10 _let_59 _let_58 _let_52 _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_44 (not _let_54)))) (ASSUME :args (_let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.int _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.times_times X_a BOUND_VARIABLE_21056)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_44 false _let_12 false _let_54)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_49) :args _let_48) (REWRITE :args ((=> _let_37 (not _let_52)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) (REFL :args _let_51) :args _let_50)) _let_49 :args (_let_43 true _let_36)) _let_47 _let_46 _let_45 :args (false false _let_44 false _let_43 true _let_10 false _let_42 false _let_41)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combb X_b X_c X_a (tptp.ti (tptp.fun X_b X_c) B_1_1) B_2_1) (tptp.combb X_b X_c X_a B_1_1 B_2_1))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combb X_b X_c X_a B_1_1 (tptp.ti (tptp.fun X_a X_b) B_2_1)) (tptp.combb X_b X_c X_a B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a B_1_1 B_2_1))) (= (tptp.ti (tptp.fun X_a X_c) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combc X_a X_b X_c (tptp.ti (tptp.fun X_a (tptp.fun X_b X_c)) B_1_1) B_2_1) (tptp.combc X_a X_b X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combc X_a X_b X_c B_1_1 (tptp.ti X_b B_2_1)) (tptp.combc X_a X_b X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c B_1_1 B_2_1))) (= (tptp.ti (tptp.fun X_a X_c) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combs X_a X_b X_c (tptp.ti (tptp.fun X_a (tptp.fun X_b X_c)) B_1_1) B_2_1) (tptp.combs X_a X_b X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.combs X_a X_b X_c B_1_1 (tptp.ti (tptp.fun X_a X_b) B_2_1)) (tptp.combs X_a X_b X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c B_1_1 B_2_1))) (= (tptp.ti (tptp.fun X_a X_c) _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_div X_a) (= (tptp.div_mod X_a (tptp.ti X_a B_1_1)) (tptp.div_mod X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.div_mod X_a B_1_1))) (=> (tptp.semiring_div X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.group_add X_a) (= (tptp.minus_minus X_a (tptp.ti X_a B_1_1)) (tptp.minus_minus X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a B_1_1))) (=> (tptp.group_add X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.ti tptp.nat B_1_1)) (tptp.minus_minus tptp.nat B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat B_1_1))) (= (tptp.ti (tptp.fun tptp.nat 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) (X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1)) (tptp.plus_plus X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1))) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.monoid_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1)) (tptp.plus_plus X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1))) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1)) (tptp.plus_plus X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1)) (tptp.plus_plus X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.power X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.dvd X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.semiring X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.mult_zero X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.mult_zero X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1)) (tptp.times_times X_a B_1_1)))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.multInv (tptp.ti tptp.int B_1_1) B_2_1) (tptp.multInv B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.multInv B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.multInv B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.multInv B_1_1 B_2_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.d22set (tptp.ti tptp.int B_1_1)) (tptp.d22set B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.d22set B_1_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.zfact (tptp.ti tptp.int B_1_1)) (tptp.zfact B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.zfact B_1_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$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 $$unsorted)) (let ((_let_1 (tptp.zcong B_1_1 B_2_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (= (tptp.ti _let_9 tptp.zprime) tptp.zprime) (forall ((B_1_1 $$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) (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 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a B_1_1))) (=> (tptp.number X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$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 $$unsorted)) (= (tptp.product_Pair tptp.int tptp.int (tptp.ti tptp.int B_1_1) B_2_1) (tptp.product_Pair tptp.int tptp.int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.product_Pair tptp.int tptp.int B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.product_Pair tptp.int tptp.int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.int tptp.int B_1_1 B_2_1))) (= (tptp.ti (tptp.product_prod tptp.int tptp.int) _let_1) _let_1))) (forall ((B_1_1 $$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 $$unsorted)) (let ((_let_1 (tptp.quadRes B_1_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.sr (tptp.ti tptp.int B_1_1)) (tptp.sr B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.sr B_1_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.standardRes (tptp.ti tptp.int B_1_1) B_2_1) (tptp.standardRes B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.standardRes B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.standardRes B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.standardRes B_1_1 B_2_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((X_a $$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)))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (= (tptp.collect X_a (tptp.ti (tptp.fun X_a tptp.bool) B_1_1)) (tptp.collect X_a B_1_1))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a B_1_1))) (= (tptp.ti (tptp.fun X_a tptp.bool) _let_1) _let_1))) (= (tptp.ti _let_9 tptp.twoSqu658283162sum2sq) tptp.twoSqu658283162sum2sq) (forall ((B_1_1 $$unsorted)) (= (tptp.twoSqu1929807760sum2sq (tptp.ti (tptp.product_prod tptp.int tptp.int) B_1_1)) (tptp.twoSqu1929807760sum2sq B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.twoSqu1929807760sum2sq B_1_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.inv (tptp.ti tptp.int B_1_1) B_2_1) (tptp.inv B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.inv B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.inv B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.inv B_1_1 B_2_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.wset (tptp.ti tptp.int B_1_1) B_2_1) (tptp.wset B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.wset B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.wset B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.wset B_1_1 B_2_1))) (= (tptp.ti (tptp.fun tptp.int tptp.bool) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) tptp.fconj) tptp.fconj) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (= (tptp.member X_a (tptp.ti X_a B_1_1)) (tptp.member X_a B_1_1))) (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (let ((_let_1 (tptp.member X_a B_1_1))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (= (tptp.ti tptp.int tptp.m) tptp.m) (= (tptp.ti tptp.int tptp.s1) tptp.s1) (= (tptp.ti tptp.int tptp.s) tptp.s) (= (tptp.ti tptp.int tptp.t) tptp.t) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_38 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_38 _let_2)) _let_41 _let_39 (=> (= tptp.t _let_1) (= _let_7 _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_17 _let_2) tptp.t))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_32 _let_13)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y $$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.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_1))) (tptp.zero_zero X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y_1) _let_2)))) (or (not (= (tptp.ti X_a X) _let_1)) (not (= (tptp.ti X_a Y_1) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y_1 $$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.hAPP X_a 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_1) _let_2)) _let_1) (and (= (tptp.ti X_a X) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))) (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 $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_3 $$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_3) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= (tptp.ti X_a A_3) _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 $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_3) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1) (= (tptp.ti X_a A_3) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.one_one X_a)) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.bit1 tptp.pls)) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) (tptp.bit1 tptp.pls))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_38 _let_13)) _let_37 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_13)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq _let_15)) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W) W))) (forall ((K_1 $$unsorted)) (= (tptp.number_number_of tptp.int K_1) (tptp.ti tptp.int K_1))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z_1) W) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int W) Z_1))) (forall ((Z_1 $$unsorted) (W $$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_1) W)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1)))))) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int V)) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) W)))) (forall ((K $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.number_number_of X_a X)) (tptp.number_number_of X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X) Y_1)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_1 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z2) Z3))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 K_1)))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1)) (= (tptp.ti tptp.int Z_1) (tptp.ti tptp.int W))))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int X_1))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Y) Z_1)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 Z_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)))))) (forall ((K $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_24 tptp.pls)) (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)))))) (forall ((K $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((Z_2 $$unsorted) (W_1 $$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) Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_2) W_1)) (not (= (tptp.ti tptp.int Z_2) (tptp.ti tptp.int W_1))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int K_1))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_1)) (tptp.hAPP tptp.int tptp.int _let_1 J_1)))))))) (forall ((V_3 $$unsorted)) (= (= (tptp.number_number_of tptp.nat V_3) (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) V_3) tptp.pls)))) (forall ((V_3 $$unsorted)) (= (= (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat V_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V_3) tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$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)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_1)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) V_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a V)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a W)) Z_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) W))) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) W)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X) X)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y_1) Y_1))) _let_1)) (and (= (tptp.ti X_a X) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X_1 $$unsorted) (Y $$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.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) X_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y) Y))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$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.number_number_of X_a X)) (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) X) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$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.number_number_of X_a Y_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.pls) Y_1)))))) (forall ((V_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.number_number_of tptp.nat V_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) V_3)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (forall ((V_3 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a V_3))) (let ((_let_2 (tptp.number_number_of X_a W_1))) (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 ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K1 $$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) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) (tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((K $$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 ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((Z_3 $$unsorted) (Z_1 $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_2) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) Z_3) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int W_2) Z_3)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int W) Z_1)))))))) (= _let_35 _let_28) (= _let_28 _let_35) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.number_number_of X_a X)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X) (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.bit1 tptp.pls)) Y_1)))))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat _let_34) _let_34) _let_5) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int tptp.pls) W) tptp.pls)) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.bit0 K_1)) L_1) (tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K_1) L_1)))) (forall ((K $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z_1) (tptp.one_one tptp.int)) (tptp.ti tptp.int Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.one_one tptp.int)) Z_1) (tptp.ti tptp.int Z_1))) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.number_number_of tptp.int V)) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) W)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z2) W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int W))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 Z1)) (tptp.hAPP tptp.int tptp.int _let_1 Z2))))) (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)) (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 ((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 $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) L))))) (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 ((X_a $$unsorted) (X $$unsorted) (A_6 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.member X_a X) A_6)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_6 X)))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (= (tptp.collect X_a P_1) (tptp.ti (tptp.fun X_a tptp.bool) P_1))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.bit0 K)) (tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) L))))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 V_3) V_2)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.number_number_of tptp.nat V_3)) (tptp.number_number_of tptp.nat V_2))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 tptp.pls) V_2))) _let_3)))))) (forall ((Z_2 $$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_2)) (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_2))))) (= _let_33 _let_34) (= _let_34 _let_33) (forall ((W $$unsorted) (Z_1 $$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) W) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int W) (tptp.one_one tptp.int))) Z_1))))) (forall ((W_1 $$unsorted) (Z_2 $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int W_1) (tptp.one_one tptp.int))) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((W_1 $$unsorted) (Z_2 $$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_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z_2) (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) W_1) Z_2))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_1)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) V_1))))))))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat V_1))) (let ((_let_2 (tptp.number_number_of tptp.nat V))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat _let_2) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 V_1) tptp.pls)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 V) tptp.pls)))) (and (=> _let_7 (= _let_3 _let_1)) (=> (not _let_7) (and (=> _let_6 (= _let_3 _let_2)) (=> (not _let_6) (= _let_3 (tptp.number_number_of tptp.nat (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) V_1))))))))))))))) (forall ((Z_1 $$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) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int)) Z_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((X $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.number_number_of X_a X) (tptp.number_number_of X_a Y_1)) (= (tptp.ti tptp.int X) (tptp.ti tptp.int Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((W_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W_1))) (let ((_let_2 (tptp.ti X_a X))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.bit1 K) (tptp.bit1 L)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L)))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.bit0 K) (tptp.bit0 L)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L)))) (forall ((X_1 $$unsorted) (Y $$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_1) Y)) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X) X)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y_1) Y_1)) _let_1) (and (= (tptp.ti X_a X) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.hAPP X_b X_b (tptp.times_times X_b (tptp.hAPP X_b X_b (tptp.plus_plus X_b A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.plus_plus X_b (tptp.hAPP X_b X_b (tptp.times_times X_b A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.times_times X_b B) _let_1))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_b (tptp.number_number_of X_b V)))) (= (tptp.hAPP X_b X_b _let_1 (tptp.hAPP X_b X_b (tptp.plus_plus X_b B) C)) (tptp.hAPP X_b X_b (tptp.plus_plus X_b (tptp.hAPP X_b X_b _let_1 B)) (tptp.hAPP X_b X_b _let_1 C))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z2) Z3))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int X_1))) (let ((_let_2 (tptp.plus_plus tptp.int Y))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_2 Z_1)) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Z_1)))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z_1) W) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int W) Z_1))) (= _let_1 _let_16) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.times_times 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_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_1)) (tptp.hAPP tptp.int tptp.int _let_1 J_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_2) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y $$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_1) _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_1) Y)))))))))) (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 $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y_1 $$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.hAPP X_a 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_1) _let_2))) _let_1)) (and (= (tptp.ti X_a X) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X $$unsorted) (Y_1 $$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 X_a) _let_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X) X)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y_1) Y_1)))) (or (not (= (tptp.ti X_a X) _let_1)) (not (= (tptp.ti X_a Y_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) X_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y) Y))) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit1 tptp.pls))) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) (tptp.number_number_of X_a (tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (= _let_2 (tptp.number_number_of tptp.int _let_3)) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.bit1 K_1)) L_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K_1) L_1))) L_1))) (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Ma) N) _let_1) (and (= (tptp.ti tptp.int Ma) _let_1) (= (tptp.ti tptp.int N) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3) _let_1) (= (tptp.ti X_a A_3) _let_1)))))) (forall ((K_1 $$unsorted)) (not (= (tptp.bit1 K_1) tptp.pls))) (forall ((L_1 $$unsorted)) (not (= tptp.pls (tptp.bit1 L_1)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (not (= (tptp.bit1 K_1) (tptp.bit0 L_1)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (not (= (tptp.bit0 K_1) (tptp.bit1 L_1)))) (forall ((K $$unsorted)) (= (= (tptp.bit0 K) tptp.pls) (= (tptp.ti tptp.int K) tptp.pls))) (forall ((L $$unsorted)) (= (= tptp.pls (tptp.bit0 L)) (= tptp.pls (tptp.ti tptp.int L)))) (= (tptp.bit0 tptp.pls) tptp.pls) (= tptp.pls _let_1) (forall ((K1 $$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 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) (tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 tptp.pls))) (forall ((K1 $$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 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit0 K)) (tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (not (= _let_1 _let_2)) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K_1) tptp.pls) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int tptp.pls) K_1) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.bit0 K_1)) (tptp.bit0 L_1)) (tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K_1) L_1)))) (forall ((K_1 $$unsorted)) (= (tptp.bit0 K_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K_1) K_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z_1) (tptp.zero_zero tptp.int)) (tptp.ti tptp.int Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.zero_zero tptp.int)) Z_1) (tptp.ti tptp.int Z_1))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int I_1) K_1)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int J_1) K_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a _let_1) _let_1)) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.bit0 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) A_1)) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a Z_1) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a Z_1) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a Z_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.plus_plus X_a Z_1) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a Z_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.plus_plus X_a Z_1) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_3) _let_1))))))))) (forall ((X_a $$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.hAPP X_a X_a (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.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.number_number_of X_a tptp.pls)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a X)) (tptp.number_number_of X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X) Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a W)) Z_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) W))) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) W)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a W)))))) (forall ((K $$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 $$unsorted) (L $$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))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.bit1 W_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 W_1) _let_1))))))) (forall ((K $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 _let_1))) (forall ((W_1 $$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.bit0 W_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 W_1) _let_1))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.bit1 K_1)) (tptp.bit0 L_1)) (tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K_1) L_1)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.bit0 K_1)) (tptp.bit1 L_1)) (tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K_1) L_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_32 _let_2)) (forall ((K_1 $$unsorted)) (= (tptp.bit1 K_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int)) K_1)) K_1))) (forall ((Z_1 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int)) Z_1)) Z_1) (tptp.zero_zero tptp.int)))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int Z_2) (tptp.one_one tptp.int)))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_2)) (= (tptp.ti tptp.int W_1) (tptp.ti tptp.int Z_2)))))) (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.hAPP X_b X_b (tptp.times_times X_b _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_1) Y)) _let_2) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2))) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1)) X_1)) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit0 W)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.zero_zero X_a)) _let_1)) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit1 W)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.one_one X_a)) _let_1)) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.number_number_of X_a (tptp.bit1 tptp.pls))))) (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int)) Z_2)) Z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Z_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a X)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.number_number_of X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) Y_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_semiring X_a) (= (tptp.hAPP X_a 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 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_ring X_a) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a _let_1) _let_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.number_number_of X_a X)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X) (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.bit1 tptp.pls)) Y_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_23 _let_7)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_2))) (let ((_let_4 (tptp.power_power tptp.int B))) (let ((_let_5 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_2)))) (let ((_let_7 (tptp.power_power tptp.int A_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) B)) _let_3) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int _let_7 _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_6 (tptp.hAPP tptp.nat tptp.int _let_7 _let_5))) B))) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_6 A_1)) (tptp.hAPP tptp.nat tptp.int _let_4 _let_5)))) (tptp.hAPP tptp.nat tptp.int _let_4 _let_3))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) B)) _let_2) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1)) A_1)) B))) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B) _let_2)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int X_1))) (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_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) X_1) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))))) (or (= _let_1 _let_2) (= _let_1 (tptp.one_one tptp.int))))))))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 tptp.s)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 tptp.s) _let_13)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 tptp.s) _let_13))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.power_power tptp.int A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.number_number_of tptp.nat (tptp.bit1 _let_1))))))) (forall ((X_1 $$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) X_1) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((R_1 $$unsorted) (Q_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) A_1)) (=> (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int R_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) Q_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 R_1) A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Q_1)))))))) (forall ((R_1 $$unsorted) (Q_1 $$unsorted) (A_1 $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int R_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) Q_1))) (=> (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_1) (tptp.one_one tptp.int)))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 _let_30)) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a X_1))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a _let_2) _let_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) X_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_6 _let_31) _let_13)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int 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_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) X_2) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 X_2) _let_1)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) Y_2) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 Y_2) _let_1))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2)))))))))) (not (forall ((S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int 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_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) S_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong tptp.s1 S_1) _let_1)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_31 _let_19) _let_13)) (forall ((X $$unsorted) (N $$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 X) N))) (or (= N _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X))))))) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (P_3 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a X_1))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_1 P_3)) Q_1) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat P_3) Q_1))))))) (forall ((N_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int P_3) N_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_3) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1))))))))) (forall ((N_1 $$unsorted) (B $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int P_3) N_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_3) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int X_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.nat tptp.int _let_1 Y)) Z_1) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Y) Z_1))))) (forall ((N_1 $$unsorted) (M $$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_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) N_1) M)))))))) (forall ((N_1 $$unsorted) (M $$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_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N_1) M)) (= (tptp.ti tptp.int M) (tptp.ti tptp.int N_1)))))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.times_times tptp.int K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 M)) (tptp.hAPP tptp.int tptp.int _let_3 N_1))) (=> (not (= (tptp.ti tptp.int K_1) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N_1)))))))) (forall ((K $$unsorted) (N $$unsorted) (Ma $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int N) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K) Ma)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N))))) (forall ((C_1 $$unsorted) (X $$unsorted) (Ta $$unsorted) (A_3 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int X))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) A_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 D)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Ta))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int C_1) D))) Ta)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_30)) (forall ((Z_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Z_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_1) N_1)))))) (forall ((Y $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) Y)))))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V_3))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.number_number_of tptp.nat V_3)) (tptp.number_number_of tptp.nat V_2))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 tptp.pls)))))) (forall ((X_a $$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))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Ly)) (tptp.hAPP X_a X_a (tptp.times_times X_a Rx) Ry)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Rx)) (tptp.hAPP X_a X_a (tptp.times_times X_a Ly) Ry))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.times_times X_a Lx) Ly)))) (let ((_let_2 (tptp.times_times X_a Rx))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 Ry)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 Ry)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a Rx) Ry))) (let ((_let_2 (tptp.times_times X_a Lx))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_2 Ly)) _let_1) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (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)) (let ((_let_1 (tptp.times_times X_a Lx))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Ly)) Rx) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Rx)) Ly)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a Lx))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Ly)) Rx) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a Ly) Rx))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Lx))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a Rx) Ry)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 Rx)) Ry)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Lx))) (let ((_let_2 (tptp.times_times X_a Rx))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 Ry)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 Ry)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B) (tptp.hAPP X_a X_a (tptp.times_times X_a B) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C) (tptp.hAPP X_a X_a (tptp.plus_plus X_a C) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (let ((_let_2 (tptp.plus_plus X_a C))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 D_2)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 D_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a C) D_2)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 C)) D_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 C)) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a C) D_2)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) (tptp.one_one tptp.nat)) (tptp.ti X_a X_1))))) (forall ((X $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) _let_3))) (or (= _let_3 _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X)))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Z_1) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Z_1) Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Z_1) Z_1))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V)) (tptp.number_number_of tptp.nat V_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.number_number_of tptp.nat (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) V_1)))))))) (forall ((V_1 $$unsorted) (K_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V_1)) 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) tptp.pls)))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int V) V_1))) K_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat _let_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_2 N_1)) _let_1))))))) (forall ((X_a $$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.hAPP tptp.nat tptp.nat (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 $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a _let_1) A_1) _let_1))))) _let_29 (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (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.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (= (= (tptp.ti X_a B_2) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B_2) A_3)) (= (tptp.ti X_a A_3) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a X_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a Y) Z_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 Y)) (tptp.hAPP X_a X_a _let_1 Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C_1 $$unsorted) (D $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_2))) (let ((_let_2 (tptp.times_times X_a A_3))) (= (and (not (= (tptp.ti X_a A_3) (tptp.ti X_a B_2))) (not (= (tptp.ti X_a C_1) (tptp.ti X_a D)))) (not (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_2 C_1)) (tptp.hAPP X_a X_a _let_1 D)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_2 D)) (tptp.hAPP X_a X_a _let_1 C_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) M)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) M)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) M))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((W_1 $$unsorted) (Y_1 $$unsorted) (X $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a X))) (let ((_let_2 (tptp.times_times X_a W_1))) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_2 Y_1)) (tptp.hAPP X_a X_a _let_1 Z_2)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_2 Z_2)) (tptp.hAPP X_a X_a _let_1 Y_1))) (or (= (tptp.ti X_a W_1) (tptp.ti X_a X)) (= (tptp.ti X_a Y_1) (tptp.ti X_a Z_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) Y)) Q_1) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) Q_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) Q_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (P_3 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a X_1))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 P_3)) (tptp.hAPP tptp.nat X_a _let_1 Q_1)) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat P_3) Q_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 _let_1)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N_1 $$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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a R_1))) (=> (not (= (tptp.ti X_a R_1) (tptp.zero_zero X_a))) (=> (and (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (not (= (tptp.ti X_a C) (tptp.ti X_a D_2)))) (not (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.hAPP X_a X_a _let_1 C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) (tptp.hAPP X_a X_a _let_1 D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a M) M) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a 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 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a M) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) M)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.one_one X_a))) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) M)) M) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.one_one X_a))) M))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_3 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat W_1))) (let ((_let_2 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_3) _let_1) _let_2) (and (= (tptp.ti X_a A_3) _let_2) (not (= _let_1 (tptp.zero_zero tptp.nat)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 _let_2)) (forall ((Y $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) Y))))))) (forall ((Y $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int X_1) Y))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) N_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat W))) (let ((_let_3 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) _let_2))) (let ((_let_4 (= _let_2 (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 (tptp.one_one X_a))) (=> (not _let_4) (= _let_3 _let_1)))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 (tptp.number_number_of tptp.int (tptp.bit1 _let_3)))) (forall ((B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_3) Q_4)) R_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_3) B_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) B_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Q_4)))))))))) (forall ((B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_3) Q_4)) R_3)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) R_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) B_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Q_4) _let_1)))))))))) (forall ((B $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted) (Q_1 $$unsorted) (R_1 $$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))) (let ((_let_4 (tptp.times_times tptp.int B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 Q_4)) R_3)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) R_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_3) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_4) Q_1))))))))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_3) Q_4)) R_3))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) Q_1)) 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_3) B_3)) (=> (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_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_3) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q_4))))))))))))))) (forall ((B $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B))) (let ((_let_4 (tptp.times_times tptp.int B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 Q_4)) R_3)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 R_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q_4))))))))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_3) Q_4)) R_3))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) Q_1)) R_1) _let_5) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_5) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_3) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_4) Q_1)))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power tptp.int X_1))) (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)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_6 _let_19) _let_13)) (forall ((Y $$unsorted) (X_1 $$unsorted) (P_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_1) P_3)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3) Y)))))) (forall ((P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (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_2)) (forall ((M_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M_2))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) M_2) P_2))) (or (= _let_1 (tptp.one_one tptp.int)) (= _let_1 (tptp.ti tptp.int P_2)))))))))) (forall ((P_3 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (let ((_let_3 (tptp.ti tptp.int P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (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_3))))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_28) _let_5)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_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 A_1) B)) (=> (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_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_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B) N_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord626643107strict X_a) (forall ((V $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X_1 $$unsorted) (A_1 $$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_1) 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)) (=> (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a U_1) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a U_1) X_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a V) Y))) A_1))))))))))))) (forall ((Y $$unsorted) (N_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.zero_zero X_a)))))) (not (forall ((S1 $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1))) tptp.m)) (tptp.one_one tptp.int)))))))) _let_20 (forall ((K $$unsorted)) (= (= (tptp.bit1 K) tptp.min) (= (tptp.ti tptp.int K) tptp.min))) (forall ((L $$unsorted)) (= (= tptp.min (tptp.bit1 L)) (= tptp.min (tptp.ti tptp.int L)))) (= (tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K_1 $$unsorted)) (not (= (tptp.bit0 K_1) tptp.min))) (forall ((L_1 $$unsorted)) (not (= tptp.min (tptp.bit0 L_1)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 tptp.min))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_25 tptp.min)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min)))))) (forall ((K $$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))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_27 tptp.min))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 tptp.pls)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.min))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 _let_1)) (forall ((K $$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 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_25 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_24 tptp.min))) (forall ((K $$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_16 _let_19)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) tptp.min))))) (forall ((K $$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 ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.ti tptp.int N))) (let ((_let_3 (tptp.ti tptp.int Ma))) (let ((_let_4 (tptp.one_one tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Ma) N) _let_4) (or (and (= _let_3 _let_4) (= _let_2 _let_4)) (and (= _let_3 _let_1) (= _let_2 _let_1))))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M))) (let ((_let_2 (tptp.one_one tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int M) N_1) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.number_number_of tptp.int tptp.min))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B_2 A_3) Ma)))) (forall ((K_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 K_1) M))) (forall ((D_2 $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (=> (= (tptp.ti tptp.int B) (tptp.ti tptp.int C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 D_2) M)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B C) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 C) M))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.number_number_of tptp.int tptp.min)) P_3)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.one_one tptp.int)) P_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y $$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_1) Y)) (=> (not (= (tptp.ti X_a X_1) (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_1) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B) _let_1) (or (= (tptp.ti X_a A_1) _let_1) (= (tptp.ti X_a B) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (=> (not (= (tptp.ti X_a B) _let_1)) (not (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_n68954251visors X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) B_2) _let_1) (or (= (tptp.ti X_a A_3) _let_1) (= (tptp.ti X_a B_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (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.semiring X_a) (forall ((A_1 $$unsorted) (E_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) E_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B) E_1)) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) E_1)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (not (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) _let_1) A_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (N_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) N_1) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B) N_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a _let_1) A_1) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$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.hAPP X_a X_a (tptp.times_times X_a B) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((B $$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.hAPP X_a X_a (tptp.times_times X_a B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dvd X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (K_1 $$unsorted)) (=> (= A_1 (tptp.hAPP X_a X_a (tptp.times_times X_a B) K_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) B) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a _let_1) N_1) _let_1))))) (forall ((X_a $$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 ((N_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) N_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted) (N_1 $$unsorted) (B $$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_1)) B)) (=> (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_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)) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N_1 $$unsorted) (M $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) M)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1)))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (I_1 $$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_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) I_1)) (=> (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_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))))) (forall ((X $$unsorted) (N $$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 X) N))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X)) (= N _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.hAPP tptp.nat X_a _let_1 M)) N_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 B) C)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) (tptp.one_one tptp.nat)) (tptp.ti X_a A_1))))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong M (tptp.zero_zero tptp.int)) M))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int A_3) (tptp.ti tptp.int B_2)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) (tptp.one_one tptp.int)))) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) M) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) M)) M))) (forall ((C_1 $$unsorted) (D $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_3) D)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_2) D)) Ma))))) (forall ((C_1 $$unsorted) (D $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int D))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.hAPP tptp.int tptp.int _let_1 A_3)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C_1 (tptp.hAPP tptp.int tptp.int _let_1 B_2)) Ma)))))) (forall ((K_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) K_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) K_1)) M)))) (forall ((K_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 A_1) (tptp.hAPP tptp.int tptp.int _let_1 B)) M))))) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) C) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) D_2)) M))))) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) C) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int B) D_2)) M))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) C) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int B) C)) M)))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 Y) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) Z_1) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) Z_1)) M)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a (tptp.number_number_of X_a tptp.min)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$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) _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)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$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)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (=> (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.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere1490568538miring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$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) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$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) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) B_2)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_2) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_3) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$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))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) B_2))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_2))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_3) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_2) _let_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.hAPP X_a X_a (tptp.times_times X_a A_1) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (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 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$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) 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.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord893533164strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (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) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (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) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_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 A_1) B)) (=> (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.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C_1))) (=> (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.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) A_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a B) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (B $$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.hAPP X_a X_a (tptp.times_times X_a A_1) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$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) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.times_times X_a C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 A_3)) (tptp.hAPP X_a X_a _let_4 B_2))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) A_3)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) C_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) C_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) A_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C))))))))))) (forall ((X_a $$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_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 X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (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) (forall ((N_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B) N_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_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 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a M) N_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_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 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)))))))) (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.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (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_3) B_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (B_2 $$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.hAPP X_a X_a (tptp.times_times X_a A_3) C_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) 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_3) B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (N_3 $$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_1) N_3)) (=> (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_1)) (tptp.hAPP tptp.nat X_a _let_1 N_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (N $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) A_3)) (= (= (tptp.hAPP tptp.nat X_a _let_1 Ma) (tptp.hAPP tptp.nat X_a _let_1 N)) (= Ma N))))))) (forall ((X_a $$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_3 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_3) N) _let_1) (and (= (tptp.ti X_a A_3) _let_1) (not (= N (tptp.zero_zero tptp.nat))))))))) (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 $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))))))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B) A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M))))))))))) (forall ((M $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 X_1) M)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 _let_1) M))))))))) (forall ((M $$unsorted) (Y $$unsorted) (X_1 $$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 X_1)) (=> (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_1 Y) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) M)) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y)))))))))))) (forall ((N_1 $$unsorted) (M $$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_1) 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_1) M))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (exists ((K_2 $$unsorted)) (= (tptp.ti tptp.int B_2) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_3) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Ma) K_2)))))) (forall ((X $$unsorted) (P_2 $$unsorted)) (= (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.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_2) X)))) (forall ((A_3 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 (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_3)))) (forall ((M $$unsorted) (N_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int M) N_1))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_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))) (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)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (=> (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.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 C) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_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.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)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (=> (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.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_3) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) D_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) A_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X_1 $$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 _let_3 X_1)) (=> (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.hAPP X_a X_a (tptp.times_times X_a Y) X_1)) X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) Y)) X_1))))))))))) (forall ((X_a $$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.hAPP X_a X_a (tptp.plus_plus X_a _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_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.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B) N_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)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (N_3 $$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_1) N_3)) (=> (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_3)) (tptp.hAPP tptp.nat X_a _let_1 N_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted) (A_1 $$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_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_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a B_2))) (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_2)) (= (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 X)) (tptp.hAPP tptp.nat X_a _let_1 Y_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) X) Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$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.hAPP X_a X_a (tptp.times_times X_a A_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((N_1 $$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_1))) (let ((_let_3 (= N_1 (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_1 $$unsorted) (N_3 $$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_1) N_3)) (=> (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_1)) (tptp.hAPP tptp.nat X_a _let_1 N_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted) (A_1 $$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_1))) (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_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a B_2))) (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_2)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 X)) (tptp.hAPP tptp.nat X_a _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) Y_1)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real (tptp.bit0 _let_1))) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X_1) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1)) X_1)) _let_2))))) (forall ((M $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) X_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 _let_1) M)) (= (tptp.ti tptp.int X_1) _let_1))))))) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) M)) (= (tptp.ti tptp.int A_1) _let_1))))))) (forall ((B $$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)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (= (tptp.ti tptp.int A_1) (tptp.ti tptp.int B))))))))))) (forall ((P_3 $$unsorted) (Y $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y) N_1))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.power_power tptp.int X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 Y) _let_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Y) Z_1)) _let_1) P_3)))))) (forall ((Y $$unsorted) (X_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 _let_1) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong Y _let_1) P_3))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) Y) _let_1) P_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1278240602ring_1 X_a) (forall ((V $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X_1 $$unsorted) (A_1 $$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_1) 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)) (=> (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a U_1) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a U_1) X_1)) (tptp.hAPP X_a X_a (tptp.times_times X_a V) Y))) A_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_3)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_3)) (tptp.hAPP tptp.nat X_a _let_1 N_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.power_power X_a A_1) N_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a B) N_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.ti X_a A_1) (tptp.ti X_a B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$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_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_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.ti X_a X_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X_1) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) N_1))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (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.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) B) _let_1) P_3)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B _let_1) P_3)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) A_1)) (=> (and (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_3))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong B _let_1) P_3)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) B) _let_1) P_3)))))))) (forall ((N_1 $$unsorted) (P_3 $$unsorted) (M $$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_3))) (=> (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_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int M) N_1))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 N_1))))))))) _let_21 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_23 _let_22)) (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))))) (= _let_22 _let_7) (=> (not _let_21) (not _let_20)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real X) X)))) (= X _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int V) W)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.number_number_of X_a V)) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a Y) Z_1))))))))) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K_1) tptp.pls) (tptp.ti tptp.int K_1))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.bit0 K_1)) (tptp.bit0 L_1)) (tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K_1) L_1)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int Z2) W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int W))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 Z1)) (tptp.hAPP tptp.int tptp.int _let_1 Z2))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) B) (tptp.ti tptp.int C)) (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int C) B)))) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong C D_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) C) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int B) D_2)) M))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$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.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D)) (= (tptp.ti X_a C_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a B_2) A_3)) E)) D)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2)) E)) C_1) (tptp.ti X_a D)))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_b (tptp.number_number_of X_b V)))) (= (tptp.hAPP X_b X_b _let_1 (tptp.hAPP X_b X_b (tptp.minus_minus X_b B) C)) (tptp.hAPP X_b X_b (tptp.minus_minus X_b (tptp.hAPP X_b X_b _let_1 B)) (tptp.hAPP X_b X_b _let_1 C))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.hAPP X_b X_b (tptp.times_times X_b (tptp.hAPP X_b X_b (tptp.minus_minus X_b A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.minus_minus X_b (tptp.hAPP X_b X_b (tptp.times_times X_b A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.times_times X_b B) _let_1))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.bit1 K_1)) (tptp.bit0 L_1)) (tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K_1) L_1)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.bit1 K_1)) (tptp.bit1 L_1)) (tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K_1) L_1)))) (forall ((L_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int tptp.pls))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.bit0 L_1)) (tptp.bit0 (tptp.hAPP tptp.int tptp.int _let_1 L_1))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K) L)) (tptp.zero_zero tptp.int))))))) (forall ((A_1 $$unsorted) (R_1 $$unsorted) (B $$unsorted) (M $$unsorted) (C $$unsorted) (D_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int R_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) (tptp.hAPP tptp.int tptp.int _let_1 B))) M)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int C) (tptp.hAPP tptp.int tptp.int _let_1 D_2))) N_1)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int C) N_1))) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) M)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int D_2) N_1))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Ma) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_3) B_2))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2)) E)) C_1)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a B_2) A_3)) E)) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a B_2) A_3)) E)) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_3 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_3) E)) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B_2) E)) D))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2)) E)) C_1)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.number_number_of X_a V)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.number_number_of X_a W)) C)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.number_number_of X_a (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int V) W))) C))))) (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 _let_2 X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti tptp.int X_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 _let_1)))))))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int Z_2) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((L_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int tptp.pls) (tptp.bit1 L_1)) (tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int tptp.min) L_1)))) (forall ((L_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int tptp.min))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.bit0 L_1)) (tptp.bit1 (tptp.hAPP tptp.int tptp.int _let_1 L_1))))) (forall ((L_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int tptp.min))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.bit1 L_1)) (tptp.bit0 (tptp.hAPP tptp.int tptp.int _let_1 L_1))))) (forall ((A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_3) _let_2) _let_1) P_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 _let_2) P_2)))))) (forall ((I_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.power_power tptp.nat I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ti tptp.int A_1))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) A_1) _let_1) P_3)) (or (= _let_2 _let_1) (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1)))))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) A_1) _let_1) P_3)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1)) P_3)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X_1 $$unsorted) (Y $$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.hAPP X_a X_a (tptp.minus_minus X_a X_1) Y)) _let_2) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP tptp.nat X_a (tptp.power_power X_a X_1) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.power_power X_a Y) _let_2))) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1)) X_1)) Y)))))))) (forall ((A_1 $$unsorted) (B $$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.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) B)) _let_2) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1)) A_1)) B))) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B) _let_2)))))) (forall ((A_1 $$unsorted) (B $$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))) (let ((_let_5 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times tptp.int (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.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_1) B)) _let_3) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.nat tptp.int _let_7 _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_6 (tptp.hAPP tptp.nat tptp.int _let_7 _let_5))) B))) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int 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 ((N_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int _let_1) N_1))) (or (= _let_2 (tptp.one_one tptp.int)) (= _let_2 _let_1))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int 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))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.legendre A_1 P_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes P_3) 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_3)))) (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 $$unsorted) (X $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes Ma) X)) (exists ((Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int Y_2) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X) Ma))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real X_1) Y)) _let_2) (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X_1) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Y) _let_2))) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1)) X_1)) Y)))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N_1) M)) (or (= M (tptp.zero_zero tptp.nat)) (= M N_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)) M)))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X))) (= X Y_1))))) (forall ((B $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat B) C))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat C))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 A_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 B)))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X_1) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Y) N_1))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) N_1))) (let ((_let_2 (tptp.zero_zero tptp.nat))) (let ((_let_3 (= M _let_2))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) (tptp.one_one tptp.nat))) N_1))))))))) (forall ((P_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.power_power tptp.nat P_3))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M))) (let ((_let_4 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat P_3) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) _let_1))))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X_1) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Y) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat X_1) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat X_1) Y))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) A_1) B)) (or (= B (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) A_1) B)))))) (forall ((Ma $$unsorted) (K $$unsorted) (N $$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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) 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) N))))))) (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) Ma) _let_1) (and (= N _let_1) (= Ma _let_1))))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat Ma) N) _let_1) (and (not (= N _let_1)) (= Ma _let_1))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X_1) N_1)) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y))))))) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (B $$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_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat B) N_1))) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat X) N) _let_1) (or (= X _let_1) (= N (tptp.zero_zero tptp.nat)))))) (forall ((X_1 $$unsorted) (Q_1 $$unsorted) (N_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (= X_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Q_1) N_1)) 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_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N_1) X_1))))))))) (forall ((X $$unsorted) (Y_1 $$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.hAPP tptp.real 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_1) _let_2)) _let_1) (and (= X _let_1) (= Y_1 _let_1)))))) (forall ((A_1 $$unsorted) (N_1 $$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)) N_1)) (=> (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_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real X_2) N_1) A_1) (forall ((Y_2 $$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_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real Y_2) N_1) A_1)) (= Y_2 X_2)))))))) (forall ((A_1 $$unsorted) (N_1 $$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)) N_1)) (=> (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_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.power_power tptp.real R_2) N_1) A_1)))))) (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) Ma)) Ma)) (= N (tptp.one_one tptp.nat)))))) (forall ((X_1 $$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_1) X_1))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$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) (tptp.zero_zero tptp.nat)) N_1))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat I_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 J_1)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 K_1)) J_1)))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat _let_1) N_1) _let_1))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) (tptp.zero_zero tptp.nat)) M)) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) M) (tptp.zero_zero tptp.nat))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) M) _let_1) (= M N_1))))) (not (= (tptp.zero_zero tptp.real) (tptp.one_one tptp.real))) (forall ((X $$unsorted) (Y_1 $$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 _let_1 X) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.minus_minus tptp.real X) Y_1)) (tptp.zero_zero tptp.real))))))) (forall ((X $$unsorted) (Y_1 $$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) X) Y_1)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X) Y_1)) (not (= X Y_1)))))) (forall ((X $$unsorted) (Y_1 $$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) X) Y_1)) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X) Y_1)) (= X Y_1))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_1)))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= Ma N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) Ma))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X_1 Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1))))))) (forall ((N_1 $$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) N_1) N_1)))) (forall ((N_1 $$unsorted) (M $$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_1) M)) (not (= M N_1)))) (forall ((S $$unsorted) (T_3 $$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) T_3)) (not (= S T_3)))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 N) Ma)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Ma) N)) _let_2) (=> (=> (= Ma N) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N) Ma)) _let_2) _let_2))))))) (forall ((N_1 $$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.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) N_1)) K_1)))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat L_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$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_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X_1))) (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_1)))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X_1)))))))))))) (forall ((A_1 $$unsorted) (B $$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)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 X_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Z_1) X_1))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$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)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))) (=> (= B 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 $$unsorted) (X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X)))) (=> (and _let_3 (not _let_4)) (=> (and _let_4 (not _let_3)) (tptp.hBOOL P_1)))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (not (= Y X_1)))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (not (= X_1 Y)))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)))) (=> (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) _let_3))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (not (= X_1 Y)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$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_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X_1))) (=> (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_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X_1))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 C))) (=> (= A_1 B) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 A_1)))))))))) (forall ((N_1 $$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_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z_1)))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)) (= X_1 Y)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M)) (= M N_1)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$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)) (=> (= B C) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 C)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (= A_1 B) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)))) (=> _let_3 (=> (not (= A_1 B)) (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))))))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y)))) (=> _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X_1)))) (= X_1 Y))))))) (forall ((Y_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)) (= X Y_1)))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (=> (= X_1 Y) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_1) Y)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)))) (=> (not (= A_1 B)) (=> _let_3 (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))))))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X)))))) (= _let_3 _let_3))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)))) (= (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X)))) (and _let_3 (not (= X Y_1)))))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)))) (= _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X)))) (= X Y_1))))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (= X Y_1) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X))))))) (forall ((X_1 $$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_1) X_1)))) (not (and _let_1 (not _let_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) M))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat X_1))) (let ((_let_2 (tptp.plus_plus tptp.nat Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_2 Z_1)) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 Z_1)))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) K_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (= Ma N)))) (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N) K)) (= Ma N))) (forall ((M $$unsorted) (N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1)) N_1) M)) (forall ((N_1 $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) M)) N_1) M)) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat I_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 J_1)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) K_1))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat K_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)))) (forall ((M $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real Z1))) (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.hAPP tptp.real tptp.real _let_1 Z2)) Z3) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Z2) Z3))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Z_1) W) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real W) Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.one_one tptp.real)) Z_1) Z_1)) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M)) (= M N_1)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$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_1))) (=> (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 $$unsorted) (N_1 $$unsorted)) (=> (= M N_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_1)))) (forall ((M $$unsorted) (N_1 $$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_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M)))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_1))) (forall ((N $$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 N)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N))))))))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat M))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) K_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))))) (forall ((N $$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 N)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N) K)) (= Ma N)))))) (forall ((I_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat N_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) I_1) N_1)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) I_1)))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) L_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) L_1))))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat L_1))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))) (forall ((M $$unsorted) (N_1 $$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) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) M))) (forall ((M $$unsorted) (N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) M))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) K_1))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) K_1)))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.real Z_1))) (let ((_let_2 (tptp.ord_less_eq 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 X_1) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X_1)) (tptp.hAPP tptp.real tptp.real _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted) (D_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) B)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a C) D_2)))))) (forall ((N_1 $$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) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((N_1 $$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) N_1) (tptp.zero_zero tptp.nat))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)) (not (= N_1 (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) M)))))))) (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N) Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.zero_zero tptp.nat)) N_1) N_1)) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) (tptp.zero_zero tptp.nat)) M)) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Ma) N) _let_1) (and (= Ma _let_1) (= N _let_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1) M) (= N_1 (tptp.zero_zero tptp.nat)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) M)) (tptp.zero_zero tptp.nat))) (forall ((N_1 $$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) (tptp.zero_zero tptp.nat)) N_1))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) _let_1)) (= N _let_1)))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat Ma) N) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N)))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1) (tptp.zero_zero tptp.nat)))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat _let_1) N_1) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) _let_1) _let_1))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) N) _let_1) (or (= Ma _let_1) (= N _let_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (or (= Ma N) (= K (tptp.zero_zero tptp.nat)))))) (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) K)) (or (= Ma N) (= K (tptp.zero_zero tptp.nat))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real C_1))) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real _let_1 A_3) (tptp.hAPP tptp.real tptp.real _let_1 B_2)) (= A_3 B_2))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real A_3) C_1) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real B_2) C_1)) (= A_3 B_2)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) J_1)) I_1)))) (forall ((J_1 $$unsorted) (I_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) I_1)) I_1)))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (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 Ma) N))))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) M)))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) J_1)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) K_1))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) L_1)))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_1)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) L_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat K_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1))))))) (forall ((I_1 $$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.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) J_1)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_1)))))) (forall ((M $$unsorted) (N_1 $$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) M) N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) M))) (forall ((I_2 $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_2) K)) J_2)))))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) N)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N)) (not (= Ma N)))))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) N)) (= Ma N))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1)) (=> (not (= M N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)) (= M N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$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)) (=> (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.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat B) C)))))))) (forall ((N $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N))))))))) (forall ((K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$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.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N_1) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N_1) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1)))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) M)))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N)) (exists ((K_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Ma) K_2))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N))))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) M)))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) J_1)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$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_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) K_1))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_1 $$unsorted) (J_1 $$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_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) L_1)))))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N_1)))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N_1 $$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.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) K_1)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N_1))))))))) (forall ((I_1 $$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.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_1)) J_1)))) (forall ((J_2 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) K)) I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_2) K))))))) (forall ((M $$unsorted) (K_1 $$unsorted) (N_1 $$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 K_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) M)) K_1))))))) (forall ((N_1 $$unsorted) (M $$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_1) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) M))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 J_1)) K_1))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J_2 $$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_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_2) K)) J_2))))))) (forall ((N_1 $$unsorted) (M $$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_1) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) N_1) M))) (forall ((K $$unsorted) (I_2 $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) J_2)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) I_2) K) (= J_2 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat K) I_2))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat I_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) K_1) J_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 J_1)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) K_1)))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) K_1)) I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) I_1)) K_1)))) (forall ((I_1 $$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.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat J_1) I_1)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) K_1)) I_1)))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat M) N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) K_1)))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) _let_1)) (= Ma _let_1)))) (forall ((M $$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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) M)))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$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_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) K_1))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 J_1)))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) L_1)))))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.one_one tptp.nat)) N_1) N_1)) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) N)) (and (= Ma _let_1) (= N _let_1))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) (tptp.one_one tptp.nat)) N_1)) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) N) _let_1) (and (= Ma _let_1) (= N _let_1))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real Z1) Z2)) W) (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Z1) W)) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Z2) W)))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a X_1))) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a _let_1 Y)) (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a Y) B))) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_1) A_1)) B))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 M) N_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N_1) M)))))))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Ma) N))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)))))) (forall ((P_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat A_3) B_2))) (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_3) B_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))) (exists ((D_4 $$unsorted)) (and (= A_3 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat B_2) D_4)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_4))))))))) (forall ((P_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat A_3) B_2))) (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_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (forall ((D_4 $$unsorted)) (=> (= A_3 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat B_2) D_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_4))))))) (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) N))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (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) N)))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) K))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$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_1) 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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) K_1)))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 J_1))))))))) (forall ((X $$unsorted) (Y_1 $$unsorted) (Z_2 $$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_2)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real X) Z_2)) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Y_1) Z_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y_1))))))) (forall ((X $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.times_times tptp.real Z_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Z_2)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y_1)))))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real Z_1))) (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.zero_zero tptp.real)) Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X_1)) (tptp.hAPP tptp.real tptp.real _let_1 Y))))))))) (forall ((Y $$unsorted) (X_1 $$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_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real X_1) Y))))))) (forall ((X $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Z_2)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real X) Z_2)) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Y_1) Z_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y_1))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (= M (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) N_1)) (or (= N_1 (tptp.one_one tptp.nat)) (= M (tptp.zero_zero tptp.nat))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real (tptp.plus_plus tptp.real (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real X) X)) (tptp.hAPP tptp.real tptp.real (tptp.times_times tptp.real Y_1) Y_1)) _let_1) (and (= X _let_1) (= Y_1 _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) X_1)) _let_1) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_1) _let_1)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_1) _let_1))))))) (forall ((K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) K_1) N_1)))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K_1))) (=> (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_1))) (=> (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_1)))))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N $$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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N) 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) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) (tptp.one_one tptp.nat)))) X_1) (tptp.hAPP tptp.nat X_a _let_1 N_1))))))) (forall ((N_1 $$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_1)))) (forall ((N $$unsorted) (Ma $$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.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat Ma) N)) Ma)) (= N (tptp.one_one tptp.nat)))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a M))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N_1))) (let ((_let_3 (= N_1 (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 (tptp.hAPP X_a X_a (tptp.times_times X_a M) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat N_1) (tptp.one_one tptp.nat))))))))))))) (forall ((N $$unsorted) (P_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N)) (exists ((K_2 $$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) N)) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat K_2) (tptp.one_one tptp.nat))))))))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (I_2 $$unsorted) (J_2 $$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_2) J_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) I_2)) U)) N)))))))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (J_2 $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) J_2) I_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat I_2) J_2)) U)) Ma)) N))))))) (forall ((W $$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_1 $$unsorted) (W $$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_1) W)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z_1)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 J_1) K_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 K_1)))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z_1)) (= Z_1 W)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (or (= K (tptp.zero_zero tptp.nat)) (= Ma N))))) (forall ((I_1 $$unsorted) (U_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) U_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) U_1)) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) J_1)) U_1)) K_1))) (forall ((Ma $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)))))))) (forall ((Ma $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K))) (=> (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.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (= Ma N))))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (or (= K (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)))))))) (forall ((Ma $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat 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 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (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 Ma) N)))))))) (forall ((Ma $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N)))))))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (J_2 $$unsorted) (I_2 $$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_2) I_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat I_2) J_2)) U)) Ma)) N))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_1) I_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) U_1)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) U_1)) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat I_1) J_1)) U_1)) M)) N_1)))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (J_2 $$unsorted) (I_2 $$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_2) I_2)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat I_2) J_2)) U)) Ma) N)))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (I_2 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) I_2)) U)) N)))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted) (I_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) I_1) J_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_1) U_1)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_1) U_1)) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_1) I_1)) U_1)) N_1))))) (forall ((U $$unsorted) (Ma $$unsorted) (N $$unsorted) (I_2 $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) J_2)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat I_2) U)) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat J_2) U)) N)) (= Ma (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat J_2) I_2)) U)) N))))) (forall ((N_1 $$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 (tptp.number_number_of tptp.int N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.number_number_of tptp.int (tptp.bit0 N_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.number_number_of tptp.int (tptp.bit1 N_1)))))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) A_1)) (exists ((P_5 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5) A_1)))))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (X $$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)) X)))) (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 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int K))) (let ((_let_2 (tptp.dvd_dvd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (not (= (tptp.ti tptp.int K) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Ma) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Ma)) (tptp.hAPP tptp.int tptp.int _let_1 Ta))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.dvd X_a) (tptp.semiring_0 X_a)) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP X_a X_a (tptp.times_times X_a L) X_2)))) (exists ((X_2 $$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) (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_2) (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D $$unsorted) (D_3 $$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_3)) (forall ((X_2 $$unsorted) (K_2 $$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.hAPP X_a X_a (tptp.plus_plus X_a X_2) Ta))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_2) (tptp.hAPP X_a X_a (tptp.times_times X_a K_2) D_3))) Ta)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D $$unsorted) (D_3 $$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_3)) (forall ((X_2 $$unsorted) (K_2 $$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.hAPP X_a X_a (tptp.plus_plus X_a X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_2) (tptp.hAPP X_a X_a (tptp.times_times X_a K_2) D_3))) Ta))))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_18 _let_16)) (forall ((K $$unsorted) (P_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int X_2) 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_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K) D)))))))))))) (forall ((K $$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_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int X_2) D))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K) D)))))))))))) (forall ((A_1 $$unsorted) (M $$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.zero_zero tptp.int)) M)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) X_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 X_2) M)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (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)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Y_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 Y_2) M))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2)))))))))) (= (tptp.twoSqu1929807760sum2sq (tptp.product_Pair tptp.int tptp.int tptp.s _let_2)) _let_15) (forall ((A_1 $$unsorted) (B $$unsorted) (P_3 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int B))) (let ((_let_2 (tptp.times_times tptp.int A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.twoSqu1929807760sum2sq (tptp.product_Pair tptp.int tptp.int A_1 B))) (tptp.twoSqu1929807760sum2sq (tptp.product_Pair tptp.int tptp.int P_3 Q_1))) (tptp.twoSqu1929807760sum2sq (tptp.product_Pair tptp.int tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_2 P_3)) (tptp.hAPP tptp.int tptp.int _let_1 Q_1)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int _let_2 Q_1)) (tptp.hAPP tptp.int tptp.int _let_1 P_3)))))))) (forall ((X $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu658283162sum2sq X)) (exists ((A_5 $$unsorted) (B_4 $$unsorted)) (= (tptp.twoSqu1929807760sum2sq (tptp.product_Pair tptp.int tptp.int A_5 B_4)) (tptp.ti tptp.int X))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int B) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_1) B))))) (forall ((P_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.zfact (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) (tptp.one_one tptp.int))) (tptp.number_number_of tptp.int tptp.min)) P_3)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a X))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.times_times X_a B) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_3))) (= (= (tptp.hAPP X_a X_a _let_1 B_2) (tptp.hAPP X_a X_a _let_1 C_1)) (= (tptp.ti X_a B_2) (tptp.ti X_a C_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a B_2) A_3) (tptp.hAPP X_a X_a (tptp.plus_plus X_a C_1) A_3)) (= (tptp.ti X_a B_2) (tptp.ti X_a C_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) A_1) (tptp.hAPP X_a X_a (tptp.plus_plus X_a C) A_1)) (= (tptp.ti X_a B) (tptp.ti X_a C)))))) (forall ((X_a $$unsorted)) (=> (tptp.one X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a X))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2) (tptp.hAPP X_a X_a (tptp.minus_minus X_a C_1) D)) (= (= (tptp.ti X_a A_3) (tptp.ti X_a B_2)) (= (tptp.ti X_a C_1) (tptp.ti X_a D))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3)) (= (tptp.ti X_a A_3) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (B_2 $$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.hAPP X_a X_a (tptp.plus_plus X_a A_3) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B_2) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_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 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a C))) (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) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) C_1)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B_2) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_3)) (tptp.hAPP X_a X_a _let_3 B_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_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 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$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.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_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.plus_plus X_a C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_3) (tptp.ti X_a B_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (= (tptp.ti X_a A_3) (tptp.ti X_a B_2)) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (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.hAPP X_a X_a (tptp.minus_minus X_a A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2) (tptp.hAPP X_a X_a (tptp.minus_minus X_a C_1) D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2) (tptp.hAPP X_a X_a (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_3) B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (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.hAPP X_a X_a (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.hAPP X_a X_a (tptp.times_times X_a A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) B) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) B)) B) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$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.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$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.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_3) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((Y_1 $$unsorted) (X $$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 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y_1)) (= (= (tptp.hAPP X_a X_a (tptp.plus_plus X_a X) Y_1) _let_1) (and (= (tptp.ti X_a X) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$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))) (=> (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.hAPP X_a X_a (tptp.plus_plus X_a A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$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))) (=> (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.hAPP X_a X_a (tptp.plus_plus X_a A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_3) A_3)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_3) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_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 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) C) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) D_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$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_3) B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_3) B_2)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$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) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) _let_1)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.zfact N_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) N_1) (tptp.zero_zero tptp.int))))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int N_1) (tptp.zfact (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int N_1) _let_1)))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.number_number_of tptp.int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) P_3)) (= (tptp.inv P_3 (tptp.inv P_3 A_1)) (tptp.ti tptp.int A_1))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.inv P_3 A_1)) _let_2)))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 _let_2 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.inv P_3 A_1))))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (not (= (tptp.inv P_3 A_1) _let_2)))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (not (= (tptp.inv P_3 A_1) _let_1))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (not (= (tptp.ti tptp.int A_1) (tptp.inv P_3 A_1)))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_3) _let_1))) (not (= (tptp.inv P_3 A_1) (tptp.zero_zero tptp.int)))))))))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) (tptp.inv P_3 A_1)) (tptp.one_one tptp.int)) P_3)))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.wset A_3 P_2))) (let ((_let_2 (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_2 (tptp.ord_less_eq tptp.int) (tptp.number_number_of tptp.int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_3) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) (tptp.one_one tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.member tptp.int B_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.member tptp.int (tptp.inv P_2 B_2)) _let_1))))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.wset A_3 P_2))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.one_one tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) _let_3))) (let ((_let_5 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.number_number_of tptp.int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_5 A_3) _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_5 _let_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_5 B_2) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.member tptp.int (tptp.inv P_2 B_2)) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.member tptp.int B_2) _let_1)))))))))))))) (forall ((P_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int A_3) (tptp.wset A_3 P_2)))))) (forall ((B_2 $$unsorted) (P_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.member tptp.int B_2))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.wset (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_3) _let_3) P_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.wset A_3 P_2))))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_3) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.member tptp.int B_2) (tptp.wset A_3 P_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B_2))))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) (tptp.one_one 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.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_3) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.member tptp.int B_2) (tptp.wset A_3 P_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B_2) _let_1))))))))) (forall ((B_2 $$unsorted) (P_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int B_2))) (let ((_let_2 (tptp.member tptp.int B_2))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_4) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_2 (tptp.wset (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_3) _let_4) P_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_2 (tptp.wset A_3 P_2))) (or (= _let_1 (tptp.ti tptp.int A_3)) (= _let_1 (tptp.inv P_2 A_3))))))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.ord_less 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 _let_1 _let_3 A_3) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 _let_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int B_2) (tptp.wset A_3 P_2))))))))))) (forall ((J_1 $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_1) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 _let_1) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.quadRes P_3) A_1))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) (tptp.multInv P_3 J_1))) P_3)))))))))) (forall ((P_1 $$unsorted) (I_2 $$unsorted) (K $$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) I_2) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 K)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)))))) (forall ((J_1 $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) (tptp.multInv P_3 K_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 _let_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int J_1) K_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int _let_1) K_1)) P_3))))) (forall ((J_1 $$unsorted) (K_1 $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int (tptp.multInv P_3 J_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int J_1) K_1) A_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_1 J_1)) K_1) (tptp.hAPP tptp.int tptp.int _let_1 A_1)) P_3))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (P_3 $$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_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 Y) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.multInv P_3 X_1) (tptp.multInv P_3 Y)) P_3))))) (forall ((A_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.times_times 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.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 K_1) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 J_1)) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 K_1))) P_3)))))) (forall ((Y $$unsorted) (X_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 _let_1) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong Y _let_1) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.multInv P_3 X_1) (tptp.multInv P_3 Y)) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 Y) P_3))))))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.multInv P_3 (tptp.multInv P_3 X_1)) X_1) P_3)))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 _let_1) P_3))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.multInv P_3 X_1) _let_1) P_3)))))))) (forall ((K_1 $$unsorted) (A_1 $$unsorted) (J_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.multInv P_3 J_1))) (let ((_let_2 (tptp.times_times tptp.int _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 (tptp.zero_zero tptp.int)) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int _let_2 J_1)) K_1) (tptp.hAPP tptp.int tptp.int _let_2 A_1)) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) _let_1)) P_3))))))))) (forall ((J_1 $$unsorted) (A_1 $$unsorted) (K_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int J_1) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 (tptp.zero_zero tptp.int)) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_1 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int A_1) (tptp.multInv P_3 K_1))) K_1)) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_1 A_1) P_3)))))))) (forall ((A_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int A_1))) (let ((_let_2 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 _let_2) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 _let_2) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 K_1))) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 J_1))) P_3)))))))))) (forall ((J_1 $$unsorted) (K_1 $$unsorted) (A_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int A_1))) (let ((_let_2 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_1 _let_2) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong K_1 _let_2) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 _let_2) P_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 J_1)) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.multInv P_3 K_1))) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong J_1 K_1) P_3))))))))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.multInv P_3 X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) _let_1)) (tptp.multInv P_3 _let_1)) X_1) P_3))))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (tptp.multInv P_3 X_1))) (let ((_let_2 (tptp.multInv P_3 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong _let_2 (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) _let_1)) _let_2)) P_3)))))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.multInv P_3 X_1)) X_1) (tptp.one_one tptp.int)) P_3)))))) (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.zero_zero tptp.int)) P_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) (tptp.multInv P_3 X_1)) (tptp.one_one tptp.int)) P_3)))))) (forall ((X $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_5 $$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) _let_1) A_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int A_5) _let_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 A_5))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X)))) (forall ((P_1 $$unsorted) (I_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_2) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int K) (tptp.one_one tptp.int)))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)))))) (forall ((P_1 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 K)) (=> (forall ((I $$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) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)))))) (forall ((P_1 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int K) (tptp.one_one tptp.int)))) (=> (forall ((I $$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.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)))))) (forall ((Ma $$unsorted) (K $$unsorted) (F_1 $$unsorted)) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F_1 M_2)) (tptp.hAPP tptp.nat tptp.nat F_1 N_2))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat F_1 Ma)) K)) (tptp.hAPP tptp.nat tptp.nat F_1 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat Ma) K)))))) (forall ((P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int P_2) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_2)) (= (tptp.d22set _let_1) (tptp.wset _let_1 P_2))))) (forall ((A_3 $$unsorted) (B_2 $$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) A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int B_2) (tptp.d22set A_3))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int B_2) (tptp.d22set A_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_2) A_3))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int B_2) (tptp.d22set A_3))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) B_2))))) (forall ((A_3 $$unsorted) (B_2 $$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.one_one tptp.int)) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.member tptp.int B_2) (tptp.d22set A_3))))))) (forall ((N $$unsorted) (P_1 $$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 N)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) N)) (forall ((I $$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) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 K_2))))))) (forall ((I_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 tptp.nat) I_1) J_1)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat I_1) K_2) J_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D) (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z) X_2)) (= _let_2 _let_2))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D) (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z)) (= _let_2 _let_2))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D) (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z)) (= _let_2 _let_2))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D) (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z) X_2)) (= _let_2 _let_2))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_3) N)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B_2) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_3) B_2))))))) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int A_1) N_1)) (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int B) N_1))) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))))))) (forall ((A_1 $$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.dvd_dvd tptp.nat) _let_1) A_1)) (= A_1 _let_1)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) _let_1) A_3)) (= A_3 _let_1)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (not (= A_3 _let_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_3) _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_3))))))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1) (tptp.zero_zero tptp.nat)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) _let_1))))))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1) _let_1)) (= A_1 _let_1)))) (forall ((A_3 $$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) A_3) _let_1)) (= A_3 _let_1)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (not (= A_3 _let_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_3) _let_1))))))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.one_one tptp.nat)) A_1))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_1))))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (N $$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 A_3) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.power_power tptp.nat B_2) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_3) B_2))))))) (forall ((M $$unsorted) (N_1 $$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) M) N_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1)) (= N_1 (tptp.zero_zero tptp.nat)))))) (forall ((N_1 $$unsorted) (M $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_1)) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_1 N_1) (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (= N_1 M))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a Y) B))) (let ((_let_2 (tptp.times_times X_a A_1))) (let ((_let_3 (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_1) A_1)))) (= (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) Y)) (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_3 _let_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hAPP X_a X_a _let_2 _let_1))))))))) (forall ((P_2 $$unsorted)) (= (tptp.sr P_2) (tptp.collect tptp.int (tptp.combs tptp.int tptp.bool tptp.bool (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.int tptp.fconj (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int))) (tptp.combc tptp.int tptp.int tptp.bool (tptp.ord_less tptp.int) P_2))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a _let_1) B) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a _let_1) Y) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_a A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) B_3)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 B_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a Xa))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_1) Y)) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a _let_1 X_1)) (tptp.hAPP X_a X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) A_4)) B) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) (tptp.hAPP X_a X_a (tptp.times_times X_a A_4) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a X_1) Y)) Ya) (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) Ya)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y) Ya)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_a A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a B) B_3)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 B_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa $$unsorted) (X_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a Xa))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_1) Y)) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a _let_1 X_1)) (tptp.hAPP X_a X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) A_4)) B) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) (tptp.hAPP X_a X_a (tptp.times_times X_a A_4) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a X_1) Y)) Ya) (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.times_times X_a X_1) Ya)) (tptp.hAPP X_a X_a (tptp.times_times X_a Y) Ya)))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.number_number_of tptp.int W))) (let ((_let_3 (tptp.number_number_of tptp.int V))) (let ((_let_4 (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.number_number_of tptp.int (tptp.bit1 V))) (tptp.number_number_of tptp.int (tptp.bit0 W))))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_2)))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int _let_3) _let_2))) _let_1))) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int _let_3) _let_1)) _let_2))) _let_1))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int _let_1) (tptp.hAPP tptp.int tptp.int _let_2 B))) (tptp.hAPP tptp.int tptp.int _let_2 A_1)) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int B) _let_1)) A_1))) _let_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.semiring_div X_a) (tptp.number X_a)) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a X))) (let ((_let_2 (tptp.number_number_of X_a Y_1))) (= (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) _let_2)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a _let_2) _let_1) (tptp.zero_zero X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (B_3 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_4 $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_4) C)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a B_3) C)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_4) B_3)) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C)) (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a C))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int B) C))) C) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 B)) C)))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 B)) C) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int B) C))) C)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_3) Ma) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int B_2) Ma)) Ma)))) (forall ((X_1 $$unsorted) (M $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) M)) Y)) M) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.nat tptp.int (tptp.power_power tptp.int X_1) Y)) M))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a _let_1) B) _let_1))))) (forall ((X_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) M)) M))) (forall ((X_1 $$unsorted) (M $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) M) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Y) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 Y) M)))) (forall ((N_1 $$unsorted) (F $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) F))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int M) N_1))))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$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.hAPP tptp.int tptp.int (tptp.div_mod tptp.int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) A_1) (tptp.zero_zero tptp.int))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int _let_1) B) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a Ma) N))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) C) B)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a _let_1 C))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a M) N_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a M) N_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (B_3 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_4 $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_4) C)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a B_3) C)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_4) B_3)) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 B)) C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a B) A_1)) B) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) B)) B) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a _let_1) A_1) _let_1))))) (forall ((X $$unsorted) (N $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X) N) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Y_1) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) N) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int X) Y_1))))) (forall ((Ma $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Ma) D) (tptp.zero_zero tptp.int)) (exists ((Q_2 $$unsorted)) (= (tptp.ti tptp.int Ma) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int D) Q_2))))) (forall ((Y $$unsorted) (X_1 $$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 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) Y))))))) (forall ((K_1 $$unsorted) (M $$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 _let_1 (tptp.zero_zero tptp.int)) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int M) K_1)) M)))))) (forall ((A_1 $$unsorted) (B $$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)) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B)) B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_3) B_2)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a B_2) A_3) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$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) B)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a B) A_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.hAPP X_a X_a (tptp.times_times X_a B) C))) B) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.plus_plus X_a A_1) (tptp.hAPP X_a X_a (tptp.times_times X_a C) B))) B) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) B))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) (tptp.one_one X_a)) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a A_1) B)) B) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.times_times X_a B) A_1)) B) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((B $$unsorted) (B_3 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_4 $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a A_4) C)) (=> (= (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a B_3) C)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_4) B_3)) C))))))) (forall ((X_1 $$unsorted) (M $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) M)) Y)) M) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int X_1) Y)) M))) (forall ((X_1 $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int X_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Y) M))) M) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 Y)) M)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a A_1) B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a (tptp.minus_minus X_a (tptp.hAPP X_a X_a (tptp.div_mod X_a A_1) C)) B)) C))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a A_1))) (= (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 B)) C) (tptp.hAPP X_a X_a (tptp.div_mod X_a (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.div_mod X_a B) C))) C)))))) (forall ((X $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int X))) (let ((_let_2 (tptp.number_number_of tptp.int Y_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) _let_1) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int _let_2) _let_1) (tptp.zero_zero tptp.int)))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) (tptp.number_number_of tptp.int tptp.min)) (tptp.zero_zero tptp.int))) (forall ((A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int A_1))) (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) (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) M) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_1 B)) M) (tptp.hAPP tptp.int tptp.int _let_1 M))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong A_3 B_2) Ma)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_3) Ma) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int B_2) Ma))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_4) B)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_4) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_1) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B) (tptp.ti tptp.int A_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B)) _let_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 _let_4)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) _let_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 _let_1))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) B) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B) (tptp.ti tptp.int A_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int A_1) B))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_1) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_1) B) _let_1))))))) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.number_number_of tptp.int (tptp.bit0 V))) (tptp.number_number_of tptp.int (tptp.bit0 W))) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.number_number_of tptp.int V)) (tptp.number_number_of tptp.int W))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Q_3 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) B_1)))) (=> (= (tptp.ti tptp.int A_2) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B_1) Q_3)) Y)) (=> (and (=> _let_5 (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 Y) B_1)))) (=> (not _let_5) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 B_1) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Y) _let_1))))) (=> (not (= (tptp.ti tptp.int B_1) _let_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int A_2) B_1) (tptp.ti tptp.int Y))))))))))) (forall ((Q_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 B) R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 R_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Q_1) C))) R_1)) _let_1)))))))))) (forall ((Q_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int B))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_4) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B) R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) R_1) _let_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 C)) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Q_1) C))) R_1))))))))))) (forall ((Q_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int B))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_4) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_4) R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 R_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Q_1) C))) R_1)) (tptp.hAPP tptp.int tptp.int _let_1 C))))))))))) (forall ((Q_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int B) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int Q_1) C))) R_1))))))))))) (forall ((P_1 $$unsorted) (N $$unsorted) (K $$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 P_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int N) K))) (and (=> (= (tptp.ti tptp.int K) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) K)) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (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)) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) J) K)) (= (tptp.ti tptp.int N) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K) I)) J))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 J)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 K) _let_1)) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) J) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int N) (tptp.hAPP tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int K) I)) J))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 J)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X) (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (not (= _let_1 (tptp.zero_zero tptp.int))) (= _let_1 (tptp.one_one tptp.int))))) (forall ((B $$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)) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.number_number_of tptp.int tptp.min)) B) (tptp.hAPP tptp.int tptp.int (tptp.minus_minus tptp.int B) (tptp.one_one tptp.int))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.plus_plus tptp.int (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_eq tptp.int) (tptp.zero_zero tptp.int)) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_1 B))) (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int B) A_1)))))))) (forall ((M_1 $$unsorted) (D_1 $$unsorted)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int M_1) D_1) (tptp.zero_zero tptp.int)) (exists ((Q_2 $$unsorted)) (= (tptp.ti tptp.int M_1) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int D_1) Q_2))))) (forall ((X_1 $$unsorted) (Y $$unsorted) (M $$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)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int (tptp.standardRes M X_1)) (tptp.standardRes M Y)) (tptp.hAPP tptp.int tptp.int (tptp.times_times tptp.int X_1) Y)) M)))) (forall ((M $$unsorted) (N_1 $$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.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1)) N_1))))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat K_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat M) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat N_1) K_1)))) (forall ((M $$unsorted) (X_1 $$unsorted)) (= (tptp.standardRes M X_1) (tptp.hAPP tptp.int tptp.int (tptp.div_mod tptp.int X_1) M))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1) M))) (forall ((N_1 $$unsorted) (M $$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_1) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) N_1)))) (forall ((K_1 $$unsorted) (N_1 $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat K_1) N_1)) M)) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) N_1)))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.minus_minus tptp.nat M) N_1)) N_1))))))) (forall ((Ma $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat Ma) D) (tptp.zero_zero tptp.nat)) (exists ((Q_2 $$unsorted)) (= Ma (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat D) Q_2))))) (forall ((M $$unsorted) (N_1 $$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.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1)) N_1)))))) (forall ((M $$unsorted) (N_1 $$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) (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat M) N_1)) M))) (forall ((Ma $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (= (tptp.standardRes Ma X) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X _let_1) Ma))))) (forall ((X $$unsorted) (P_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X _let_1) P_2))) (not (= (tptp.standardRes P_2 X) _let_1))))) (forall ((X_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.zcong X_1 (tptp.standardRes M X_1)) M))) (forall ((X_1 $$unsorted) (P_3 $$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)) P_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.standardRes P_3 X_1)) P_3)))))) (forall ((X $$unsorted) (P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.int tptp.bool) tptp.bool (tptp.member tptp.int X) (tptp.sr P_2))) (= (tptp.standardRes P_2 X) (tptp.ti tptp.int X)))) (forall ((P_1 $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (= K (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat N) K))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N))) (=> (not _let_1) (forall ((I $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J) K)) (=> (= N (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat (tptp.times_times tptp.nat K) I)) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 J)))))))))) (forall ((Q_1 $$unsorted) (R_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat B))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 R_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.plus_plus tptp.nat (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.div_mod tptp.nat Q_1) C))) R_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 C))))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (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.ordere216010020id_add tptp.int) (tptp.linord219039673up_add tptp.int) (tptp.cancel146912293up_add tptp.int) (tptp.ring_11004092258visors tptp.int) (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) (tptp.linordered_semidom tptp.int) (tptp.ab_semigroup_mult tptp.int) (tptp.comm_monoid_mult tptp.int) (tptp.ab_semigroup_add tptp.int) (tptp.ordered_semiring tptp.int) (tptp.no_zero_divisors tptp.int) (tptp.comm_monoid_add tptp.int) (tptp.linordered_ring tptp.int) (tptp.linordered_idom tptp.int) _let_12 (tptp.semiring_div tptp.int) (tptp.comm_semiring 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.ring_div 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.plus 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.semiring_div tptp.nat) (tptp.comm_semiring 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.plus 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.real_normed_algebra 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.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.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.plus 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_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.combb X_b X_c X_a P Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.combc X_a X_b X_c P Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) P R) Q))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.combs X_a X_b X_c P Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) P R) (tptp.hAPP X_a X_b Q R)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) _let_11 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.96/2.16 )
% 1.96/2.16 % SZS output end Proof for NUM924+7
% 1.96/2.16 % cvc5---1.0.5 exiting
% 1.96/2.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------