%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM926+6 : 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 10:49:13 EDT 2023

% Result   : Theorem 0.88s 1.10s
% Output   : Proof 0.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.18  % Problem    : NUM926+6 : TPTP v8.1.2. Released v5.3.0.
% 0.18/0.19  % Command    : do_cvc5 %s %d
% 0.18/0.40  % Computer : n001.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit   : 300
% 0.18/0.40  % WCLimit    : 300
% 0.18/0.40  % DateTime   : Fri Aug 25 17:16:59 EDT 2023
% 0.18/0.40  % CPUTime    : 
% 0.25/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.88/1.10  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.zmBqPoI8xO/cvc5---1.0.5_32424.p...
% 0.88/1.10  ------- get file name : TPTP file name is NUM926+6
% 0.88/1.10  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32424.smt2...
% 0.88/1.10  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.88/1.10  % SZS status Theorem for NUM926+6
% 0.88/1.10  % SZS output start Proof for NUM926+6
% 0.88/1.10  (
% 0.88/1.10  (let ((_let_1 (not (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))))) (let ((_let_2 (tptp.order tptp.int))) (let ((_let_3 (tptp.zero_neq_one tptp.int))) (let ((_let_4 (tptp.bit1 tptp.pls))) (let ((_let_5 (tptp.zero_zero tptp.int))) (let ((_let_6 (tptp.one_one tptp.int))) (let ((_let_7 (tptp.bit0 _let_4))) (let ((_let_8 (tptp.number_number_of tptp.int _let_7))) (let ((_let_9 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_7)) tptp.m) _let_6))) (let ((_let_10 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_11 (= (tptp.legendre _let_10 _let_9) _let_6))) (let ((_let_12 (tptp.quadRes _let_9 _let_10))) (let ((_let_13 (tptp.number_number_of tptp.nat _let_7))) (let ((_let_14 (tptp.power_power tptp.int tptp.s _let_13))) (let ((_let_15 (tptp.plus_plus tptp.int _let_14 _let_6))) (let ((_let_16 (tptp.minus_minus tptp.int _let_14 _let_10))) (let ((_let_17 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.ord_less_eq X_a X_1 Y_1) (=> (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (tptp.ord_less X_a X_1 Y_1)))))))) (let ((_let_18 (tptp.zero_zero tptp.nat))) (let ((_let_19 (tptp.number_number_of tptp.nat tptp.pls))) (let ((_let_20 (tptp.number_number_of tptp.int tptp.pls))) (let ((_let_21 (tptp.power_power tptp.int tptp.s1 _let_13))) (let ((_let_22 (tptp.times_times tptp.int _let_9 tptp.t))) (let ((_let_23 (tptp.number_number_of tptp.nat _let_4))) (let ((_let_24 (tptp.one_one tptp.nat))) (let ((_let_25 (tptp.ord_less tptp.int _let_6 tptp.t))) (let ((_let_26 (=> _let_25 (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))))) (let ((_let_27 (= tptp.t _let_6))) (let ((_let_28 (=> _let_27 (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))))) (let ((_let_29 (tptp.ord_less_eq tptp.int _let_6 tptp.t))) (let ((_let_30 (tptp.ti tptp.int tptp.t))) (let ((_let_31 (= _let_30 tptp.t))) (let ((_let_32 (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.zero_neq_one X_a) (= (tptp.ti X_a _let_1) _let_1)))))) (let ((_let_33 (= tptp.t _let_30))) (let ((_let_34 (tptp.ti tptp.int _let_6))) (let ((_let_35 (= _let_6 _let_34))) (let ((_let_36 (= _let_30 _let_34))) (let ((_let_37 (SYMM (ASSUME :args (_let_31))))) (let ((_let_38 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (not (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))))) (let ((_let_39 (not _let_27))) (let ((_let_40 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (not (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int)) (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2))))))))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_38 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (not (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))) _let_40) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_38 false _let_40)))) (let ((_let_42 (not _let_3))) (let ((_let_43 (or _let_42 _let_35))) (let ((_let_44 (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (or (not (tptp.zero_neq_one X_a)) (= _let_1 (tptp.ti X_a _let_1))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (not _let_29))) (let ((_let_47 (not _let_2))) (let ((_let_48 (or _let_47 _let_46 _let_36 _let_25))) (let ((_let_49 (forall ((X_a $$unsorted) (BOUND_VARIABLE_10622 $$unsorted) (BOUND_VARIABLE_10620 $$unsorted)) (or (not (tptp.order X_a)) (not (tptp.ord_less_eq X_a BOUND_VARIABLE_10620 BOUND_VARIABLE_10622)) (= (tptp.ti X_a BOUND_VARIABLE_10620) (tptp.ti X_a BOUND_VARIABLE_10622)) (tptp.ord_less X_a BOUND_VARIABLE_10620 BOUND_VARIABLE_10622))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (not (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int)) (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2))))))))) (let ((_let_52 (not _let_25))) (let ((_let_53 (not _let_35))) (let ((_let_54 (not _let_36))) (let ((_let_55 (not _let_33))) (let ((_let_56 (and _let_33 _let_39 _let_35))) (let ((_let_57 (ASSUME :args (_let_39)))) (let ((_let_58 (ASSUME :args (_let_35)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_56)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_37 _let_58) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_37) (SYMM _let_58) :args (=)) (FALSE_INTRO _let_57))) :args (_let_39 _let_33 _let_35))) :args (_let_33 _let_39 _let_35))) :args (true _let_56)) (CONG (REFL :args (_let_55)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_27))) (REFL :args (_let_53)) (REFL :args (_let_54)) :args (or))) :args ((or _let_27 _let_55 _let_54 _let_53))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_25 _let_46 _let_47 _let_36 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_51) _let_52))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_38 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (not (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int X _let_2) (tptp.power_power tptp.int Y _let_2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))) _let_51) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_41 :args (_let_51 false _let_38)) :args (_let_52 false _let_51)) (ASSUME :args (_let_29)) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.int tptp.t _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ord_less_eq X_a BOUND_VARIABLE_10620 BOUND_VARIABLE_10622) false))))) :args (_let_49)))) _let_50 :args (_let_48 false _let_49)) :args (_let_36 true _let_25 false _let_29 false _let_2 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_35 (not _let_43)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.int QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.zero_neq_one X_a) false))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_35 false _let_3 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_38) _let_39))) _let_41 :args (_let_39 false _let_38)) _let_37 :args (false false _let_36 false _let_35 true _let_27 false _let_33)) :args ((forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (= (tptp.minus_minus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.minus_minus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (= (tptp.minus_minus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.minus_minus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a B_1_1 B_2_1))) (=> (tptp.ab_group_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.minus_minus tptp.nat (tptp.ti tptp.nat B_1_1) B_2_1) (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.minus_minus tptp.nat B_1_1 (tptp.ti tptp.nat B_2_1)) (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat B_1_1 B_2_1))) (= (tptp.ti tptp.nat _let_1) _let_1))) _let_32 (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.power X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.plus_plus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1 B_2_1))) (=> (tptp.semiring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (= (tptp.plus_plus X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.plus_plus X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1_1 B_2_1))) (=> (tptp.ab_group_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.dvd X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.semiring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.mult_zero X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.mult_zero X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.mult_zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.times_times X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.times_times X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1_1 B_2_1))) (=> (tptp.power X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero_neq_one X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.mult_zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$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) (B_3 $$unsorted)) (= (tptp.zcong (tptp.ti tptp.int B_1_1) B_2_1 B_3) (tptp.zcong B_1_1 B_2_1 B_3))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (= (tptp.zcong B_1_1 (tptp.ti tptp.int B_2_1) B_3) (tptp.zcong B_1_1 B_2_1 B_3))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3 $$unsorted)) (= (tptp.zcong B_1_1 B_2_1 (tptp.ti tptp.int B_3)) (tptp.zcong B_1_1 B_2_1 B_3))) (forall ((B_1_1 $$unsorted)) (= (tptp.zprime (tptp.ti tptp.int B_1_1)) (tptp.zprime B_1_1))) (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 ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.ord_less X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.ord_less X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.ord_less X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.ord_less X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.ord_less_eq X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.ord_less_eq X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.order X_a) (= (tptp.ord_less_eq X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.ord_less_eq X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.power_power X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.power_power X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.power X_a) (= (tptp.power_power X_a B_1_1 (tptp.ti tptp.nat B_2_1)) (tptp.power_power X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.power_power X_a B_1_1 B_2_1))) (=> (tptp.power X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.product_Pair tptp.int tptp.int (tptp.ti tptp.int B_1_1) B_2_1) (tptp.product_Pair tptp.int tptp.int B_1_1 B_2_1))) (forall ((B_1_1 $$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) (B_2_1 $$unsorted)) (= (tptp.quadRes (tptp.ti tptp.int B_1_1) B_2_1) (tptp.quadRes B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.quadRes B_1_1 (tptp.ti tptp.int B_2_1)) (tptp.quadRes B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.dvd_dvd X_a (tptp.ti X_a B_1_1) B_2_1) (tptp.dvd_dvd X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.dvd X_a) (= (tptp.dvd_dvd X_a B_1_1 (tptp.ti X_a B_2_1)) (tptp.dvd_dvd X_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted)) (= (tptp.twoSqu420862341sum2sq (tptp.ti tptp.int B_1_1)) (tptp.twoSqu420862341sum2sq B_1_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.twoSqu579703163sum2sq (tptp.ti (tptp.product_prod tptp.int tptp.int) B_1_1)) (tptp.twoSqu579703163sum2sq B_1_1))) (forall ((B_1_1 $$unsorted)) (let ((_let_1 (tptp.twoSqu579703163sum2sq B_1_1))) (= (tptp.ti tptp.int _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) _let_31 _let_29 _let_28 _let_26 (tptp.ord_less tptp.int tptp.t _let_9) (tptp.zprime _let_9) (= _let_15 _let_22) (tptp.twoSqu420862341sum2sq _let_22) (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.power_power tptp.int (tptp.plus_plus tptp.int A_1 B) _let_2) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.power_power tptp.int A_1 _let_2) (tptp.times_times tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1) A_1) B)) (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.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_5 (tptp.number_number_of tptp.int _let_2))) (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int A_1 B) _let_3) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.power_power tptp.int A_1 _let_3) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_5 (tptp.power_power tptp.int A_1 _let_4)) B)) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_5 A_1) (tptp.power_power tptp.int B _let_4))) (tptp.power_power tptp.int B _let_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.power_power X_a (tptp.plus_plus X_a X_1 Y_1) _let_2) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_2) (tptp.power_power X_a Y_1 _let_2)) (tptp.times_times X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1) X_1) Y_1)))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.monoid_mult X_b) (tptp.number X_b)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b W))) (= (tptp.power_power X_b _let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times X_b _let_1 _let_1)))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (= (tptp.times_times tptp.int A_1 (tptp.power_power tptp.int A_1 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (tptp.power_power tptp.int A_1 (tptp.number_number_of tptp.nat (tptp.bit1 _let_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a _let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.times_times X_a X_1 X_1) (tptp.power_power X_a X_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times X_a A_1 A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a X_1 N))) (= (tptp.power_power X_a X_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.times_times X_a _let_1 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int (tptp.bit1 tptp.pls) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V (tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_ring X_a) (= (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))))))) (not (forall ((T_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int tptp.s (tptp.number_number_of tptp.nat _let_2)) _let_1) (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_2)) tptp.m) _let_1) T_1))))))) (forall ((W $$unsorted)) (tptp.ord_less_eq tptp.int W W)) (forall ((Z $$unsorted) (W $$unsorted)) (or (tptp.ord_less_eq tptp.int Z W) (tptp.ord_less_eq tptp.int W Z))) (forall ((Z_1 $$unsorted) (W_1 $$unsorted)) (= (tptp.ord_less tptp.int Z_1 W_1) (and (tptp.ord_less_eq tptp.int Z_1 W_1) (not (= (tptp.ti tptp.int Z_1) (tptp.ti tptp.int W_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (tptp.ord_less tptp.int X_1 Y_1) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y_1)) (tptp.ord_less tptp.int Y_1 X_1))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq tptp.int I J) (=> (tptp.ord_less_eq tptp.int J K) (tptp.ord_less_eq tptp.int I K)))) (forall ((Z $$unsorted) (W $$unsorted)) (=> (tptp.ord_less_eq tptp.int Z W) (=> (tptp.ord_less_eq tptp.int W Z) (= (tptp.ti tptp.int Z) (tptp.ti tptp.int W))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.power_power X_a (tptp.power_power X_a X_1 P) Q) (tptp.power_power X_a X_1 (tptp.times_times tptp.nat P Q)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.power_power X_a X_1 (tptp.one_one tptp.nat)) (tptp.ti X_a X_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.power_power tptp.int (tptp.power_power tptp.int X_1 Y_1) Z) (tptp.power_power tptp.int X_1 (tptp.times_times tptp.nat Y_1 Z)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (forall ((V_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a V_2))) (let ((_let_2 (tptp.number_number_of X_a W_1))) (= (tptp.ord_less_eq X_a _let_1 _let_2) (not (tptp.ord_less X_a _let_2 _let_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a X_2) (tptp.number_number_of X_a Y_2)) (tptp.ord_less tptp.int X_2 Y_2))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_2) (tptp.number_number_of X_a Y_2)) (tptp.ord_less_eq tptp.int X_2 Y_2))))) (forall ((Z_2 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (=> (tptp.ord_less tptp.int W_2 W) (=> (tptp.ord_less_eq tptp.int Z_2 Z) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int W_2 Z_2) (tptp.plus_plus tptp.int W Z))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.times_times X_a (tptp.power_power X_a X_1 P) (tptp.power_power X_a X_1 Q)) (tptp.power_power X_a X_1 (tptp.plus_plus tptp.nat P Q)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.power_power tptp.int X_1 (tptp.plus_plus tptp.nat Y_1 Z)) (tptp.times_times tptp.int (tptp.power_power tptp.int X_1 Y_1) (tptp.power_power tptp.int X_1 Z)))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus tptp.nat Z Z))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.nat Z (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus tptp.nat Z Z))) (= (tptp.plus_plus tptp.nat _let_24 _let_24) _let_13) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) (tptp.bit1 L_1)) (tptp.ord_less tptp.int K_1 L_1))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq tptp.int K_1 L_1))) (not (tptp.ord_less tptp.int tptp.pls tptp.pls)) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) (tptp.bit0 L_1)) (tptp.ord_less tptp.int K_1 L_1))) (tptp.ord_less_eq tptp.int tptp.pls tptp.pls) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K_1) (tptp.bit0 L_1)) (tptp.ord_less_eq tptp.int K_1 L_1))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.number_number_of tptp.int K_1) (tptp.number_number_of tptp.int L_1)) (tptp.ord_less tptp.int K_1 L_1))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.number_number_of tptp.int K_1) (tptp.number_number_of tptp.int L_1)) (tptp.ord_less_eq tptp.int K_1 L_1))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less tptp.int I J) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int I K) (tptp.plus_plus tptp.int J K)))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq tptp.int I J) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int K I) (tptp.plus_plus tptp.int K J)))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat V_1))) (let ((_let_2 (tptp.number_number_of tptp.nat V))) (let ((_let_3 (tptp.plus_plus tptp.nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less tptp.int V_1 tptp.pls))) (let ((_let_5 (tptp.ord_less tptp.int V tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int V V_1))))))))))))) (= _let_23 _let_24) (= _let_24 _let_23) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K_1) tptp.pls) (tptp.ord_less tptp.int K_1 tptp.pls))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int tptp.pls (tptp.bit1 K_1)) (tptp.ord_less_eq tptp.int tptp.pls K_1))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K_1) (tptp.bit0 L_1)) (tptp.ord_less tptp.int K_1 L_1))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq tptp.int K_1 L_1))) (forall ((W $$unsorted) (Z $$unsorted)) (=> (tptp.ord_less tptp.int W Z) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int W (tptp.one_one tptp.int)) Z))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int W_1 (tptp.one_one tptp.int)) Z_1) (tptp.ord_less tptp.int W_1 Z_1))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less tptp.int W_1 (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int))) (tptp.ord_less_eq tptp.int W_1 Z_1))) (tptp.zprime _let_8) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.twoSqu420862341sum2sq X_1) (=> (tptp.twoSqu420862341sum2sq Y_1) (tptp.twoSqu420862341sum2sq (tptp.times_times tptp.int X_1 Y_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) (tptp.times_times X_a Ly Ry)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Lx Ly))) (= (tptp.times_times X_a _let_1 (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a Rx (tptp.times_times X_a _let_1 Ry))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a Rx Ry))) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) _let_1) (tptp.times_times X_a Lx (tptp.times_times X_a Ly _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) Rx) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) Ly))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (= (tptp.times_times X_a (tptp.times_times X_a Lx Ly) Rx) (tptp.times_times X_a Lx (tptp.times_times X_a Ly Rx)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a Lx (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a (tptp.times_times X_a Lx Rx) Ry))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times X_a Lx (tptp.times_times X_a Rx Ry)) (tptp.times_times X_a Rx (tptp.times_times X_a Lx Ry)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.times_times X_a A_1 B) (tptp.times_times X_a B A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B) (tptp.plus_plus X_a C D)) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a B D)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B) C) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) B))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 B) C) (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a B C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a C D)) (tptp.plus_plus X_a (tptp.plus_plus X_a A_1 C) D))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.plus_plus X_a C D)) (tptp.plus_plus X_a C (tptp.plus_plus X_a A_1 D)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a C A_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (= (tptp.number_number_of X_a X_2) (tptp.number_number_of X_a Y_2)) (= (tptp.ti tptp.int X_2) (tptp.ti tptp.int Y_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((W_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W_1))) (let ((_let_2 (tptp.ti X_a X_2))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit1 K_1) (tptp.bit1 L_1)) (= (tptp.ti tptp.int K_1) (tptp.ti tptp.int L_1)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit0 K_1) (tptp.bit0 L_1)) (= (tptp.ti tptp.int K_1) (tptp.ti tptp.int L_1)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times tptp.int (tptp.times_times tptp.int Z1 Z2) Z3) (tptp.times_times tptp.int Z1 (tptp.times_times tptp.int Z2 Z3)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int Z W) (tptp.times_times tptp.int W Z))) (forall ((K $$unsorted)) (= (tptp.number_number_of tptp.int K) (tptp.ti tptp.int K))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int Z1 Z2) Z3) (tptp.plus_plus tptp.int Z1 (tptp.plus_plus tptp.int Z2 Z3)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.int X_1 (tptp.plus_plus tptp.int Y_1 Z)) (tptp.plus_plus tptp.int Y_1 (tptp.plus_plus tptp.int X_1 Z)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int Z W) (tptp.plus_plus tptp.int W Z))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) tptp.pls) (tptp.ord_less tptp.int K_1 tptp.pls))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) (tptp.bit0 L_1)) (tptp.ord_less tptp.int K_1 L_1))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) tptp.pls) (tptp.ord_less tptp.int K_1 tptp.pls))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int tptp.pls (tptp.bit0 K_1)) (tptp.ord_less tptp.int tptp.pls K_1))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.pls (tptp.bit1 K_1)) (tptp.ord_less_eq tptp.int tptp.pls K_1))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K_1) (tptp.bit1 L_1)) (tptp.ord_less_eq tptp.int K_1 L_1))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K_1) tptp.pls) (tptp.ord_less_eq tptp.int K_1 tptp.pls))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.pls (tptp.bit0 K_1)) (tptp.ord_less_eq tptp.int tptp.pls K_1))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less tptp.int W_1 (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int))) (or (tptp.ord_less tptp.int W_1 Z_1) (= (tptp.ti tptp.int W_1) (tptp.ti tptp.int Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power X_a A_1 (tptp.times_times tptp.nat _let_1 N)) (tptp.power_power X_a (tptp.power_power X_a A_1 N) _let_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a X_2) (tptp.one_one X_a)) (tptp.ord_less tptp.int X_2 (tptp.bit1 tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.one_one X_a) (tptp.number_number_of X_a Y_2)) (tptp.ord_less tptp.int (tptp.bit1 tptp.pls) Y_2))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_2) (tptp.one_one X_a)) (tptp.ord_less_eq tptp.int X_2 (tptp.bit1 tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_2 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.one_one X_a) (tptp.number_number_of X_a Y_2)) (tptp.ord_less_eq tptp.int (tptp.bit1 tptp.pls) Y_2))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_2 $$unsorted) (Z_1 $$unsorted)) (= (= (tptp.plus_plus X_a (tptp.times_times X_a W_1 Y_2) (tptp.times_times X_a X_2 Z_1)) (tptp.plus_plus X_a (tptp.times_times X_a W_1 Z_1) (tptp.times_times X_a X_2 Y_2))) (or (= (tptp.ti X_a W_1) (tptp.ti X_a X_2)) (= (tptp.ti X_a Y_2) (tptp.ti X_a Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 M) (tptp.times_times X_a B M)) (tptp.times_times X_a (tptp.plus_plus X_a A_1 B) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.times_times X_a (tptp.plus_plus X_a A_1 B) C) (tptp.plus_plus X_a (tptp.times_times X_a A_1 C) (tptp.times_times X_a B C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (= (and (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (not (= (tptp.ti X_a C_1) (tptp.ti X_a D_1)))) (not (= (tptp.plus_plus X_a (tptp.times_times X_a A_2 C_1) (tptp.times_times X_a B_1 D_1)) (tptp.plus_plus X_a (tptp.times_times X_a A_2 D_1) (tptp.times_times X_a B_1 C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.times_times X_a X_1 (tptp.plus_plus X_a Y_1 Z)) (tptp.plus_plus X_a (tptp.times_times X_a X_1 Y_1) (tptp.times_times X_a X_1 Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.one_one X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Q $$unsorted)) (= (tptp.power_power X_a (tptp.times_times X_a X_1 Y_1) Q) (tptp.times_times X_a (tptp.power_power X_a X_1 Q) (tptp.power_power X_a Y_1 Q)))))) (forall ((K $$unsorted)) (not (= (tptp.bit1 K) tptp.pls))) (forall ((L $$unsorted)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K $$unsorted) (L $$unsorted)) (not (= (tptp.bit1 K) (tptp.bit0 L)))) (forall ((K $$unsorted) (L $$unsorted)) (not (= (tptp.bit0 K) (tptp.bit1 L)))) (forall ((K_1 $$unsorted)) (= (= (tptp.bit0 K_1) tptp.pls) (= (tptp.ti tptp.int K_1) tptp.pls))) (forall ((L_1 $$unsorted)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls (tptp.ti tptp.int L_1)))) (= (tptp.bit0 tptp.pls) tptp.pls) (forall ((W $$unsorted)) (= (tptp.times_times tptp.int tptp.pls W) tptp.pls)) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.times_times tptp.int (tptp.bit0 K) L) (tptp.bit0 (tptp.times_times tptp.int K L)))) (forall ((K $$unsorted)) (= (tptp.plus_plus tptp.int K tptp.pls) (tptp.ti tptp.int K))) (forall ((K $$unsorted)) (= (tptp.plus_plus tptp.int tptp.pls K) (tptp.ti tptp.int K))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K) (tptp.bit0 L)) (tptp.bit0 (tptp.plus_plus tptp.int K L)))) (forall ((K $$unsorted)) (= (tptp.bit0 K) (tptp.plus_plus tptp.int K K))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int Z (tptp.one_one tptp.int)) (tptp.ti tptp.int Z))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int (tptp.one_one tptp.int) Z) (tptp.ti tptp.int Z))) (forall ((V $$unsorted) (W $$unsorted)) (= (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.times_times tptp.int V W)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.plus_plus tptp.int Z1 Z2) W) (tptp.plus_plus tptp.int (tptp.times_times tptp.int Z1 W) (tptp.times_times tptp.int Z2 W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (= (tptp.times_times tptp.int W (tptp.plus_plus tptp.int Z1 Z2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int W Z1) (tptp.times_times tptp.int W Z2)))) (forall ((V $$unsorted) (W $$unsorted)) (= (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.plus_plus tptp.int V W)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$unsorted)) (=> (tptp.ord_less_eq tptp.int tptp.pls V) (=> (tptp.ord_less_eq tptp.int tptp.pls V_1) (= (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.times_times tptp.int V V_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$unsorted)) (=> (tptp.ord_less_eq tptp.int tptp.pls V) (=> (tptp.ord_less_eq tptp.int tptp.pls V_1) (= (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.plus_plus tptp.int V V_1)))))))) (forall ((X_1 $$unsorted)) (tptp.ord_less_eq tptp.int X_1 (tptp.power_power tptp.int X_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b (tptp.plus_plus X_b A_1 B) _let_1) (tptp.plus_plus X_b (tptp.times_times X_b A_1 _let_1) (tptp.times_times X_b B _let_1))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b _let_1 (tptp.plus_plus X_b B C)) (tptp.plus_plus X_b (tptp.times_times X_b _let_1 B) (tptp.times_times X_b _let_1 C))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 M) M) (tptp.times_times X_a (tptp.plus_plus X_a A_1 (tptp.one_one X_a)) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted)) (= (tptp.plus_plus X_a M (tptp.times_times X_a A_1 M)) (tptp.times_times X_a (tptp.plus_plus X_a A_1 (tptp.one_one X_a)) M))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.plus_plus X_a M M) (tptp.times_times X_a (tptp.plus_plus X_a _let_1 _let_1) M)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a tptp.pls) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.number_number_of X_a tptp.pls)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.times_times X_a (tptp.number_number_of X_a W) Z)) (tptp.times_times X_a (tptp.number_number_of X_a (tptp.times_times tptp.int V W)) Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (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.times_times tptp.int V W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.times_times tptp.int V W)) (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.plus_plus X_a (tptp.number_number_of X_a W) Z)) (tptp.plus_plus X_a (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)) Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (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.plus_plus tptp.int V W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)) (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)))))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit1 K) (tptp.bit0 L)) (tptp.bit1 (tptp.plus_plus tptp.int K L)))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K) (tptp.bit1 L)) (tptp.bit1 (tptp.plus_plus tptp.int K L)))) (forall ((K $$unsorted)) (= (tptp.bit1 K) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) K) K))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit1 W)) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.one_one X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.times_times X_a A_1 (tptp.number_number_of X_a (tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.number_number_of X_a (tptp.bit1 tptp.pls))))) (= _let_6 (tptp.number_number_of tptp.int _let_4)) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.times_times tptp.int (tptp.bit1 K) L) (tptp.plus_plus tptp.int (tptp.bit0 (tptp.times_times tptp.int K L)) L))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.times_times X_a (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.bit0 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.number_number_of tptp.nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.times_times X_a (tptp.times_times X_a A_1 A_1) A_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.power_power tptp.int (tptp.power_power tptp.int X_1 _let_2) _let_2) (tptp.power_power tptp.int X_1 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a Z (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z $$unsorted)) (= (tptp.times_times X_a Z (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus X_a Z Z))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_semiring X_a) (= (tptp.plus_plus X_a _let_1 _let_1) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls))))))) (tptp.ord_less tptp.int _let_5 _let_9) (tptp.dvd_dvd tptp.int _let_9 _let_15) (forall ((P $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (let ((_let_3 (tptp.ti tptp.int P))) (=> (tptp.zprime P) (=> (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.ord_less_eq tptp.int (tptp.number_number_of tptp.int (tptp.bit1 _let_2)) P)))))))) (= (tptp.twoSqu579703163sum2sq (tptp.product_Pair tptp.int tptp.int tptp.s _let_6)) _let_22) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.power_power tptp.real (tptp.plus_plus tptp.real X_1 Y_1) _let_2) (tptp.plus_plus tptp.real (tptp.plus_plus tptp.real (tptp.power_power tptp.real X_1 _let_2) (tptp.power_power tptp.real Y_1 _let_2)) (tptp.times_times tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1) X_1) Y_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.times_times tptp.real (tptp.number_number_of tptp.real (tptp.bit0 _let_1)) (tptp.power_power tptp.real X_1 _let_2)) (tptp.power_power tptp.real (tptp.times_times tptp.real (tptp.number_number_of tptp.real _let_1) X_1) _let_2))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1 N))) (=> (tptp.ord_less X_a (tptp.one_one X_a) A_1) (tptp.ord_less X_a _let_1 (tptp.times_times X_a A_1 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.ord_less X_a _let_1 A_1) (tptp.ord_less X_a _let_1 (tptp.times_times X_a A_1 (tptp.power_power X_a A_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (=> (tptp.ord_less X_a (tptp.one_one X_a) A_1) (=> (tptp.ord_less_eq X_a (tptp.power_power X_a A_1 M) (tptp.power_power X_a A_1 N)) (tptp.ord_less_eq tptp.nat M N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.ord_less X_a (tptp.one_one X_a) B_1) (= (tptp.ord_less_eq X_a (tptp.power_power X_a B_1 X_2) (tptp.power_power X_a B_1 Y_2)) (tptp.ord_less_eq tptp.nat X_2 Y_2)))))) (tptp.zcong _let_14 _let_21 _let_9) (and (tptp.ord_less_eq tptp.int _let_5 tptp.s) (tptp.ord_less tptp.int tptp.s _let_9) (tptp.zcong tptp.s1 tptp.s _let_9)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (and (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) X) (tptp.ord_less tptp.int X _let_1) (tptp.zcong tptp.s1 X _let_1) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (=> (and (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) Y) (tptp.ord_less tptp.int Y _let_1) (tptp.zcong tptp.s1 Y _let_1)) (= (tptp.ti tptp.int Y) (tptp.ti tptp.int X)))))))) (not (forall ((S $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) (tptp.one_one tptp.int)))) (not (and (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) S) (tptp.ord_less tptp.int S _let_1) (tptp.zcong tptp.s1 S _let_1)))))) (tptp.zcong _let_21 _let_10 _let_9) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.power_power X_a A_2 N_1) _let_1) (and (= (tptp.ti X_a A_2) _let_1) (not (= N_1 (tptp.zero_zero tptp.nat))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.ord_less_eq tptp.nat M N) (tptp.dvd_dvd X_a (tptp.power_power X_a A_1 M) (tptp.power_power X_a A_1 N)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (M $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.dvd_dvd X_a X_1 Y_1) (=> (tptp.ord_less_eq tptp.nat N M) (tptp.dvd_dvd X_a (tptp.power_power X_a X_1 N) (tptp.power_power X_a Y_1 M))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd X_a (tptp.power_power X_a A_1 N) B) (=> (tptp.ord_less_eq tptp.nat M N) (tptp.dvd_dvd X_a (tptp.power_power X_a A_1 M) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.power_power X_a A_1 N) (tptp.power_power X_a B N)) (=> (tptp.ord_less_eq X_a _let_1 A_1) (=> (tptp.ord_less_eq X_a _let_1 B) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (= (tptp.ti X_a A_1) (tptp.ti X_a B)))))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) M) (=> (tptp.ord_less tptp.int M N) (not (tptp.dvd_dvd tptp.int N M))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 M) (=> (tptp.ord_less_eq tptp.int _let_1 N) (=> (tptp.dvd_dvd tptp.int M N) (=> (tptp.dvd_dvd tptp.int N M) (= (tptp.ti tptp.int M) (tptp.ti tptp.int N)))))))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.dvd_dvd tptp.int (tptp.times_times tptp.int K M) (tptp.times_times tptp.int K N)) (=> (not (= (tptp.ti tptp.int K) (tptp.zero_zero tptp.int))) (tptp.dvd_dvd tptp.int M N)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.dvd_dvd X_a X_1 Y_1) (tptp.dvd_dvd X_a (tptp.power_power X_a X_1 N) (tptp.power_power X_a Y_1 N)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (not (= (tptp.power_power X_a A_1 N) _let_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.power_power X_a _let_1 N))) (let ((_let_3 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 _let_1))))))))) (forall ((Z $$unsorted) (N $$unsorted)) (=> (tptp.dvd_dvd tptp.int Z N) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) N) (tptp.ord_less_eq tptp.int Z N)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.ord_less X_a A_1 B) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) A_1) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (tptp.ord_less X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a B N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a _let_1 A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a A_1 _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.zero_zero X_a) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (= (= (tptp.ti X_a B_1) (tptp.plus_plus X_a B_1 A_2)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.plus_plus X_a A_2 A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (= tptp.pls _let_5) (not (= _let_5 _let_6)) (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.zero_zero tptp.int) Z) (tptp.ti tptp.int Z))) (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int Z (tptp.zero_zero tptp.int)) (tptp.ti tptp.int Z))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a _let_1 A_1) (tptp.ord_less_eq X_a _let_1 (tptp.power_power X_a A_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.ord_less_eq X_a A_1 B) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) A_1) (tptp.ord_less_eq X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a B N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less X_a _let_1 A_1) (tptp.ord_less X_a _let_1 (tptp.power_power X_a A_1 N))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.zcong (tptp.power_power tptp.int X_1 Y_1) _let_1 P) (tptp.zcong (tptp.power_power tptp.int X_1 (tptp.times_times tptp.nat Y_1 Z)) _let_1 P)))) (forall ((K_1 $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (= (tptp.dvd_dvd tptp.int K_1 (tptp.plus_plus tptp.int N_1 (tptp.times_times tptp.int K_1 Ma))) (tptp.dvd_dvd tptp.int K_1 N_1))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (D_1 $$unsorted)) (=> (tptp.dvd_dvd tptp.int A_2 D_1) (= (tptp.dvd_dvd tptp.int A_2 (tptp.plus_plus tptp.int X_2 Ta)) (tptp.dvd_dvd tptp.int A_2 (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int X_2 (tptp.times_times tptp.int C_1 D_1)) Ta))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (=> (tptp.ord_less X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a B N)) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) B) (tptp.ord_less X_a A_1 B)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (=> (tptp.ord_less_eq tptp.nat N N_2) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) A_1) (=> (tptp.ord_less_eq X_a A_1 (tptp.one_one X_a)) (tptp.ord_less_eq X_a (tptp.power_power X_a A_1 N_2) (tptp.power_power X_a A_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (=> (tptp.ord_less tptp.nat N N_2) (=> (tptp.ord_less X_a (tptp.zero_zero X_a) A_1) (=> (tptp.ord_less X_a A_1 (tptp.one_one X_a)) (tptp.ord_less X_a (tptp.power_power X_a A_1 N_2) (tptp.power_power X_a A_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less X_a (tptp.plus_plus X_a A_2 A_2) _let_1) (tptp.ord_less X_a A_2 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.plus_plus X_a (tptp.times_times X_a X_2 X_2) (tptp.times_times X_a Y_2 Y_2)) _let_1) (and (= (tptp.ti X_a X_2) _let_1) (= (tptp.ti X_a Y_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (R_1 $$unsorted)) (=> (not (= (tptp.ti X_a R_1) (tptp.zero_zero X_a))) (=> (and (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (not (= (tptp.ti X_a C) (tptp.ti X_a D)))) (not (= (tptp.plus_plus X_a A_1 (tptp.times_times X_a R_1 C)) (tptp.plus_plus X_a B (tptp.times_times X_a R_1 D))))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (P $$unsorted)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd tptp.int P (tptp.power_power tptp.int A_1 N)) (tptp.dvd_dvd tptp.int P A_1)))) (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) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.ord_less tptp.int (tptp.bit1 W_1) _let_1) (tptp.ord_less tptp.int W_1 _let_1)))) (not (tptp.ord_less tptp.int tptp.pls _let_5)) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.ord_less tptp.int (tptp.bit0 W_1) _let_1) (tptp.ord_less tptp.int W_1 _let_1)))) (= _let_5 _let_20) (tptp.ord_less tptp.int _let_5 _let_6) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int _let_1 A_1) (=> (tptp.ord_less tptp.int _let_1 (tptp.times_times tptp.int A_1 B)) (tptp.ord_less tptp.int _let_1 B))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less tptp.int I J) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) K) (tptp.ord_less tptp.int (tptp.times_times tptp.int K I) (tptp.times_times tptp.int K J))))) (forall ((Z $$unsorted)) (not (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z) Z) (tptp.zero_zero tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1 N))) (=> (tptp.ord_less X_a (tptp.zero_zero X_a) A_1) (=> (tptp.ord_less X_a A_1 (tptp.one_one X_a)) (tptp.ord_less X_a (tptp.times_times X_a A_1 _let_1) _let_1))))))) (forall ((N $$unsorted) (B $$unsorted) (A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int P N))) (=> (tptp.zprime P) (=> (not (tptp.dvd_dvd tptp.int P A_1)) (=> (tptp.dvd_dvd tptp.int _let_1 (tptp.times_times tptp.int A_1 B)) (tptp.dvd_dvd tptp.int _let_1 B)))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int P N))) (=> (tptp.zprime P) (=> (not (tptp.dvd_dvd tptp.int P B)) (=> (tptp.dvd_dvd tptp.int _let_1 (tptp.times_times tptp.int A_1 B)) (tptp.dvd_dvd tptp.int _let_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.plus_plus X_a (tptp.times_times X_a X_1 X_1) (tptp.times_times X_a Y_1 Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less_eq X_a (tptp.plus_plus X_a (tptp.times_times X_a X_2 X_2) (tptp.times_times X_a Y_2 Y_2)) _let_1) (and (= (tptp.ti X_a X_2) _let_1) (= (tptp.ti X_a Y_2) _let_1))))))) (forall ((V_2 $$unsorted) (V_3 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int V_2 V_3))) (= (tptp.ord_less tptp.nat (tptp.number_number_of tptp.nat V_2) (tptp.number_number_of tptp.nat V_3)) (and (=> _let_1 (tptp.ord_less tptp.int tptp.pls V_3)) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (not (tptp.ord_less X_a (tptp.plus_plus X_a (tptp.times_times X_a X_1 X_1) (tptp.times_times X_a Y_1 Y_1)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less X_a _let_1 (tptp.plus_plus X_a (tptp.times_times X_a X_2 X_2) (tptp.times_times X_a Y_2 Y_2))) (or (not (= (tptp.ti X_a X_2) _let_1)) (not (= (tptp.ti X_a Y_2) _let_1)))))))) (forall ((V_2 $$unsorted) (V_3 $$unsorted)) (= (tptp.ord_less_eq tptp.nat (tptp.number_number_of tptp.nat V_2) (tptp.number_number_of tptp.nat V_3)) (=> (not (tptp.ord_less_eq tptp.int V_2 V_3)) (tptp.ord_less_eq tptp.int V_2 tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W))) (= (tptp.number_number_of X_a (tptp.bit0 W)) (tptp.plus_plus X_a (tptp.plus_plus X_a (tptp.zero_zero X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.one_one tptp.nat)) (tptp.ti X_a A_1))))) (forall ((Z_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.one_one tptp.int) Z_1) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) Z_1))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) Ma) (= (= (tptp.times_times tptp.int Ma N_1) _let_1) (and (= (tptp.ti tptp.int Ma) _let_1) (= (tptp.ti tptp.int N_1) _let_1)))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.ord_less tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z_1) Z_1) _let_1) (tptp.ord_less tptp.int Z_1 _let_1)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.zero_zero X_a) (tptp.number_number_of X_a Y_2)) (tptp.ord_less tptp.int tptp.pls Y_2))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a X_2) (tptp.zero_zero X_a)) (tptp.ord_less tptp.int X_2 tptp.pls))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_2 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.number_number_of X_a Y_2)) (tptp.ord_less_eq tptp.int tptp.pls Y_2))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_2 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_2) (tptp.zero_zero X_a)) (tptp.ord_less_eq tptp.int X_2 tptp.pls))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 Z) (tptp.ord_less tptp.int _let_1 (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a _let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (tptp.ord_less_eq X_a (tptp.zero_zero 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_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less_eq X_a (tptp.power_power X_a X_1 _let_1) (tptp.power_power X_a Y_1 _let_1)) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) Y_1) (tptp.ord_less_eq X_a X_1 Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y_1 $$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.power_power X_a X_1 _let_2) (tptp.power_power X_a Y_1 _let_2)) (=> (tptp.ord_less_eq X_a _let_1 X_1) (=> (tptp.ord_less_eq X_a _let_1 Y_1) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (not (tptp.ord_less 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 $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less X_a _let_1 (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus X_a (tptp.power_power X_a X_2 _let_2) (tptp.power_power X_a Y_2 _let_2)) _let_1) (and (= (tptp.ti X_a X_2) _let_1) (= (tptp.ti X_a Y_2) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a A_1 N))) (= (tptp.times_times X_a _let_1 A_1) (tptp.times_times X_a A_1 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (N $$unsorted)) (= (tptp.power_power X_a (tptp.times_times X_a A_1 B) N) (tptp.times_times X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a B N)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.plus_plus tptp.nat M N)) (tptp.times_times X_a (tptp.power_power X_a A_1 M) (tptp.power_power X_a A_1 N)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.power_power X_a _let_1 N) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.times_times tptp.nat M N)) (tptp.power_power X_a (tptp.power_power X_a A_1 M) N))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.ord_less X_a (tptp.power_power X_a X_1 _let_1) (tptp.power_power X_a Y_1 _let_1)) (=> (tptp.ord_less_eq X_a (tptp.zero_zero X_a) Y_1) (tptp.ord_less X_a X_1 Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_1) (tptp.power_power X_a Y_1 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_eq X_a (tptp.plus_plus X_a (tptp.power_power X_a X_2 _let_2) (tptp.power_power X_a Y_2 _let_2)) _let_1) (and (= (tptp.ti X_a X_2) _let_1) (= (tptp.ti X_a Y_2) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.ord_less X_a (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_1) (tptp.power_power X_a Y_1 _let_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less X_a _let_1 (tptp.plus_plus X_a (tptp.power_power X_a X_2 _let_2) (tptp.power_power X_a Y_2 _let_2))) (or (not (= (tptp.ti X_a X_2) _let_1)) (not (= (tptp.ti X_a Y_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.power_power X_a A_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.ord_less_eq X_a _let_1 A_1) (tptp.ord_less_eq X_a _let_1 (tptp.power_power X_a A_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (=> (tptp.ord_less_eq tptp.nat N N_2) (=> (tptp.ord_less_eq X_a (tptp.one_one X_a) A_1) (tptp.ord_less_eq X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a A_1 N_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A_2 $$unsorted)) (=> (tptp.ord_less X_a (tptp.one_one X_a) A_2) (= (= (tptp.power_power X_a A_2 Ma) (tptp.power_power X_a A_2 N_1)) (= Ma N_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.ord_less X_a (tptp.one_one X_a) B_1) (= (tptp.ord_less X_a (tptp.power_power X_a B_1 X_2) (tptp.power_power X_a B_1 Y_2)) (tptp.ord_less tptp.nat X_2 Y_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (=> (tptp.ord_less X_a (tptp.one_one X_a) A_1) (=> (tptp.ord_less X_a (tptp.power_power X_a A_1 M) (tptp.power_power X_a A_1 N)) (tptp.ord_less tptp.nat M N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_2 $$unsorted)) (=> (tptp.ord_less tptp.nat N N_2) (=> (tptp.ord_less X_a (tptp.one_one X_a) A_1) (tptp.ord_less X_a (tptp.power_power X_a A_1 N) (tptp.power_power X_a A_1 N_2))))))) (tptp.zcong _let_14 _let_10 _let_9) (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (P $$unsorted)) (=> (not (tptp.zcong X_1 (tptp.zero_zero tptp.int) P)) (=> (tptp.zcong (tptp.power_power tptp.int Y_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_1 P) (not (tptp.dvd_dvd tptp.int P Y_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int X_1))) (let ((_let_2 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_2 X_1) (=> (tptp.ord_less tptp.int X_1 (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls)))) (or (= _let_1 _let_2) (= _let_1 (tptp.one_one tptp.int)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a (tptp.power_power X_a A_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) K)) _let_1) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((P_1 $$unsorted)) (= (tptp.zprime P_1) (and (tptp.ord_less tptp.int (tptp.one_one tptp.int) P_1) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M_1))) (=> (and (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) M_1) (tptp.dvd_dvd tptp.int M_1 P_1)) (or (= _let_1 (tptp.one_one tptp.int)) (= _let_1 (tptp.ti tptp.int P_1))))))))) (not (forall ((S1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.zcong (tptp.power_power tptp.int S1 (tptp.number_number_of tptp.nat _let_1)) (tptp.number_number_of tptp.int tptp.min) (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_1)) tptp.m) (tptp.one_one tptp.int))))))) _let_11 (forall ((X_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.ord_less tptp.nat _let_1 (tptp.power_power tptp.nat X_2 N_1)) (or (tptp.ord_less tptp.nat _let_1 X_2) (= N_1 _let_1))))) (forall ((X_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.ord_less tptp.nat _let_1 (tptp.power_power tptp.nat X_2 N_1)) (or (= N_1 _let_1) (tptp.ord_less tptp.nat _let_1 X_2))))) (forall ((X_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.number_number_of tptp.nat W_1))) (= (tptp.ord_less tptp.nat _let_1 (tptp.power_power tptp.nat X_2 _let_2)) (or (= _let_2 _let_1) (tptp.ord_less tptp.nat _let_1 X_2)))))) (forall ((M $$unsorted) (N $$unsorted) (I $$unsorted)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) I) (=> (tptp.ord_less tptp.nat (tptp.power_power tptp.nat I M) (tptp.power_power tptp.nat I N)) (tptp.ord_less tptp.nat M N)))) (forall ((K_1 $$unsorted)) (= (= (tptp.bit1 K_1) tptp.min) (= (tptp.ti tptp.int K_1) tptp.min))) (forall ((L_1 $$unsorted)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min (tptp.ti tptp.int L_1)))) (= (tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K $$unsorted)) (not (= (tptp.bit0 K) tptp.min))) (forall ((L $$unsorted)) (not (= tptp.min (tptp.bit0 L)))) (not (tptp.ord_less tptp.int tptp.min tptp.min)) (tptp.ord_less_eq tptp.int tptp.min tptp.min) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (not (tptp.ord_less tptp.real _let_1 (tptp.times_times tptp.real X_2 X_2))) (= X_2 _let_1)))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) tptp.min) (tptp.ord_less tptp.int K_1 tptp.min))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int tptp.min (tptp.bit1 K_1)) (tptp.ord_less tptp.int tptp.min K_1))) (not (tptp.ord_less tptp.int tptp.pls tptp.min)) (tptp.ord_less tptp.int tptp.min tptp.pls) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int tptp.min (tptp.bit0 K_1)) (tptp.ord_less tptp.int tptp.min K_1))) (tptp.ord_less tptp.int tptp.min _let_5) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K_1) tptp.min) (tptp.ord_less_eq tptp.int K_1 tptp.min))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.min (tptp.bit1 K_1)) (tptp.ord_less_eq tptp.int tptp.min K_1))) (not (tptp.ord_less_eq tptp.int tptp.pls tptp.min)) (tptp.ord_less_eq tptp.int tptp.min tptp.pls) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K_1) tptp.min) (tptp.ord_less_eq tptp.int K_1 tptp.min))) (not (= _let_20 _let_10)) (forall ((I $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.dvd_dvd tptp.nat (tptp.power_power tptp.nat I M) (tptp.power_power tptp.nat I N)) (=> (tptp.ord_less tptp.nat (tptp.one_one tptp.nat) I) (tptp.ord_less_eq tptp.nat M N)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted)) (= (tptp.power_power X_a X_1 (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((A_1 $$unsorted)) (= (tptp.power_power X_a A_1 (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (= _let_19 _let_18) (= _let_18 _let_19) (forall ((K_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.min (tptp.bit0 K_1)) (tptp.ord_less tptp.int tptp.min K_1))) (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) tptp.min) (tptp.ord_less_eq tptp.int K_1 tptp.min))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M))) (let ((_let_2 (tptp.one_one tptp.int))) (=> (= (tptp.times_times tptp.int M N) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.number_number_of tptp.int tptp.min))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.ti tptp.int N_1))) (let ((_let_3 (tptp.ti tptp.int Ma))) (let ((_let_4 (tptp.one_one tptp.int))) (= (= (tptp.times_times tptp.int Ma N_1) _let_4) (or (and (= _let_3 _let_4) (= _let_2 _let_4)) (and (= _let_3 _let_1) (= _let_2 _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.ord_less X_a _let_1 A_1) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (tptp.ord_less X_a _let_1 (tptp.power_power X_a A_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X_1 $$unsorted) (N $$unsorted)) (=> (or (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (= (tptp.ti X_a X_1) (tptp.one_one X_a))) (tptp.dvd_dvd X_a X_1 (tptp.power_power X_a X_1 N)))))) (forall ((V_2 $$unsorted)) (= (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat V_2)) (tptp.ord_less tptp.int tptp.pls V_2))) (forall ((V_2 $$unsorted)) (= (= (tptp.number_number_of tptp.nat V_2) (tptp.zero_zero tptp.nat)) (tptp.ord_less_eq tptp.int V_2 tptp.pls))) (forall ((V_2 $$unsorted)) (= (= (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat V_2)) (tptp.ord_less_eq tptp.int V_2 tptp.pls))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (tptp.zcong A_2 B_1 Ma) (tptp.zcong B_1 A_2 Ma))) (forall ((K $$unsorted) (M $$unsorted)) (tptp.zcong K K M)) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (=> (tptp.zcong B C M) (tptp.zcong A_1 C M)))) (tptp.ord_less tptp.nat _let_18 _let_13) (forall ((V_1 $$unsorted) (K $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V_1) K)))) (let ((_let_2 (tptp.ord_less tptp.int V tptp.pls))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.times_times tptp.int V V_1)) K))))))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat V) (tptp.number_number_of tptp.nat V_1)))) (let ((_let_2 (tptp.ord_less tptp.int V tptp.pls))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.nat))) (=> (not _let_2) (= _let_1 (tptp.number_number_of tptp.nat (tptp.times_times tptp.int V V_1)))))))) _let_17 (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (tptp.ord_less tptp.int A_1 C) (=> (tptp.ord_less tptp.int B C) (or (tptp.ord_less_eq tptp.int A_1 B) (tptp.ord_less_eq tptp.int B A_1))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.zcong A_2 B_1 (tptp.zero_zero tptp.int)) (= (tptp.ti tptp.int A_2) (tptp.ti tptp.int B_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.zcong A_1 B (tptp.one_one tptp.int))) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (=> (tptp.zcong C D M) (tptp.zcong (tptp.times_times tptp.int A_1 C) (tptp.times_times tptp.int B D) M)))) (forall ((K $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (tptp.zcong (tptp.times_times tptp.int K A_1) (tptp.times_times tptp.int K B) M))) (forall ((K $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (tptp.zcong (tptp.times_times tptp.int A_1 K) (tptp.times_times tptp.int B K) M))) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (tptp.zcong (tptp.times_times tptp.int A_1 M) (tptp.times_times tptp.int B M) M)) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (=> (tptp.zcong C D M) (tptp.zcong (tptp.plus_plus tptp.int A_1 C) (tptp.plus_plus tptp.int B D) M)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((N $$unsorted)) (= (tptp.power_power X_a (tptp.number_number_of X_a tptp.min) (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat W_1))) (let ((_let_2 (tptp.zero_zero X_a))) (= (= (tptp.power_power X_a A_2 _let_1) _let_2) (and (= (tptp.ti X_a A_2) _let_2) (not (= _let_1 (tptp.zero_zero tptp.nat)))))))))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int _let_1 A_1) (=> (tptp.ord_less tptp.int A_1 M) (=> (tptp.ord_less tptp.int _let_1 B) (=> (tptp.ord_less tptp.int B A_1) (not (tptp.zcong A_1 B M)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (tptp.zcong A_2 B_1 Ma) (exists ((K_2 $$unsorted)) (= (tptp.ti tptp.int B_1) (tptp.plus_plus tptp.int A_2 (tptp.times_times tptp.int Ma K_2)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat W))) (let ((_let_3 (tptp.power_power X_a _let_1 _let_2))) (let ((_let_4 (= _let_2 (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 (tptp.one_one X_a))) (=> (not _let_4) (= _let_3 _let_1)))))))))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 A_1) (=> (tptp.ord_less tptp.int A_1 M) (=> (tptp.ord_less_eq tptp.int _let_1 B) (=> (tptp.ord_less tptp.int B M) (=> (tptp.zcong A_1 B M) (= (tptp.ti tptp.int A_1) (tptp.ti tptp.int B))))))))) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 A_1) (=> (tptp.ord_less tptp.int A_1 M) (=> (tptp.zcong A_1 _let_1 M) (= (tptp.ti tptp.int A_1) _let_1)))))) (forall ((N $$unsorted) (P $$unsorted) (M $$unsorted)) (=> (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) M) (=> (tptp.zprime P) (=> (tptp.dvd_dvd tptp.int P (tptp.times_times tptp.int M N)) (or (tptp.dvd_dvd tptp.int P M) (tptp.dvd_dvd tptp.int P N)))))) _let_12 (tptp.dvd_dvd tptp.int _let_9 _let_16) (forall ((J $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.power_power tptp.int _let_1 K))) (let ((_let_3 (tptp.power_power tptp.int _let_1 J))) (=> (tptp.ord_less tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) M) (=> (tptp.zcong _let_3 _let_2 M) (= _let_3 _let_2))))))) (= _let_16 _let_15) (=> (not _let_12) (not _let_11)) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (=> (tptp.zcong C D M) (tptp.zcong (tptp.minus_minus tptp.int A_1 C) (tptp.minus_minus tptp.int B D) M)))) (forall ((K $$unsorted)) (= (tptp.minus_minus tptp.int K tptp.pls) (tptp.ti tptp.int K))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit0 K) (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus tptp.int K L)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.minus_minus tptp.int Z1 Z2) W) (tptp.minus_minus tptp.int (tptp.times_times tptp.int Z1 W) (tptp.times_times tptp.int Z2 W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (= (tptp.times_times tptp.int W (tptp.minus_minus tptp.int Z1 Z2)) (tptp.minus_minus tptp.int (tptp.times_times tptp.int W Z1) (tptp.times_times tptp.int W Z2)))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.dvd_dvd tptp.int K (tptp.minus_minus tptp.int M N)) (=> (tptp.dvd_dvd tptp.int K N) (tptp.dvd_dvd tptp.int K M)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.minus_minus tptp.int V W)) (tptp.minus_minus X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b _let_1 (tptp.minus_minus X_b B C)) (tptp.minus_minus X_b (tptp.times_times X_b _let_1 B) (tptp.times_times X_b _let_1 C))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b (tptp.minus_minus X_b A_1 B) _let_1) (tptp.minus_minus X_b (tptp.times_times X_b A_1 _let_1) (tptp.times_times X_b B _let_1))))))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit1 K) (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus tptp.int K L)))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.minus_minus tptp.int (tptp.bit1 K) (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus tptp.int K L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.pls (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus tptp.int tptp.pls L)))) (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int K_1 L_1) (tptp.ord_less tptp.int (tptp.minus_minus tptp.int K_1 L_1) (tptp.zero_zero tptp.int)))) (forall ((A_1 $$unsorted) (R_1 $$unsorted) (B $$unsorted) (M $$unsorted) (C $$unsorted) (D $$unsorted) (N $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.minus_minus tptp.int A_1 (tptp.times_times tptp.int R_1 B)) M) (tptp.times_times tptp.int (tptp.minus_minus tptp.int C (tptp.times_times tptp.int R_1 D)) N)) (tptp.minus_minus tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int A_1 M) (tptp.times_times tptp.int C N)) (tptp.times_times tptp.int R_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B M) (tptp.times_times tptp.int D N)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (tptp.zcong A_2 B_1 Ma) (tptp.dvd_dvd tptp.int Ma (tptp.minus_minus tptp.int A_2 B_1)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.minus_minus X_a (tptp.number_number_of X_a W) C)) (tptp.minus_minus X_a (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)) C))))) (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int A_1 (tptp.one_one tptp.int)))) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) X_1) (=> (tptp.ord_less tptp.int X_1 A_1) (=> (not (= (tptp.ti tptp.int X_1) _let_1)) (tptp.ord_less tptp.int X_1 _let_1)))))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int W_1 (tptp.minus_minus tptp.int Z_1 (tptp.one_one tptp.int))) (tptp.ord_less tptp.int W_1 Z_1))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.pls (tptp.bit1 L)) (tptp.bit1 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.min (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((L $$unsorted)) (= (tptp.minus_minus tptp.int tptp.min (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus tptp.int tptp.min L)))) (forall ((A_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.minus_minus tptp.int P_1 _let_1))) (= (tptp.zcong (tptp.times_times tptp.int A_2 _let_2) _let_1 P_1) (tptp.zcong A_2 _let_2 P_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.times_times tptp.int (tptp.twoSqu579703163sum2sq (tptp.product_Pair tptp.int tptp.int A_1 B)) (tptp.twoSqu579703163sum2sq (tptp.product_Pair tptp.int tptp.int P Q))) (tptp.twoSqu579703163sum2sq (tptp.product_Pair tptp.int tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int A_1 P) (tptp.times_times tptp.int B Q)) (tptp.minus_minus tptp.int (tptp.times_times tptp.int A_1 Q) (tptp.times_times tptp.int B P)))))) (forall ((A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.zprime P) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) A_1) (=> (tptp.zcong (tptp.times_times tptp.int A_1 A_1) _let_1 P) (or (tptp.zcong A_1 _let_1 P) (tptp.zcong A_1 (tptp.minus_minus tptp.int P _let_1) P))))))) (forall ((A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ti tptp.int A_1))) (=> (tptp.zprime P) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) A_1) (=> (tptp.ord_less tptp.int A_1 P) (=> (tptp.zcong (tptp.times_times tptp.int A_1 A_1) _let_1 P) (or (= _let_2 _let_1) (= _let_2 (tptp.minus_minus tptp.int P _let_1)))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.times_times tptp.int (tptp.plus_plus tptp.int A_1 B) (tptp.minus_minus tptp.int A_1 B)) (tptp.minus_minus tptp.int (tptp.power_power tptp.int A_1 _let_1) (tptp.power_power tptp.int B _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.power_power X_a (tptp.minus_minus X_a X_1 Y_1) _let_2) (tptp.minus_minus X_a (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_2) (tptp.power_power X_a Y_1 _let_2)) (tptp.times_times X_a (tptp.times_times X_a (tptp.number_number_of X_a _let_1) X_1) Y_1)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat _let_1))) (= (tptp.power_power tptp.int (tptp.minus_minus tptp.int A_1 B) _let_2) (tptp.plus_plus tptp.int (tptp.minus_minus tptp.int (tptp.power_power tptp.int A_1 _let_2) (tptp.times_times tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int _let_1) A_1) B)) (tptp.power_power tptp.int B _let_2)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat _let_2))) (let ((_let_4 (tptp.number_number_of tptp.nat (tptp.bit0 _let_1)))) (let ((_let_5 (tptp.number_number_of tptp.int _let_2))) (= (tptp.power_power tptp.int (tptp.minus_minus tptp.int A_1 B) _let_3) (tptp.minus_minus tptp.int (tptp.plus_plus tptp.int (tptp.minus_minus tptp.int (tptp.power_power tptp.int A_1 _let_3) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_5 (tptp.power_power tptp.int A_1 _let_4)) B)) (tptp.times_times tptp.int (tptp.times_times tptp.int _let_5 A_1) (tptp.power_power tptp.int B _let_4))) (tptp.power_power tptp.int B _let_3))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int tptp.min))) (let ((_let_2 (tptp.power_power tptp.int _let_1 N))) (or (= _let_2 (tptp.one_one tptp.int)) (= _let_2 _let_1))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) M) _let_1))) (=> (tptp.zprime _let_2) (= (tptp.legendre (tptp.number_number_of tptp.int tptp.min) _let_2) _let_1))))) (forall ((M $$unsorted)) (=> (tptp.ord_less tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) M) (not (tptp.zcong (tptp.one_one tptp.int) (tptp.number_number_of tptp.int tptp.min) M)))) (forall ((X_1 $$unsorted) (P $$unsorted)) (=> (tptp.ord_less tptp.int (tptp.number_number_of tptp.int (tptp.bit0 (tptp.bit1 tptp.pls))) P) (=> (tptp.zcong X_1 (tptp.number_number_of tptp.int tptp.min) P) (not (tptp.zcong X_1 (tptp.one_one tptp.int) P))))) (forall ((A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.legendre A_1 P))) (let ((_let_2 (tptp.quadRes P A_1))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.zcong A_1 _let_3 P))) (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 ((N $$unsorted) (M $$unsorted)) (=> (tptp.dvd_dvd tptp.nat N M) (or (= M (tptp.zero_zero tptp.nat)) (= M N) (tptp.ord_less_eq tptp.nat (tptp.times_times tptp.nat (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))) N) M)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (and (tptp.dvd_dvd tptp.nat X_2 Y_2) (tptp.dvd_dvd tptp.nat Y_2 X_2)) (= X_2 Y_2))) (forall ((D $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (=> (= (tptp.ti tptp.int B) (tptp.ti tptp.int C)) (=> (tptp.zcong C D M) (tptp.zcong A_1 D M))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat M N))) (let ((_let_2 (tptp.zero_zero tptp.nat))) (let ((_let_3 (= M _let_2))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.plus_plus tptp.nat N (tptp.times_times tptp.nat (tptp.minus_minus tptp.nat M (tptp.one_one tptp.nat)) N))))))))) (forall ((P $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.power_power tptp.nat P M))) (let ((_let_3 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.times_times tptp.nat P (tptp.power_power tptp.nat P (tptp.minus_minus tptp.nat M _let_1)))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.minus_minus tptp.nat (tptp.power_power tptp.nat X_1 _let_1) (tptp.power_power tptp.nat Y_1 _let_1)) (tptp.times_times tptp.nat (tptp.plus_plus tptp.nat X_1 Y_1) (tptp.minus_minus tptp.nat X_1 Y_1))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (=> (tptp.dvd_dvd tptp.nat D A_1) (=> (tptp.dvd_dvd tptp.nat D (tptp.plus_plus tptp.nat A_1 B)) (tptp.dvd_dvd tptp.nat D B)))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd tptp.nat A_1 B) (tptp.dvd_dvd tptp.nat (tptp.times_times tptp.nat C A_1) (tptp.times_times tptp.nat C B)))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd tptp.nat A_1 B) (tptp.dvd_dvd tptp.nat (tptp.times_times tptp.nat A_1 C) (tptp.times_times tptp.nat B C)))) (forall ((M $$unsorted)) (tptp.zcong M (tptp.zero_zero tptp.int) M)) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.times_times tptp.nat N_1 Ma) _let_1) (and (= N_1 _let_1) (= Ma _let_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.minus_minus tptp.int A_1 B) (tptp.ti tptp.int C)) (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int C B)))) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (=> (tptp.zcong A_2 B_1 Ma) (= (tptp.zcong C_1 (tptp.times_times tptp.int D_1 A_2) Ma) (tptp.zcong C_1 (tptp.times_times tptp.int D_1 B_1) Ma)))) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (=> (tptp.zcong A_2 B_1 Ma) (= (tptp.zcong C_1 (tptp.times_times tptp.int A_2 D_1) Ma) (tptp.zcong C_1 (tptp.times_times tptp.int B_1 D_1) Ma)))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (=> (tptp.zcong A_1 B M) (tptp.zcong (tptp.plus_plus tptp.int A_1 C) (tptp.plus_plus tptp.int B C) M))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.power_power tptp.nat Ma N_1) _let_1) (and (not (= N_1 _let_1)) (= Ma _let_1))))) (forall ((N $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.dvd_dvd tptp.nat X_1 Y_1) (tptp.dvd_dvd tptp.nat (tptp.power_power tptp.nat X_1 N) (tptp.power_power tptp.nat Y_1 N)))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (M $$unsorted)) (=> (tptp.zcong X_1 Y_1 M) (tptp.zcong (tptp.power_power tptp.int X_1 Z) (tptp.power_power tptp.int Y_1 Z) M))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd tptp.nat A_1 B) (or (= B (tptp.zero_zero tptp.nat)) (tptp.ord_less_eq tptp.nat A_1 B)))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (tptp.dvd_dvd tptp.nat (tptp.times_times tptp.nat Ma K_1) (tptp.times_times tptp.nat N_1 K_1)) (or (= K_1 (tptp.zero_zero tptp.nat)) (tptp.dvd_dvd tptp.nat Ma N_1)))) (forall ((M $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int _let_1 X_1) (=> (tptp.ord_less tptp.int X_1 M) (not (tptp.zcong X_1 _let_1 M)))))) (forall ((M $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int _let_1 X_1) (=> (tptp.ord_less tptp.int _let_1 Y_1) (=> (tptp.ord_less tptp.int _let_1 M) (=> (tptp.zcong X_1 Y_1 M) (=> (tptp.ord_less tptp.int X_1 M) (=> (tptp.ord_less tptp.int Y_1 M) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y_1)))))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.dvd_dvd tptp.int N M) (or (tptp.ord_less_eq tptp.int M (tptp.zero_zero tptp.int)) (tptp.ord_less_eq tptp.int N M)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N $$unsorted)) (=> (not (= N (tptp.zero_zero tptp.nat))) (=> (tptp.dvd_dvd tptp.nat (tptp.power_power tptp.nat X_1 N) Y_1) (tptp.dvd_dvd tptp.nat X_1 Y_1)))) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd tptp.nat (tptp.power_power tptp.nat A_1 N) (tptp.power_power tptp.nat B N)) (=> (not (= N (tptp.zero_zero tptp.nat))) (tptp.dvd_dvd tptp.nat A_1 B)))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (= (tptp.zcong A_2 (tptp.zero_zero tptp.int) Ma) (tptp.dvd_dvd tptp.int Ma A_2))) (forall ((X_2 $$unsorted) (P_1 $$unsorted)) (= (tptp.zcong X_2 (tptp.zero_zero tptp.int) P_1) (tptp.dvd_dvd tptp.int P_1 X_2))) (forall ((X_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.power_power tptp.nat X_2 N_1) _let_1) (or (= X_2 _let_1) (= N_1 (tptp.zero_zero tptp.nat)))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd tptp.int P (tptp.times_times tptp.int M N)) (or (tptp.dvd_dvd tptp.int P M) (tptp.dvd_dvd tptp.int P N))))) (forall ((M $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 X_1) (=> (tptp.ord_less tptp.int X_1 M) (=> (tptp.zcong X_1 _let_1 M) (= (tptp.ti tptp.int X_1) _let_1)))))) (forall ((P $$unsorted) (Y_1 $$unsorted) (N $$unsorted)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (=> (tptp.dvd_dvd tptp.int P Y_1) (tptp.dvd_dvd tptp.int P (tptp.power_power tptp.int Y_1 N))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.zprime P) (=> (not (tptp.zcong X_1 _let_1 P)) (=> (not (tptp.zcong Y_1 _let_1 P)) (not (tptp.zcong (tptp.times_times tptp.int X_1 Y_1) _let_1 P))))))) (forall ((X_1 $$unsorted) (Q $$unsorted) (N $$unsorted) (R_1 $$unsorted)) (=> (= X_1 (tptp.plus_plus tptp.nat (tptp.times_times tptp.nat Q N) R_1)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) R_1) (=> (tptp.ord_less tptp.nat R_1 N) (not (tptp.dvd_dvd tptp.nat N X_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.zprime P) (=> (tptp.ord_less tptp.int _let_1 A_1) (=> (and (not (tptp.zcong A_1 _let_1 P)) (not (tptp.zcong B _let_1 P))) (not (tptp.zcong (tptp.times_times tptp.int A_1 B) _let_1 P))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.zprime P) (=> (tptp.ord_less tptp.int _let_1 A_1) (=> (tptp.zcong (tptp.times_times tptp.int A_1 B) _let_1 P) (or (tptp.zcong A_1 _let_1 P) (tptp.zcong B _let_1 P))))))) (forall ((Y_1 $$unsorted) (N $$unsorted) (P $$unsorted)) (=> (tptp.zprime P) (=> (tptp.dvd_dvd tptp.int P (tptp.power_power tptp.int Y_1 N)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (tptp.dvd_dvd tptp.int P Y_1))))) (forall ((Ma $$unsorted) (X_2 $$unsorted)) (= (tptp.quadRes Ma X_2) (exists ((Y $$unsorted)) (tptp.zcong (tptp.power_power tptp.int Y (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_2 Ma)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus tptp.real (tptp.power_power tptp.real X_2 _let_2) (tptp.power_power tptp.real Y_2 _let_2)) _let_1) (and (= X_2 _let_1) (= Y_2 _let_1)))))) (forall ((R_1 $$unsorted) (Q $$unsorted) (A_1 $$unsorted)) (=> (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) A_1) (=> (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int R_1 (tptp.times_times tptp.int A_1 Q))) (=> (tptp.ord_less tptp.int R_1 A_1) (tptp.ord_less_eq tptp.int (tptp.one_one tptp.int) Q))))) (not (= (tptp.zero_zero tptp.real) (tptp.one_one tptp.real))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less_eq tptp.real X_2 Y_2) (tptp.ord_less_eq tptp.real (tptp.minus_minus tptp.real X_2 Y_2) (tptp.zero_zero tptp.real)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less tptp.real X_2 Y_2) (and (tptp.ord_less_eq tptp.real X_2 Y_2) (not (= X_2 Y_2))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less_eq tptp.real X_2 Y_2) (or (tptp.ord_less tptp.real X_2 Y_2) (= X_2 Y_2)))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.real (tptp.one_one tptp.real) Z) Z)) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.real Z W) (tptp.times_times tptp.real W Z))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times tptp.real (tptp.times_times tptp.real Z1 Z2) Z3) (tptp.times_times tptp.real Z1 (tptp.times_times tptp.real Z2 Z3)))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.ord_less_eq tptp.real X_1 Y_1) (tptp.ord_less_eq tptp.real (tptp.plus_plus tptp.real Z X_1) (tptp.plus_plus tptp.real Z Y_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (tptp.minus_minus X_a (tptp.plus_plus X_a A_1 C) (tptp.plus_plus X_a B D)) (tptp.plus_plus X_a (tptp.minus_minus X_a A_1 B) (tptp.minus_minus X_a C D)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.times_times tptp.real C_1 A_2) (tptp.times_times tptp.real C_1 B_1)) (= A_2 B_1)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.times_times tptp.real A_2 C_1) (tptp.times_times tptp.real B_1 C_1)) (= A_2 B_1)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.real (tptp.plus_plus tptp.real Z1 Z2) W) (tptp.plus_plus tptp.real (tptp.times_times tptp.real Z1 W) (tptp.times_times tptp.real Z2 W)))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.minus_minus X_a (tptp.times_times X_a X_1 Y_1) (tptp.times_times X_a A_1 B)) (tptp.plus_plus X_a (tptp.times_times X_a X_1 (tptp.minus_minus X_a Y_1 B)) (tptp.times_times X_a (tptp.minus_minus X_a X_1 A_1) B)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (=> (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) Z) (=> (tptp.ord_less tptp.real X_1 Y_1) (tptp.ord_less tptp.real (tptp.times_times tptp.real Z X_1) (tptp.times_times tptp.real Z Y_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.ord_less tptp.real _let_1 X_1) (=> (tptp.ord_less tptp.real _let_1 Y_1) (tptp.ord_less tptp.real _let_1 (tptp.times_times tptp.real X_1 Y_1)))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (=> (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) Z_1) (= (tptp.ord_less_eq tptp.real (tptp.times_times tptp.real Z_1 X_2) (tptp.times_times tptp.real Z_1 Y_2)) (tptp.ord_less_eq tptp.real X_2 Y_2)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (=> (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) Z_1) (= (tptp.ord_less_eq tptp.real (tptp.times_times tptp.real X_2 Z_1) (tptp.times_times tptp.real Y_2 Z_1)) (tptp.ord_less_eq tptp.real X_2 Y_2)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (=> (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) Z_1) (= (tptp.ord_less tptp.real (tptp.times_times tptp.real X_2 Z_1) (tptp.times_times tptp.real Y_2 Z_1)) (tptp.ord_less tptp.real X_2 Y_2)))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (= (tptp.plus_plus tptp.real (tptp.times_times tptp.real X_2 X_2) (tptp.times_times tptp.real Y_2 Y_2)) _let_1) (and (= X_2 _let_1) (= Y_2 _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.minus_minus X_a (tptp.times_times X_a X_1 X_1) _let_1) (tptp.times_times X_a (tptp.plus_plus X_a X_1 _let_1) (tptp.minus_minus X_a X_1 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((X_1 $$unsorted) (N $$unsorted)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (= (tptp.times_times X_a (tptp.power_power X_a X_1 (tptp.minus_minus tptp.nat N (tptp.one_one tptp.nat))) X_1) (tptp.power_power X_a X_1 N)))))) (forall ((N $$unsorted)) (tptp.ord_less_eq tptp.real (tptp.one_one tptp.real) (tptp.power_power tptp.real (tptp.number_number_of tptp.real (tptp.bit0 (tptp.bit1 tptp.pls))) N))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2)) (=> (tptp.ord_less tptp.int R_2 B_2) (=> (tptp.ord_less tptp.int _let_1 B_2) (tptp.ord_less_eq tptp.int _let_1 Q_1)))))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2) _let_1) (=> (tptp.ord_less_eq tptp.int _let_1 R_2) (=> (tptp.ord_less tptp.int _let_1 B_2) (tptp.ord_less_eq tptp.int Q_1 _let_1)))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q $$unsorted) (R_1 $$unsorted)) (=> (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q_1) R_2) (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q) R_1)) (=> (tptp.ord_less_eq tptp.int (tptp.zero_zero tptp.int) R_2) (=> (tptp.ord_less tptp.int R_2 B) (=> (tptp.ord_less tptp.int R_1 B) (tptp.ord_less_eq tptp.int Q_1 Q)))))) (forall ((B $$unsorted) (Q $$unsorted) (R_1 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q) R_1) _let_2) (=> (tptp.ord_less_eq tptp.int _let_1 _let_2) (=> (tptp.ord_less tptp.int R_2 B_2) (=> (tptp.ord_less_eq tptp.int _let_1 R_1) (=> (tptp.ord_less tptp.int _let_1 B_2) (=> (tptp.ord_less_eq tptp.int B_2 B) (tptp.ord_less_eq tptp.int Q Q_1)))))))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q $$unsorted) (R_1 $$unsorted)) (=> (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q_1) R_2) (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q) R_1)) (=> (tptp.ord_less_eq tptp.int R_1 (tptp.zero_zero tptp.int)) (=> (tptp.ord_less tptp.int B R_1) (=> (tptp.ord_less tptp.int B R_2) (tptp.ord_less_eq tptp.int Q Q_1)))))) (forall ((B $$unsorted) (Q $$unsorted) (R_1 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int (tptp.times_times tptp.int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus tptp.int (tptp.times_times tptp.int B Q) R_1) _let_2) (=> (tptp.ord_less tptp.int _let_2 _let_1) (=> (tptp.ord_less tptp.int R_1 B) (=> (tptp.ord_less_eq tptp.int _let_1 R_2) (=> (tptp.ord_less tptp.int _let_1 B_2) (=> (tptp.ord_less_eq tptp.int B_2 B) (tptp.ord_less_eq tptp.int Q_1 Q)))))))))) (forall ((R_1 $$unsorted) (Q $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less tptp.int _let_1 A_1) (=> (= (tptp.ti tptp.int A_1) (tptp.plus_plus tptp.int R_1 (tptp.times_times tptp.int A_1 Q))) (=> (tptp.ord_less_eq tptp.int _let_1 R_1) (tptp.ord_less_eq tptp.int Q (tptp.one_one tptp.int))))))) (tptp.ord_less_eq tptp.int _let_5 _let_8) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a M N))) (let ((_let_2 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_2 (= _let_1 (tptp.one_one X_a))) (=> (not _let_2) (= _let_1 (tptp.times_times X_a M (tptp.power_power X_a M (tptp.minus_minus tptp.nat N (tptp.one_one tptp.nat)))))))))))) (forall ((Z $$unsorted) (W $$unsorted)) (=> (tptp.ord_less_eq tptp.real Z W) (=> (tptp.ord_less_eq tptp.real W Z) (= Z W)))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq tptp.real I J) (=> (tptp.ord_less_eq tptp.real J K) (tptp.ord_less_eq tptp.real I K)))) (forall ((Z $$unsorted) (W $$unsorted)) (or (tptp.ord_less_eq tptp.real Z W) (tptp.ord_less_eq tptp.real W Z))) (forall ((W $$unsorted)) (tptp.ord_less_eq tptp.real W W)) (tptp.ord_less_eq tptp.int _let_5 _let_5) (tptp.ord_less_eq tptp.int _let_5 _let_6) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 X_1) (=> (tptp.ord_less_eq tptp.int _let_1 Y_1) (tptp.ord_less_eq tptp.int _let_1 (tptp.times_times tptp.int X_1 Y_1)))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 X_1) (=> (tptp.ord_less_eq tptp.int _let_1 Y_1) (tptp.ord_less_eq tptp.int _let_1 (tptp.plus_plus tptp.int X_1 Y_1)))))) (forall ((N $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 X_1) (tptp.ord_less_eq tptp.int _let_1 (tptp.power_power tptp.int X_1 N))))) (tptp.ord_less_eq tptp.int _let_5 (tptp.number_number_of tptp.int (tptp.bit1 _let_4))) (forall ((X_a $$unsorted)) (=> (tptp.linord626643107strict X_a) (forall ((V $$unsorted) (U $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less X_a X_1 A_1) (=> (tptp.ord_less X_a Y_1 A_1) (=> (tptp.ord_less_eq X_a _let_1 U) (=> (tptp.ord_less_eq X_a _let_1 V) (=> (= (tptp.plus_plus X_a U V) (tptp.one_one X_a)) (tptp.ord_less X_a (tptp.plus_plus X_a (tptp.times_times X_a U X_1) (tptp.times_times X_a V Y_1)) A_1)))))))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) N) (=> (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) A_1) (exists ((R $$unsorted)) (and (tptp.ord_less tptp.real (tptp.zero_zero tptp.real) R) (= (tptp.power_power tptp.real R N) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.dvd_dvd X_a A_1 (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (=> (not (tptp.ord_less X_a X_1 Y_1)) (tptp.ord_less X_a Y_1 X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd X_a A_1 B) (=> (tptp.dvd_dvd X_a B C) (tptp.dvd_dvd X_a A_1 C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.dvd_dvd X_a A_1 A_1)))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a _let_1 A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.times_times X_a A_1 _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_n68954251visors X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.times_times X_a A_2 B_1) _let_1) (or (= (tptp.ti X_a A_2) _let_1) (= (tptp.ti X_a B_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (=> (not (= (tptp.ti X_a B) _let_1)) (not (= (tptp.times_times X_a A_1 B) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.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 $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.times_times X_a (tptp.plus_plus X_a A_1 B) C) (tptp.plus_plus X_a (tptp.times_times X_a A_1 C) (tptp.times_times X_a B C)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring X_a) (forall ((A_1 $$unsorted) (E $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.plus_plus X_a (tptp.times_times X_a A_1 E) (tptp.plus_plus X_a (tptp.times_times X_a B E) C)) (tptp.plus_plus X_a (tptp.times_times X_a (tptp.plus_plus X_a A_1 B) E) C))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.dvd_dvd X_a _let_1 A_1) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.dvd_dvd X_a A_1 (tptp.times_times X_a A_1 B))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.dvd_dvd X_a A_1 (tptp.times_times X_a B A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd X_a A_1 B) (tptp.dvd_dvd X_a A_1 (tptp.times_times X_a B C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (tptp.dvd_dvd X_a A_1 C) (tptp.dvd_dvd X_a A_1 (tptp.times_times X_a B C)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd X_a A_1 B) (=> (tptp.dvd_dvd X_a C D) (tptp.dvd_dvd X_a (tptp.times_times X_a A_1 C) (tptp.times_times X_a B D))))))) (forall ((X_a $$unsorted)) (=> (tptp.dvd X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (K $$unsorted)) (=> (= A_1 (tptp.times_times X_a B K)) (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)) (=> (tptp.dvd_dvd X_a (tptp.times_times X_a A_1 B) C) (tptp.dvd_dvd X_a A_1 C))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.dvd_dvd X_a (tptp.times_times X_a A_1 B) C) (tptp.dvd_dvd X_a B C))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.dvd_dvd X_a A_1 B) (=> (tptp.dvd_dvd X_a A_1 C) (tptp.dvd_dvd X_a A_1 (tptp.plus_plus X_a B C))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.dvd_dvd X_a (tptp.one_one X_a) A_1)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.dvd_dvd X_a X_1 Y_1) (=> (tptp.dvd_dvd X_a X_1 Z) (tptp.dvd_dvd X_a X_1 (tptp.minus_minus X_a Y_1 Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.times_times X_a A_1 A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less_eq X_a _let_1 (tptp.times_times X_a A_2 B_1)) (or (and (tptp.ord_less_eq X_a _let_1 A_2) (tptp.ord_less_eq X_a _let_1 B_1)) (and (tptp.ord_less_eq X_a A_2 _let_1) (tptp.ord_less_eq X_a B_1 _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less_eq X_a (tptp.times_times X_a A_2 B_1) _let_1) (or (and (tptp.ord_less_eq X_a _let_1 A_2) (tptp.ord_less_eq X_a B_1 _let_1)) (and (tptp.ord_less_eq X_a A_2 _let_1) (tptp.ord_less_eq X_a _let_1 B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a _let_1 A_1) (=> (tptp.ord_less_eq X_a _let_1 B) (tptp.ord_less_eq X_a _let_1 (tptp.times_times X_a A_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a _let_1 A_1) (=> (tptp.ord_less_eq X_a B _let_1) (tptp.ord_less_eq 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 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a _let_1 A_1) (=> (tptp.ord_less_eq X_a B _let_1) (tptp.ord_less_eq X_a (tptp.times_times X_a B A_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ord_less_eq X_a A_1 _let_1) (=> (tptp.ord_less_eq X_a _let_1 B) (tptp.ord_less_eq X_a (tptp.times_times X_a A_1 B) _let_1))))))) (tptp.semiri456707255roduct tptp.int) (tptp.linord626643107strict tptp.int) (tptp.linord219039673up_add tptp.int) (tptp.ring_11004092258visors tptp.int) (tptp.ordere453448008miring tptp.int) (tptp.linord581940658strict tptp.int) (tptp.ring_n68954251visors tptp.int) (tptp.linordered_semidom tptp.int) (tptp.comm_monoid_mult tptp.int) (tptp.no_zero_divisors tptp.int) (tptp.linordered_ring tptp.int) (tptp.linordered_idom tptp.int) (tptp.comm_semiring_1 tptp.int) (tptp.comm_semiring tptp.int) (tptp.number_semiring tptp.int) (tptp.ab_group_add tptp.int) _let_3 (tptp.linorder tptp.int) (tptp.monoid_mult tptp.int) (tptp.comm_ring_1 tptp.int) (tptp.semiring_1 tptp.int) (tptp.semiring_0 tptp.int) (tptp.mult_zero tptp.int) _let_2 (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.ring tptp.int) (tptp.number tptp.int) (tptp.dvd tptp.int) (tptp.semiri456707255roduct tptp.nat) (tptp.ordere453448008miring tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.comm_monoid_mult tptp.nat) (tptp.no_zero_divisors tptp.nat) (tptp.comm_semiring_1 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.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.number tptp.nat) (tptp.dvd tptp.nat) (tptp.order tptp.bool) (tptp.semiri456707255roduct tptp.real) (tptp.linord626643107strict tptp.real) (tptp.linord219039673up_add tptp.real) (tptp.ring_11004092258visors tptp.real) (tptp.ordere453448008miring tptp.real) (tptp.linord581940658strict tptp.real) (tptp.ring_n68954251visors tptp.real) (tptp.linordered_semidom tptp.real) (tptp.comm_monoid_mult tptp.real) (tptp.no_zero_divisors 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.linorder tptp.real) (tptp.monoid_mult tptp.real) (tptp.comm_ring_1 tptp.real) (tptp.semiring_1 tptp.real) (tptp.semiring_0 tptp.real) (tptp.mult_zero 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.ring tptp.real) (tptp.number 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))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.88/1.10  )
% 0.88/1.10  % SZS output end Proof for NUM926+6
% 0.88/1.10  % cvc5---1.0.5 exiting
% 0.95/1.11  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------