TSTP Solution File: ITP094^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP094^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 03:18:11 EDT 2023
% Result : Timeout 299.87s 300.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.17 % Problem : ITP094^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.18 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n031.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Sun Aug 27 14:54:54 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.26/0.58 %----Proving TH0
% 0.26/0.59 %------------------------------------------------------------------------------
% 0.26/0.59 % File : ITP094^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.59 % Domain : Interactive Theorem Proving
% 0.26/0.59 % Problem : Sledgehammer Liouville_Numbers problem prob_128__5866194_1
% 0.26/0.59 % Version : Especial.
% 0.26/0.59 % English :
% 0.26/0.59
% 0.26/0.59 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.59 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.59 % Source : [Des21]
% 0.26/0.59 % Names : Liouville_Numbers/prob_128__5866194_1 [Des21]
% 0.26/0.59
% 0.26/0.59 % Status : Theorem
% 0.26/0.59 % Rating : 0.38 v8.1.0, 0.36 v7.5.0
% 0.26/0.59 % Syntax : Number of formulae : 450 ( 208 unt; 105 typ; 0 def)
% 0.26/0.59 % Number of atoms : 818 ( 457 equ; 0 cnn)
% 0.26/0.59 % Maximal formula atoms : 7 ( 2 avg)
% 0.26/0.59 % Number of connectives : 1906 ( 173 ~; 17 |; 91 &;1377 @)
% 0.26/0.59 % ( 0 <=>; 248 =>; 0 <=; 0 <~>)
% 0.26/0.59 % Maximal formula depth : 16 ( 5 avg)
% 0.26/0.59 % Number of types : 12 ( 11 usr)
% 0.26/0.59 % Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<)
% 0.26/0.59 % Number of symbols : 95 ( 94 usr; 19 con; 0-6 aty)
% 0.26/0.59 % Number of variables : 598 ( 66 ^; 485 !; 47 ?; 598 :)
% 0.26/0.59 % SPC : TH0_THM_EQU_NAR
% 0.26/0.59
% 0.26/0.59 % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:38.922
% 0.26/0.59 %------------------------------------------------------------------------------
% 0.26/0.59 % Could-be-implicit typings (11)
% 0.26/0.59 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.26/0.59 poly_poly_poly_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.26/0.59 set_poly_poly_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 poly_poly_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J,type,
% 0.26/0.59 poly_poly_nat: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 set_poly_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 poly_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.26/0.59 poly_nat: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.26/0.59 set_real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.59 set_nat: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Real__Oreal,type,
% 0.26/0.59 real: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Nat__Onat,type,
% 0.26/0.59 nat: $tType ).
% 0.26/0.59
% 0.26/0.59 % Explicit typings (94)
% 0.26/0.59 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 0.26/0.59 inverse_inverse_real: real > real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 finite1328464339y_real: set_poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 0.26/0.59 finite_finite_real: set_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.26/0.59 one_one_nat: nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.26/0.59 one_one_poly_nat: poly_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 one_on501200385y_real: poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 one_one_poly_real: poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 0.26/0.59 one_one_real: real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.26/0.59 zero_zero_nat: nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.26/0.59 zero_zero_poly_nat: poly_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J,type,
% 0.26/0.59 zero_z1059985641ly_nat: poly_poly_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.26/0.59 zero_z935034829y_real: poly_poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 zero_z1423781445y_real: poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.26/0.59 zero_zero_real: real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 ring_1897377867y_real: set_poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 ring_1690226883y_real: set_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 0.26/0.59 ring_1_Ints_real: set_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Nat_OSuc,type,
% 0.26/0.59 suc: nat > nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.26/0.59 ord_less_nat: nat > nat > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 ord_less_poly_real: poly_real > poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.26/0.59 ord_less_real: real > real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.26/0.59 ord_less_eq_real: real > real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oalgebraic_001t__Real__Oreal,type,
% 0.26/0.59 algebraic_real: real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oalgebraic__int_001t__Real__Oreal,type,
% 0.26/0.59 algebraic_int_real: real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Ocr__poly_001t__Real__Oreal,type,
% 0.26/0.59 cr_poly_real: ( nat > real ) > poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odegree_001t__Nat__Onat,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odegree_001t__Real__Oreal,type,
% 0.26/0.59 degree_real: poly_real > nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 divide924636027y_real: poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > nat > nat > poly_poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 divide1142363123y_real: poly_real > poly_poly_real > poly_poly_real > poly_poly_real > nat > nat > poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Odivide__poly__main_001t__Real__Oreal,type,
% 0.26/0.59 divide1561404011n_real: real > poly_real > poly_real > poly_real > nat > nat > poly_real ).
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% 0.26/0.59 thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal,type,
% 0.26/0.59 is_zero_real: poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 order_poly_poly_real: poly_poly_real > poly_poly_poly_real > nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 order_poly_real: poly_real > poly_poly_real > nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oorder_001t__Real__Oreal,type,
% 0.26/0.59 order_real: real > poly_real > nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opcr__poly_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opcr__poly_001t__Polynomial__Opoly_It__Nat__Onat_J_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.26/0.59 pcr_po273983709ly_nat: ( poly_nat > poly_nat > $o ) > ( nat > poly_nat ) > poly_poly_nat > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opcr__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 pcr_po1200519205y_real: ( poly_poly_real > poly_poly_real > $o ) > ( nat > poly_poly_real ) > poly_poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opcr__poly_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 pcr_po1314690837y_real: ( poly_real > poly_real > $o ) > ( nat > poly_real ) > poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opcr__poly_001t__Real__Oreal_001t__Real__Oreal,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opderiv_001t__Nat__Onat,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opderiv_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opderiv_001t__Real__Oreal,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly_001t__Nat__Onat,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly_001t__Real__Oreal,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Real__Oreal,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat,type,
% 0.26/0.59 poly_shift_nat: nat > poly_nat > poly_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 poly_shift_poly_real: nat > poly_poly_real > poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Opoly__shift_001t__Real__Oreal,type,
% 0.26/0.59 poly_shift_real: nat > poly_real > poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat,type,
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% 0.26/0.59 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
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% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 reflec144234502y_real: poly_poly_poly_real > poly_poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 reflec1522834046y_real: poly_poly_real > poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Oreflect__poly_001t__Real__Oreal,type,
% 0.26/0.59 reflect_poly_real: poly_real > poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Orsquarefree_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 rsquar1555552848y_real: poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Orsquarefree_001t__Real__Oreal,type,
% 0.26/0.59 rsquarefree_real: poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat,type,
% 0.26/0.59 synthetic_div_nat: poly_nat > nat > poly_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 synthe1498897281y_real: poly_poly_real > poly_real > poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Polynomial_Osynthetic__div_001t__Real__Oreal,type,
% 0.26/0.59 synthetic_div_real: poly_real > real > poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 0.26/0.59 field_1537545994s_real: set_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 0.26/0.59 dvd_dvd_nat: nat > nat > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.26/0.59 dvd_dvd_poly_nat: poly_nat > poly_nat > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 dvd_dv1946063458y_real: poly_poly_real > poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 dvd_dvd_poly_real: poly_real > poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 0.26/0.59 dvd_dvd_real: real > real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.26/0.59 collect_nat: ( nat > $o ) > set_nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 collect_poly_real: ( poly_real > $o ) > set_poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.26/0.59 collect_real: ( real > $o ) > set_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Nat__Onat,type,
% 0.26/0.59 member_nat: nat > set_nat > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.26/0.59 member1159720147y_real: poly_poly_real > set_poly_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.26/0.59 member_poly_real: poly_real > set_poly_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Real__Oreal,type,
% 0.26/0.59 member_real: real > set_real > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v_n____,type,
% 0.26/0.59 n: nat ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v_p____,type,
% 0.26/0.59 p: poly_real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v_x,type,
% 0.26/0.59 x: real ).
% 0.26/0.59
% 0.26/0.59 % Relevant facts (344)
% 0.26/0.59 thf(fact_0_poly__roots__finite,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( P != zero_z935034829y_real )
% 0.26/0.59 => ( finite1328464339y_real
% 0.26/0.59 @ ( collec927113489y_real
% 0.26/0.59 @ ^ [X: poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_poly_real2 @ P @ X )
% 0.26/0.59 = zero_z1423781445y_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_roots_finite
% 0.26/0.59 thf(fact_1_poly__roots__finite,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( P != zero_z1423781445y_real )
% 0.26/0.59 => ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [X: poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ P @ X )
% 0.26/0.59 = zero_zero_poly_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_roots_finite
% 0.26/0.59 thf(fact_2_poly__roots__finite,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( P != zero_zero_poly_real )
% 0.26/0.59 => ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [X: real] :
% 0.26/0.59 ( ( poly_real2 @ P @ X )
% 0.26/0.59 = zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_roots_finite
% 0.26/0.59 thf(fact_3_p_I2_J,axiom,
% 0.26/0.59 p != zero_zero_poly_real ).
% 0.26/0.59
% 0.26/0.59 % p(2)
% 0.26/0.59 thf(fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062,axiom,
% 0.26/0.59 ( ( pderiv_real @ p )
% 0.26/0.59 != zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % \<open>pderiv p \<noteq> 0\<close>
% 0.26/0.59 thf(fact_5_p_I3_J,axiom,
% 0.26/0.59 ( ( poly_real2 @ p @ x )
% 0.26/0.59 = zero_zero_real ) ).
% 0.26/0.59
% 0.26/0.59 % p(3)
% 0.26/0.59 thf(fact_6_poly__0,axiom,
% 0.26/0.59 ! [X2: poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_poly_real2 @ zero_z935034829y_real @ X2 )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0
% 0.26/0.59 thf(fact_7_poly__0,axiom,
% 0.26/0.59 ! [X2: poly_nat] :
% 0.26/0.59 ( ( poly_poly_nat2 @ zero_z1059985641ly_nat @ X2 )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0
% 0.26/0.59 thf(fact_8_poly__0,axiom,
% 0.26/0.59 ! [X2: poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ zero_z1423781445y_real @ X2 )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0
% 0.26/0.59 thf(fact_9_poly__0,axiom,
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( poly_nat2 @ zero_zero_poly_nat @ X2 )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0
% 0.26/0.59 thf(fact_10_poly__0,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( poly_real2 @ zero_zero_poly_real @ X2 )
% 0.26/0.59 = zero_zero_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0
% 0.26/0.59 thf(fact_11_finite__Collect__conjI,axiom,
% 0.26/0.59 ! [P2: poly_real > $o,Q: poly_real > $o] :
% 0.26/0.59 ( ( ( finite1810960971y_real @ ( collect_poly_real @ P2 ) )
% 0.26/0.59 | ( finite1810960971y_real @ ( collect_poly_real @ Q ) ) )
% 0.26/0.59 => ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [X: poly_real] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 & ( Q @ X ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_conjI
% 0.26/0.59 thf(fact_12_finite__Collect__conjI,axiom,
% 0.26/0.59 ! [P2: real > $o,Q: real > $o] :
% 0.26/0.59 ( ( ( finite_finite_real @ ( collect_real @ P2 ) )
% 0.26/0.59 | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 0.26/0.59 => ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [X: real] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 & ( Q @ X ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_conjI
% 0.26/0.59 thf(fact_13_finite__Collect__conjI,axiom,
% 0.26/0.59 ! [P2: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.26/0.59 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 0.26/0.59 => ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X: nat] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 & ( Q @ X ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_conjI
% 0.26/0.59 thf(fact_14_finite__Collect__disjI,axiom,
% 0.26/0.59 ! [P2: poly_real > $o,Q: poly_real > $o] :
% 0.26/0.59 ( ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [X: poly_real] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 | ( Q @ X ) ) ) )
% 0.26/0.59 = ( ( finite1810960971y_real @ ( collect_poly_real @ P2 ) )
% 0.26/0.59 & ( finite1810960971y_real @ ( collect_poly_real @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_disjI
% 0.26/0.59 thf(fact_15_finite__Collect__disjI,axiom,
% 0.26/0.59 ! [P2: real > $o,Q: real > $o] :
% 0.26/0.59 ( ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [X: real] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 | ( Q @ X ) ) ) )
% 0.26/0.59 = ( ( finite_finite_real @ ( collect_real @ P2 ) )
% 0.26/0.59 & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_disjI
% 0.26/0.59 thf(fact_16_finite__Collect__disjI,axiom,
% 0.26/0.59 ! [P2: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X: nat] :
% 0.26/0.59 ( ( P2 @ X )
% 0.26/0.59 | ( Q @ X ) ) ) )
% 0.26/0.59 = ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.26/0.59 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_disjI
% 0.26/0.59 thf(fact_17_poly__all__0__iff__0,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ! [X: poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_poly_real2 @ P @ X )
% 0.26/0.59 = zero_z1423781445y_real ) )
% 0.26/0.59 = ( P = zero_z935034829y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_all_0_iff_0
% 0.26/0.59 thf(fact_18_poly__all__0__iff__0,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ! [X: real] :
% 0.26/0.59 ( ( poly_real2 @ P @ X )
% 0.26/0.59 = zero_zero_real ) )
% 0.26/0.59 = ( P = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_all_0_iff_0
% 0.26/0.59 thf(fact_19_poly__all__0__iff__0,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ! [X: poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ P @ X )
% 0.26/0.59 = zero_zero_poly_real ) )
% 0.26/0.59 = ( P = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_all_0_iff_0
% 0.26/0.59 thf(fact_20_rsquarefree__roots,axiom,
% 0.26/0.59 ( rsquarefree_real
% 0.26/0.59 = ( ^ [P3: poly_real] :
% 0.26/0.59 ! [A: real] :
% 0.26/0.59 ~ ( ( ( poly_real2 @ P3 @ A )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 & ( ( poly_real2 @ ( pderiv_real @ P3 ) @ A )
% 0.26/0.59 = zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % rsquarefree_roots
% 0.26/0.59 thf(fact_21_not__finite__existsD,axiom,
% 0.26/0.59 ! [P2: real > $o] :
% 0.26/0.59 ( ~ ( finite_finite_real @ ( collect_real @ P2 ) )
% 0.26/0.59 => ? [X_1: real] : ( P2 @ X_1 ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_finite_existsD
% 0.26/0.59 thf(fact_22_not__finite__existsD,axiom,
% 0.26/0.59 ! [P2: nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.26/0.59 => ? [X_1: nat] : ( P2 @ X_1 ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_finite_existsD
% 0.26/0.59 thf(fact_23_not__finite__existsD,axiom,
% 0.26/0.59 ! [P2: poly_real > $o] :
% 0.26/0.59 ( ~ ( finite1810960971y_real @ ( collect_poly_real @ P2 ) )
% 0.26/0.59 => ? [X_1: poly_real] : ( P2 @ X_1 ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_finite_existsD
% 0.26/0.59 thf(fact_24_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_real,B: set_real,R: real > real > $o] :
% 0.26/0.59 ( ~ ( finite_finite_real @ A2 )
% 0.26/0.59 => ( ( finite_finite_real @ B )
% 0.26/0.59 => ( ! [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: real] :
% 0.26/0.59 ( ( member_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [A: real] :
% 0.26/0.59 ( ( member_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_25_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_real,B: set_nat,R: real > nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_real @ A2 )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [A: real] :
% 0.26/0.59 ( ( member_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_26_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_real,B: set_poly_real,R: real > poly_real > $o] :
% 0.26/0.59 ( ~ ( finite_finite_real @ A2 )
% 0.26/0.59 => ( ( finite1810960971y_real @ B )
% 0.26/0.59 => ( ! [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_real
% 0.26/0.59 @ ( collect_real
% 0.26/0.59 @ ^ [A: real] :
% 0.26/0.59 ( ( member_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_27_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_nat,B: set_real,R: nat > real > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A2 )
% 0.26/0.59 => ( ( finite_finite_real @ B )
% 0.26/0.59 => ( ! [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: real] :
% 0.26/0.59 ( ( member_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A: nat] :
% 0.26/0.59 ( ( member_nat @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_28_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_nat,B: set_nat,R: nat > nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A2 )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A: nat] :
% 0.26/0.59 ( ( member_nat @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_29_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_nat,B: set_poly_real,R: nat > poly_real > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A2 )
% 0.26/0.59 => ( ( finite1810960971y_real @ B )
% 0.26/0.59 => ( ! [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A: nat] :
% 0.26/0.59 ( ( member_nat @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_30_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_poly_real,B: set_real,R: poly_real > real > $o] :
% 0.26/0.59 ( ~ ( finite1810960971y_real @ A2 )
% 0.26/0.59 => ( ( finite_finite_real @ B )
% 0.26/0.59 => ( ! [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: real] :
% 0.26/0.59 ( ( member_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: real] :
% 0.26/0.59 ( ( member_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [A: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_31_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_poly_real,B: set_nat,R: poly_real > nat > $o] :
% 0.26/0.59 ( ~ ( finite1810960971y_real @ A2 )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ B )
% 0.26/0.59 & ~ ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [A: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_32_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A2: set_poly_real,B: set_poly_real,R: poly_real > poly_real > $o] :
% 0.26/0.59 ( ~ ( finite1810960971y_real @ A2 )
% 0.26/0.59 => ( ( finite1810960971y_real @ B )
% 0.26/0.59 => ( ! [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ A2 )
% 0.26/0.59 => ? [Xa: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ Xa @ B )
% 0.26/0.59 & ( R @ X3 @ Xa ) ) )
% 0.26/0.59 => ? [X3: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ X3 @ B )
% 0.26/0.59 & ~ ( finite1810960971y_real
% 0.26/0.59 @ ( collect_poly_real
% 0.26/0.59 @ ^ [A: poly_real] :
% 0.26/0.59 ( ( member_poly_real @ A @ A2 )
% 0.26/0.59 & ( R @ A @ X3 ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_33_poly__eq__poly__eq__iff,axiom,
% 0.26/0.59 ! [P: poly_real,Q2: poly_real] :
% 0.26/0.59 ( ( ( poly_real2 @ P )
% 0.26/0.59 = ( poly_real2 @ Q2 ) )
% 0.26/0.59 = ( P = Q2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_eq_poly_eq_iff
% 0.26/0.59 thf(fact_34_poly__eq__poly__eq__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real,Q2: poly_poly_real] :
% 0.26/0.59 ( ( ( poly_poly_real2 @ P )
% 0.26/0.59 = ( poly_poly_real2 @ Q2 ) )
% 0.26/0.59 = ( P = Q2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_eq_poly_eq_iff
% 0.26/0.59 thf(fact_35_n__def,axiom,
% 0.26/0.59 ( n
% 0.26/0.59 = ( degree_real @ p ) ) ).
% 0.26/0.59
% 0.26/0.59 % n_def
% 0.26/0.59 thf(fact_36_assms_I2_J,axiom,
% 0.26/0.59 algebraic_real @ x ).
% 0.26/0.59
% 0.26/0.59 % assms(2)
% 0.26/0.59 thf(fact_37_irrationsl,axiom,
% 0.26/0.59 ~ ( member_real @ x @ field_1537545994s_real ) ).
% 0.26/0.59
% 0.26/0.59 % irrationsl
% 0.26/0.59 thf(fact_38_degree__0,axiom,
% 0.26/0.59 ( ( degree_real @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % degree_0
% 0.26/0.59 thf(fact_39_degree__0,axiom,
% 0.26/0.59 ( ( degree_poly_real @ zero_z1423781445y_real )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % degree_0
% 0.26/0.59 thf(fact_40_degree__0,axiom,
% 0.26/0.59 ( ( degree_nat @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % degree_0
% 0.26/0.59 thf(fact_41_pderiv__0,axiom,
% 0.26/0.59 ( ( pderiv_real @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_0
% 0.26/0.59 thf(fact_42_pderiv__0,axiom,
% 0.26/0.59 ( ( pderiv_poly_real @ zero_z1423781445y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_0
% 0.26/0.59 thf(fact_43_pderiv__0,axiom,
% 0.26/0.59 ( ( pderiv_nat @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_0
% 0.26/0.59 thf(fact_44_pderiv__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( pderiv_real @ P )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( ( degree_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_eq_0_iff
% 0.26/0.59 thf(fact_45_pderiv__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( pderiv_poly_real @ P )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( ( degree_poly_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_eq_0_iff
% 0.26/0.59 thf(fact_46_pderiv__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( pderiv_nat @ P )
% 0.26/0.59 = zero_zero_poly_nat )
% 0.26/0.59 = ( ( degree_nat @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_eq_0_iff
% 0.26/0.59 thf(fact_47_zero__reorient,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( zero_zero_real = X2 )
% 0.26/0.59 = ( X2 = zero_zero_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_reorient
% 0.26/0.59 thf(fact_48_zero__reorient,axiom,
% 0.26/0.59 ! [X2: poly_real] :
% 0.26/0.59 ( ( zero_zero_poly_real = X2 )
% 0.26/0.59 = ( X2 = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_reorient
% 0.26/0.59 thf(fact_49_zero__reorient,axiom,
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( zero_zero_nat = X2 )
% 0.26/0.59 = ( X2 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_reorient
% 0.26/0.59 thf(fact_50_zero__reorient,axiom,
% 0.26/0.59 ! [X2: poly_poly_real] :
% 0.26/0.59 ( ( zero_z1423781445y_real = X2 )
% 0.26/0.59 = ( X2 = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_reorient
% 0.26/0.59 thf(fact_51_zero__reorient,axiom,
% 0.26/0.59 ! [X2: poly_nat] :
% 0.26/0.59 ( ( zero_zero_poly_nat = X2 )
% 0.26/0.59 = ( X2 = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_reorient
% 0.26/0.59 thf(fact_52_is__zero__null,axiom,
% 0.26/0.59 ( is_zero_real
% 0.26/0.59 = ( ^ [P3: poly_real] : ( P3 = zero_zero_poly_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % is_zero_null
% 0.26/0.59 thf(fact_53_is__zero__null,axiom,
% 0.26/0.59 ( is_zero_poly_real
% 0.26/0.59 = ( ^ [P3: poly_poly_real] : ( P3 = zero_z1423781445y_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % is_zero_null
% 0.26/0.59 thf(fact_54_is__zero__null,axiom,
% 0.26/0.59 ( is_zero_nat
% 0.26/0.59 = ( ^ [P3: poly_nat] : ( P3 = zero_zero_poly_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % is_zero_null
% 0.26/0.59 thf(fact_55_poly__cutoff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_cutoff_real @ N @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_0
% 0.26/0.59 thf(fact_56_poly__cutoff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_c1404107022y_real @ N @ zero_z1423781445y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_0
% 0.26/0.59 thf(fact_57_poly__cutoff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_cutoff_nat @ N @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_0
% 0.26/0.59 thf(fact_58_reflect__poly__at__0__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( poly_real2 @ ( reflect_poly_real @ P ) @ zero_zero_real )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 = ( P = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_at_0_eq_0_iff
% 0.26/0.59 thf(fact_59_reflect__poly__at__0__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( poly_poly_real2 @ ( reflec1522834046y_real @ P ) @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( P = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_at_0_eq_0_iff
% 0.26/0.59 thf(fact_60_reflect__poly__at__0__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( poly_nat2 @ ( reflect_poly_nat @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_zero_nat )
% 0.26/0.59 = ( P = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_at_0_eq_0_iff
% 0.26/0.59 thf(fact_61_reflect__poly__at__0__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ( poly_poly_poly_real2 @ ( reflec144234502y_real @ P ) @ zero_z1423781445y_real )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( P = zero_z935034829y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_at_0_eq_0_iff
% 0.26/0.59 thf(fact_62_reflect__poly__at__0__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( ( poly_poly_nat2 @ ( reflec781175074ly_nat @ P ) @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat )
% 0.26/0.59 = ( P = zero_z1059985641ly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_at_0_eq_0_iff
% 0.26/0.59 thf(fact_63__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062,axiom,
% 0.26/0.59 ~ ! [P4: poly_real] :
% 0.26/0.59 ( ! [I: nat] : ( member_real @ ( coeff_real @ P4 @ I ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( P4 != zero_zero_poly_real )
% 0.26/0.59 => ( ( poly_real2 @ P4 @ x )
% 0.26/0.59 != zero_zero_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % \<open>\<And>thesisa. (\<And>p. \<lbrakk>\<And>i. coeff p i \<in> \<int>; p \<noteq> 0; poly p x = 0\<rbrakk> \<Longrightarrow> thesisa) \<Longrightarrow> thesisa\<close>
% 0.26/0.59 thf(fact_64_synthetic__div__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_real,C: real] :
% 0.26/0.59 ( ( ( synthetic_div_real @ P @ C )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( ( degree_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_eq_0_iff
% 0.26/0.59 thf(fact_65_synthetic__div__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real,C: poly_real] :
% 0.26/0.59 ( ( ( synthe1498897281y_real @ P @ C )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( ( degree_poly_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_eq_0_iff
% 0.26/0.59 thf(fact_66_synthetic__div__eq__0__iff,axiom,
% 0.26/0.59 ! [P: poly_nat,C: nat] :
% 0.26/0.59 ( ( ( synthetic_div_nat @ P @ C )
% 0.26/0.59 = zero_zero_poly_nat )
% 0.26/0.59 = ( ( degree_nat @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_eq_0_iff
% 0.26/0.59 thf(fact_67_poly__shift__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_shift_real @ N @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_0
% 0.26/0.59 thf(fact_68_poly__shift__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_shift_poly_real @ N @ zero_z1423781445y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_0
% 0.26/0.59 thf(fact_69_poly__shift__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( poly_shift_nat @ N @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_0
% 0.26/0.59 thf(fact_70_order__root,axiom,
% 0.26/0.59 ! [P: poly_real,A3: real] :
% 0.26/0.59 ( ( ( poly_real2 @ P @ A3 )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 = ( ( P = zero_zero_poly_real )
% 0.26/0.59 | ( ( order_real @ A3 @ P )
% 0.26/0.59 != zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_root
% 0.26/0.59 thf(fact_71_order__root,axiom,
% 0.26/0.59 ! [P: poly_poly_real,A3: poly_real] :
% 0.26/0.59 ( ( ( poly_poly_real2 @ P @ A3 )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( ( P = zero_z1423781445y_real )
% 0.26/0.59 | ( ( order_poly_real @ A3 @ P )
% 0.26/0.59 != zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_root
% 0.26/0.59 thf(fact_72_order__root,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real,A3: poly_poly_real] :
% 0.26/0.59 ( ( ( poly_poly_poly_real2 @ P @ A3 )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( ( P = zero_z935034829y_real )
% 0.26/0.59 | ( ( order_poly_poly_real @ A3 @ P )
% 0.26/0.59 != zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_root
% 0.26/0.59 thf(fact_73_leading__coeff__0__iff,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ P @ ( degree_real @ P ) )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 = ( P = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_0_iff
% 0.26/0.59 thf(fact_74_leading__coeff__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_real @ P @ ( degree_poly_real @ P ) )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( P = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_0_iff
% 0.26/0.59 thf(fact_75_leading__coeff__0__iff,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( coeff_nat @ P @ ( degree_nat @ P ) )
% 0.26/0.59 = zero_zero_nat )
% 0.26/0.59 = ( P = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_0_iff
% 0.26/0.59 thf(fact_76_leading__coeff__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_poly_real @ P @ ( degree360860553y_real @ P ) )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( P = zero_z935034829y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_0_iff
% 0.26/0.59 thf(fact_77_leading__coeff__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( ( coeff_poly_nat @ P @ ( degree_poly_nat @ P ) )
% 0.26/0.59 = zero_zero_poly_nat )
% 0.26/0.59 = ( P = zero_z1059985641ly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_0_iff
% 0.26/0.59 thf(fact_78_divide__poly__main__0,axiom,
% 0.26/0.59 ! [R2: poly_real,D: poly_real,Dr: nat,N: nat] :
% 0.26/0.59 ( ( divide1561404011n_real @ zero_zero_real @ zero_zero_poly_real @ R2 @ D @ Dr @ N )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % divide_poly_main_0
% 0.26/0.59 thf(fact_79_divide__poly__main__0,axiom,
% 0.26/0.59 ! [R2: poly_poly_real,D: poly_poly_real,Dr: nat,N: nat] :
% 0.26/0.59 ( ( divide1142363123y_real @ zero_zero_poly_real @ zero_z1423781445y_real @ R2 @ D @ Dr @ N )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % divide_poly_main_0
% 0.26/0.59 thf(fact_80_divide__poly__main__0,axiom,
% 0.26/0.59 ! [R2: poly_poly_poly_real,D: poly_poly_poly_real,Dr: nat,N: nat] :
% 0.26/0.59 ( ( divide924636027y_real @ zero_z1423781445y_real @ zero_z935034829y_real @ R2 @ D @ Dr @ N )
% 0.26/0.59 = zero_z935034829y_real ) ).
% 0.26/0.59
% 0.26/0.59 % divide_poly_main_0
% 0.26/0.59 thf(fact_81_zero__poly_Otransfer,axiom,
% 0.26/0.59 ( pcr_poly_real_real
% 0.26/0.59 @ ^ [Y: real,Z: real] : ( Y = Z )
% 0.26/0.59 @ ^ [Uu: nat] : zero_zero_real
% 0.26/0.59 @ zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.transfer
% 0.26/0.59 thf(fact_82_zero__poly_Otransfer,axiom,
% 0.26/0.59 ( pcr_po1314690837y_real
% 0.26/0.59 @ ^ [Y: poly_real,Z: poly_real] : ( Y = Z )
% 0.26/0.59 @ ^ [Uu: nat] : zero_zero_poly_real
% 0.26/0.59 @ zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.transfer
% 0.26/0.59 thf(fact_83_zero__poly_Otransfer,axiom,
% 0.26/0.59 ( pcr_poly_nat_nat
% 0.26/0.59 @ ^ [Y: nat,Z: nat] : ( Y = Z )
% 0.26/0.59 @ ^ [Uu: nat] : zero_zero_nat
% 0.26/0.59 @ zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.transfer
% 0.26/0.59 thf(fact_84_zero__poly_Otransfer,axiom,
% 0.26/0.59 ( pcr_po1200519205y_real
% 0.26/0.59 @ ^ [Y: poly_poly_real,Z: poly_poly_real] : ( Y = Z )
% 0.26/0.59 @ ^ [Uu: nat] : zero_z1423781445y_real
% 0.26/0.59 @ zero_z935034829y_real ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.transfer
% 0.26/0.59 thf(fact_85_zero__poly_Otransfer,axiom,
% 0.26/0.59 ( pcr_po273983709ly_nat
% 0.26/0.59 @ ^ [Y: poly_nat,Z: poly_nat] : ( Y = Z )
% 0.26/0.59 @ ^ [Uu: nat] : zero_zero_poly_nat
% 0.26/0.59 @ zero_z1059985641ly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.transfer
% 0.26/0.59 thf(fact_86_p_I1_J,axiom,
% 0.26/0.59 ! [I2: nat] : ( member_real @ ( coeff_real @ p @ I2 ) @ ring_1_Ints_real ) ).
% 0.26/0.59
% 0.26/0.59 % p(1)
% 0.26/0.59 thf(fact_87_reflect__poly__0,axiom,
% 0.26/0.59 ( ( reflect_poly_real @ zero_zero_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_0
% 0.26/0.59 thf(fact_88_reflect__poly__0,axiom,
% 0.26/0.59 ( ( reflec1522834046y_real @ zero_z1423781445y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_0
% 0.26/0.59 thf(fact_89_reflect__poly__0,axiom,
% 0.26/0.59 ( ( reflect_poly_nat @ zero_zero_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_0
% 0.26/0.59 thf(fact_90_synthetic__div__0,axiom,
% 0.26/0.59 ! [C: real] :
% 0.26/0.59 ( ( synthetic_div_real @ zero_zero_poly_real @ C )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_0
% 0.26/0.59 thf(fact_91_synthetic__div__0,axiom,
% 0.26/0.59 ! [C: poly_real] :
% 0.26/0.59 ( ( synthe1498897281y_real @ zero_z1423781445y_real @ C )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_0
% 0.26/0.59 thf(fact_92_synthetic__div__0,axiom,
% 0.26/0.59 ! [C: nat] :
% 0.26/0.59 ( ( synthetic_div_nat @ zero_zero_poly_nat @ C )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % synthetic_div_0
% 0.26/0.59 thf(fact_93_coeff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( coeff_poly_poly_real @ zero_z935034829y_real @ N )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0
% 0.26/0.59 thf(fact_94_coeff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( coeff_poly_nat @ zero_z1059985641ly_nat @ N )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0
% 0.26/0.59 thf(fact_95_coeff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( coeff_real @ zero_zero_poly_real @ N )
% 0.26/0.59 = zero_zero_real ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0
% 0.26/0.59 thf(fact_96_coeff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( coeff_poly_real @ zero_z1423781445y_real @ N )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0
% 0.26/0.59 thf(fact_97_coeff__0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( coeff_nat @ zero_zero_poly_nat @ N )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0
% 0.26/0.59 thf(fact_98_reflect__poly__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_real )
% 0.26/0.59 => ( ( reflect_poly_real @ ( reflect_poly_real @ P ) )
% 0.26/0.59 = P ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_reflect_poly
% 0.26/0.59 thf(fact_99_reflect__poly__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_poly_real )
% 0.26/0.59 => ( ( reflec1522834046y_real @ ( reflec1522834046y_real @ P ) )
% 0.26/0.59 = P ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_reflect_poly
% 0.26/0.59 thf(fact_100_reflect__poly__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( coeff_nat @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_nat )
% 0.26/0.59 => ( ( reflect_poly_nat @ ( reflect_poly_nat @ P ) )
% 0.26/0.59 = P ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_reflect_poly
% 0.26/0.59 thf(fact_101_reflect__poly__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_poly_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_z1423781445y_real )
% 0.26/0.59 => ( ( reflec144234502y_real @ ( reflec144234502y_real @ P ) )
% 0.26/0.59 = P ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_reflect_poly
% 0.26/0.59 thf(fact_102_reflect__poly__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( ( coeff_poly_nat @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_poly_nat )
% 0.26/0.59 => ( ( reflec781175074ly_nat @ ( reflec781175074ly_nat @ P ) )
% 0.26/0.59 = P ) ) ).
% 0.26/0.59
% 0.26/0.59 % reflect_poly_reflect_poly
% 0.26/0.59 thf(fact_103_coeff__0__reflect__poly,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( coeff_real @ ( reflect_poly_real @ P ) @ zero_zero_nat )
% 0.26/0.59 = ( coeff_real @ P @ ( degree_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly
% 0.26/0.59 thf(fact_104_coeff__0__reflect__poly__0__iff,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ ( reflect_poly_real @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 = ( P = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly_0_iff
% 0.26/0.59 thf(fact_105_coeff__0__reflect__poly__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_real @ ( reflec1522834046y_real @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_zero_poly_real )
% 0.26/0.59 = ( P = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly_0_iff
% 0.26/0.59 thf(fact_106_coeff__0__reflect__poly__0__iff,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( coeff_nat @ ( reflect_poly_nat @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_zero_nat )
% 0.26/0.59 = ( P = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly_0_iff
% 0.26/0.59 thf(fact_107_coeff__0__reflect__poly__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_poly_real @ ( reflec144234502y_real @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_z1423781445y_real )
% 0.26/0.59 = ( P = zero_z935034829y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly_0_iff
% 0.26/0.59 thf(fact_108_coeff__0__reflect__poly__0__iff,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( ( coeff_poly_nat @ ( reflec781175074ly_nat @ P ) @ zero_zero_nat )
% 0.26/0.59 = zero_zero_poly_nat )
% 0.26/0.59 = ( P = zero_z1059985641ly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_0_reflect_poly_0_iff
% 0.26/0.59 thf(fact_109_degree__reflect__poly__eq,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_real )
% 0.26/0.59 => ( ( degree_real @ ( reflect_poly_real @ P ) )
% 0.26/0.59 = ( degree_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % degree_reflect_poly_eq
% 0.26/0.59 thf(fact_110_degree__reflect__poly__eq,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_poly_real )
% 0.26/0.59 => ( ( degree_poly_real @ ( reflec1522834046y_real @ P ) )
% 0.26/0.59 = ( degree_poly_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % degree_reflect_poly_eq
% 0.26/0.59 thf(fact_111_degree__reflect__poly__eq,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( ( coeff_nat @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_nat )
% 0.26/0.59 => ( ( degree_nat @ ( reflect_poly_nat @ P ) )
% 0.26/0.59 = ( degree_nat @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % degree_reflect_poly_eq
% 0.26/0.59 thf(fact_112_degree__reflect__poly__eq,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( ( coeff_poly_poly_real @ P @ zero_zero_nat )
% 0.26/0.59 != zero_z1423781445y_real )
% 0.26/0.59 => ( ( degree360860553y_real @ ( reflec144234502y_real @ P ) )
% 0.26/0.59 = ( degree360860553y_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % degree_reflect_poly_eq
% 0.26/0.59 thf(fact_113_degree__reflect__poly__eq,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( ( coeff_poly_nat @ P @ zero_zero_nat )
% 0.26/0.59 != zero_zero_poly_nat )
% 0.26/0.59 => ( ( degree_poly_nat @ ( reflec781175074ly_nat @ P ) )
% 0.26/0.59 = ( degree_poly_nat @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % degree_reflect_poly_eq
% 0.26/0.59 thf(fact_114_poly__reflect__poly__0,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( poly_real2 @ ( reflect_poly_real @ P ) @ zero_zero_real )
% 0.26/0.59 = ( coeff_real @ P @ ( degree_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_reflect_poly_0
% 0.26/0.59 thf(fact_115_poly__reflect__poly__0,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ ( reflec1522834046y_real @ P ) @ zero_zero_poly_real )
% 0.26/0.59 = ( coeff_poly_real @ P @ ( degree_poly_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_reflect_poly_0
% 0.26/0.59 thf(fact_116_poly__reflect__poly__0,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( poly_nat2 @ ( reflect_poly_nat @ P ) @ zero_zero_nat )
% 0.26/0.59 = ( coeff_nat @ P @ ( degree_nat @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_reflect_poly_0
% 0.26/0.59 thf(fact_117_poly__reflect__poly__0,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_poly_real2 @ ( reflec144234502y_real @ P ) @ zero_z1423781445y_real )
% 0.26/0.59 = ( coeff_poly_poly_real @ P @ ( degree360860553y_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_reflect_poly_0
% 0.26/0.59 thf(fact_118_poly__reflect__poly__0,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( poly_poly_nat2 @ ( reflec781175074ly_nat @ P ) @ zero_zero_poly_nat )
% 0.26/0.59 = ( coeff_poly_nat @ P @ ( degree_poly_nat @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_reflect_poly_0
% 0.26/0.59 thf(fact_119_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A3: real,P2: real > $o] :
% 0.26/0.59 ( ( member_real @ A3 @ ( collect_real @ P2 ) )
% 0.26/0.59 = ( P2 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_120_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A3: nat,P2: nat > $o] :
% 0.26/0.59 ( ( member_nat @ A3 @ ( collect_nat @ P2 ) )
% 0.26/0.59 = ( P2 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_121_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A3: poly_real,P2: poly_real > $o] :
% 0.26/0.59 ( ( member_poly_real @ A3 @ ( collect_poly_real @ P2 ) )
% 0.26/0.59 = ( P2 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_122_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A2: set_real] :
% 0.26/0.59 ( ( collect_real
% 0.26/0.59 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.26/0.59 = A2 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_123_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A2: set_nat] :
% 0.26/0.59 ( ( collect_nat
% 0.26/0.59 @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 0.26/0.59 = A2 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_124_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A2: set_poly_real] :
% 0.26/0.59 ( ( collect_poly_real
% 0.26/0.59 @ ^ [X: poly_real] : ( member_poly_real @ X @ A2 ) )
% 0.26/0.59 = A2 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_125_Collect__cong,axiom,
% 0.26/0.59 ! [P2: real > $o,Q: real > $o] :
% 0.26/0.59 ( ! [X3: real] :
% 0.26/0.59 ( ( P2 @ X3 )
% 0.26/0.59 = ( Q @ X3 ) )
% 0.26/0.59 => ( ( collect_real @ P2 )
% 0.26/0.59 = ( collect_real @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_126_Collect__cong,axiom,
% 0.26/0.59 ! [P2: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ! [X3: nat] :
% 0.26/0.59 ( ( P2 @ X3 )
% 0.26/0.59 = ( Q @ X3 ) )
% 0.26/0.59 => ( ( collect_nat @ P2 )
% 0.26/0.59 = ( collect_nat @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_127_Collect__cong,axiom,
% 0.26/0.59 ! [P2: poly_real > $o,Q: poly_real > $o] :
% 0.26/0.59 ( ! [X3: poly_real] :
% 0.26/0.59 ( ( P2 @ X3 )
% 0.26/0.59 = ( Q @ X3 ) )
% 0.26/0.59 => ( ( collect_poly_real @ P2 )
% 0.26/0.59 = ( collect_poly_real @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_128_poly__eqI,axiom,
% 0.26/0.59 ! [P: poly_real,Q2: poly_real] :
% 0.26/0.59 ( ! [N2: nat] :
% 0.26/0.59 ( ( coeff_real @ P @ N2 )
% 0.26/0.59 = ( coeff_real @ Q2 @ N2 ) )
% 0.26/0.59 => ( P = Q2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_eqI
% 0.26/0.59 thf(fact_129_poly__eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: poly_real,Z: poly_real] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [P3: poly_real,Q3: poly_real] :
% 0.26/0.59 ! [N3: nat] :
% 0.26/0.59 ( ( coeff_real @ P3 @ N3 )
% 0.26/0.59 = ( coeff_real @ Q3 @ N3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_eq_iff
% 0.26/0.59 thf(fact_130_coeff__inject,axiom,
% 0.26/0.59 ! [X2: poly_real,Y2: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ X2 )
% 0.26/0.59 = ( coeff_real @ Y2 ) )
% 0.26/0.59 = ( X2 = Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % coeff_inject
% 0.26/0.59 thf(fact_131_algebraicE,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( algebraic_real @ X2 )
% 0.26/0.59 => ~ ! [P4: poly_real] :
% 0.26/0.59 ( ! [I: nat] : ( member_real @ ( coeff_real @ P4 @ I ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( P4 != zero_zero_poly_real )
% 0.26/0.59 => ( ( poly_real2 @ P4 @ X2 )
% 0.26/0.59 != zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraicE
% 0.26/0.59 thf(fact_132_algebraicI,axiom,
% 0.26/0.59 ! [P: poly_real,X2: real] :
% 0.26/0.59 ( ! [I3: nat] : ( member_real @ ( coeff_real @ P @ I3 ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( P != zero_zero_poly_real )
% 0.26/0.59 => ( ( ( poly_real2 @ P @ X2 )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 => ( algebraic_real @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraicI
% 0.26/0.59 thf(fact_133_algebraic__def,axiom,
% 0.26/0.59 ( algebraic_real
% 0.26/0.59 = ( ^ [X: real] :
% 0.26/0.59 ? [P3: poly_real] :
% 0.26/0.59 ( ! [I4: nat] : ( member_real @ ( coeff_real @ P3 @ I4 ) @ ring_1_Ints_real )
% 0.26/0.59 & ( P3 != zero_zero_poly_real )
% 0.26/0.59 & ( ( poly_real2 @ P3 @ X )
% 0.26/0.59 = zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_def
% 0.26/0.59 thf(fact_134_algebraic__altdef,axiom,
% 0.26/0.59 ( algebraic_real
% 0.26/0.59 = ( ^ [X: real] :
% 0.26/0.59 ? [P3: poly_real] :
% 0.26/0.59 ( ! [I4: nat] : ( member_real @ ( coeff_real @ P3 @ I4 ) @ field_1537545994s_real )
% 0.26/0.59 & ( P3 != zero_zero_poly_real )
% 0.26/0.59 & ( ( poly_real2 @ P3 @ X )
% 0.26/0.59 = zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_altdef
% 0.26/0.59 thf(fact_135_zero__poly_Orep__eq,axiom,
% 0.26/0.59 ( ( coeff_poly_poly_real @ zero_z935034829y_real )
% 0.26/0.59 = ( ^ [Uu: nat] : zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.rep_eq
% 0.26/0.59 thf(fact_136_zero__poly_Orep__eq,axiom,
% 0.26/0.59 ( ( coeff_poly_nat @ zero_z1059985641ly_nat )
% 0.26/0.59 = ( ^ [Uu: nat] : zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.rep_eq
% 0.26/0.59 thf(fact_137_zero__poly_Orep__eq,axiom,
% 0.26/0.59 ( ( coeff_real @ zero_zero_poly_real )
% 0.26/0.59 = ( ^ [Uu: nat] : zero_zero_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.rep_eq
% 0.26/0.59 thf(fact_138_zero__poly_Orep__eq,axiom,
% 0.26/0.59 ( ( coeff_poly_real @ zero_z1423781445y_real )
% 0.26/0.59 = ( ^ [Uu: nat] : zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.rep_eq
% 0.26/0.59 thf(fact_139_zero__poly_Orep__eq,axiom,
% 0.26/0.59 ( ( coeff_nat @ zero_zero_poly_nat )
% 0.26/0.59 = ( ^ [Uu: nat] : zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_poly.rep_eq
% 0.26/0.59 thf(fact_140_poly__0__coeff__0,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( poly_real2 @ P @ zero_zero_real )
% 0.26/0.59 = ( coeff_real @ P @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0_coeff_0
% 0.26/0.59 thf(fact_141_poly__0__coeff__0,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ P @ zero_zero_poly_real )
% 0.26/0.59 = ( coeff_poly_real @ P @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0_coeff_0
% 0.26/0.59 thf(fact_142_poly__0__coeff__0,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( poly_nat2 @ P @ zero_zero_nat )
% 0.26/0.59 = ( coeff_nat @ P @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0_coeff_0
% 0.26/0.59 thf(fact_143_poly__0__coeff__0,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( poly_poly_poly_real2 @ P @ zero_z1423781445y_real )
% 0.26/0.59 = ( coeff_poly_poly_real @ P @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0_coeff_0
% 0.26/0.59 thf(fact_144_poly__0__coeff__0,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( poly_poly_nat2 @ P @ zero_zero_poly_nat )
% 0.26/0.59 = ( coeff_poly_nat @ P @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_0_coeff_0
% 0.26/0.59 thf(fact_145_order__0I,axiom,
% 0.26/0.59 ! [P: poly_real,A3: real] :
% 0.26/0.59 ( ( ( poly_real2 @ P @ A3 )
% 0.26/0.59 != zero_zero_real )
% 0.26/0.59 => ( ( order_real @ A3 @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_0I
% 0.26/0.59 thf(fact_146_order__0I,axiom,
% 0.26/0.59 ! [P: poly_poly_real,A3: poly_real] :
% 0.26/0.59 ( ( ( poly_poly_real2 @ P @ A3 )
% 0.26/0.59 != zero_zero_poly_real )
% 0.26/0.59 => ( ( order_poly_real @ A3 @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_0I
% 0.26/0.59 thf(fact_147_order__0I,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real,A3: poly_poly_real] :
% 0.26/0.59 ( ( ( poly_poly_poly_real2 @ P @ A3 )
% 0.26/0.59 != zero_z1423781445y_real )
% 0.26/0.59 => ( ( order_poly_poly_real @ A3 @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_0I
% 0.26/0.59 thf(fact_148_leading__coeff__neq__0,axiom,
% 0.26/0.59 ! [P: poly_poly_poly_real] :
% 0.26/0.59 ( ( P != zero_z935034829y_real )
% 0.26/0.59 => ( ( coeff_poly_poly_real @ P @ ( degree360860553y_real @ P ) )
% 0.26/0.59 != zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_neq_0
% 0.26/0.59 thf(fact_149_leading__coeff__neq__0,axiom,
% 0.26/0.59 ! [P: poly_poly_nat] :
% 0.26/0.59 ( ( P != zero_z1059985641ly_nat )
% 0.26/0.59 => ( ( coeff_poly_nat @ P @ ( degree_poly_nat @ P ) )
% 0.26/0.59 != zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_neq_0
% 0.26/0.59 thf(fact_150_leading__coeff__neq__0,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( P != zero_zero_poly_real )
% 0.26/0.59 => ( ( coeff_real @ P @ ( degree_real @ P ) )
% 0.26/0.59 != zero_zero_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_neq_0
% 0.26/0.59 thf(fact_151_leading__coeff__neq__0,axiom,
% 0.26/0.59 ! [P: poly_poly_real] :
% 0.26/0.59 ( ( P != zero_z1423781445y_real )
% 0.26/0.59 => ( ( coeff_poly_real @ P @ ( degree_poly_real @ P ) )
% 0.26/0.59 != zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_neq_0
% 0.26/0.59 thf(fact_152_leading__coeff__neq__0,axiom,
% 0.26/0.59 ! [P: poly_nat] :
% 0.26/0.59 ( ( P != zero_zero_poly_nat )
% 0.26/0.59 => ( ( coeff_nat @ P @ ( degree_nat @ P ) )
% 0.26/0.59 != zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % leading_coeff_neq_0
% 0.26/0.59 thf(fact_153_Rats__infinite,axiom,
% 0.26/0.59 ~ ( finite_finite_real @ field_1537545994s_real ) ).
% 0.26/0.59
% 0.26/0.59 % Rats_infinite
% 0.26/0.59 thf(fact_154_Rats__0,axiom,
% 0.26/0.59 member_real @ zero_zero_real @ field_1537545994s_real ).
% 0.26/0.59
% 0.26/0.59 % Rats_0
% 0.26/0.59 thf(fact_155_Ints__0,axiom,
% 0.26/0.59 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 0.26/0.59
% 0.26/0.59 % Ints_0
% 0.26/0.59 thf(fact_156_Ints__0,axiom,
% 0.26/0.59 member_poly_real @ zero_zero_poly_real @ ring_1690226883y_real ).
% 0.26/0.59
% 0.26/0.59 % Ints_0
% 0.26/0.59 thf(fact_157_Ints__0,axiom,
% 0.26/0.59 member1159720147y_real @ zero_z1423781445y_real @ ring_1897377867y_real ).
% 0.26/0.59
% 0.26/0.59 % Ints_0
% 0.26/0.59 thf(fact_158_rsquarefree__def,axiom,
% 0.26/0.59 ( rsquarefree_real
% 0.26/0.59 = ( ^ [P3: poly_real] :
% 0.26/0.59 ( ( P3 != zero_zero_poly_real )
% 0.26/0.59 & ! [A: real] :
% 0.26/0.59 ( ( ( order_real @ A @ P3 )
% 0.26/0.59 = zero_zero_nat )
% 0.26/0.59 | ( ( order_real @ A @ P3 )
% 0.26/0.59 = one_one_nat ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % rsquarefree_def
% 0.26/0.59 thf(fact_159_rsquarefree__def,axiom,
% 0.26/0.59 ( rsquar1555552848y_real
% 0.26/0.59 = ( ^ [P3: poly_poly_real] :
% 0.26/0.59 ( ( P3 != zero_z1423781445y_real )
% 0.26/0.59 & ! [A: poly_real] :
% 0.26/0.59 ( ( ( order_poly_real @ A @ P3 )
% 0.26/0.59 = zero_zero_nat )
% 0.26/0.59 | ( ( order_poly_real @ A @ P3 )
% 0.26/0.59 = one_one_nat ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % rsquarefree_def
% 0.26/0.59 thf(fact_160_poly__cutoff__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_cutoff_real @ N @ one_one_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_cutoff_real @ N @ one_one_poly_real )
% 0.26/0.59 = one_one_poly_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_1
% 0.26/0.59 thf(fact_161_poly__cutoff__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_c1404107022y_real @ N @ one_on501200385y_real )
% 0.26/0.59 = zero_z1423781445y_real ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_c1404107022y_real @ N @ one_on501200385y_real )
% 0.26/0.59 = one_on501200385y_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_1
% 0.26/0.59 thf(fact_162_poly__cutoff__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_cutoff_nat @ N @ one_one_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_cutoff_nat @ N @ one_one_poly_nat )
% 0.26/0.59 = one_one_poly_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_cutoff_1
% 0.26/0.59 thf(fact_163_order__pderiv2,axiom,
% 0.26/0.59 ! [P: poly_real,A3: real,N: nat] :
% 0.26/0.59 ( ( ( pderiv_real @ P )
% 0.26/0.59 != zero_zero_poly_real )
% 0.26/0.59 => ( ( ( order_real @ A3 @ P )
% 0.26/0.59 != zero_zero_nat )
% 0.26/0.59 => ( ( ( order_real @ A3 @ ( pderiv_real @ P ) )
% 0.26/0.59 = N )
% 0.26/0.59 = ( ( order_real @ A3 @ P )
% 0.26/0.59 = ( suc @ N ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_pderiv2
% 0.26/0.59 thf(fact_164_order__pderiv,axiom,
% 0.26/0.59 ! [P: poly_real,A3: real] :
% 0.26/0.59 ( ( ( pderiv_real @ P )
% 0.26/0.59 != zero_zero_poly_real )
% 0.26/0.59 => ( ( ( order_real @ A3 @ P )
% 0.26/0.59 != zero_zero_nat )
% 0.26/0.59 => ( ( order_real @ A3 @ P )
% 0.26/0.59 = ( suc @ ( order_real @ A3 @ ( pderiv_real @ P ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_pderiv
% 0.26/0.59 thf(fact_165_cr__poly__def,axiom,
% 0.26/0.59 ( cr_poly_real
% 0.26/0.59 = ( ^ [X: nat > real,Y3: poly_real] :
% 0.26/0.59 ( X
% 0.26/0.59 = ( coeff_real @ Y3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % cr_poly_def
% 0.26/0.59 thf(fact_166_dvd__pderiv__iff,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( dvd_dvd_poly_real @ P @ ( pderiv_real @ P ) )
% 0.26/0.59 = ( ( degree_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_pderiv_iff
% 0.26/0.59 thf(fact_167_degree__1,axiom,
% 0.26/0.59 ( ( degree_real @ one_one_poly_real )
% 0.26/0.59 = zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % degree_1
% 0.26/0.59 thf(fact_168_poly__1,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( poly_real2 @ one_one_poly_real @ X2 )
% 0.26/0.59 = one_one_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_1
% 0.26/0.59 thf(fact_169_poly__1,axiom,
% 0.26/0.59 ! [X2: poly_real] :
% 0.26/0.59 ( ( poly_poly_real2 @ one_on501200385y_real @ X2 )
% 0.26/0.59 = one_one_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % poly_1
% 0.26/0.59 thf(fact_170_poly__1,axiom,
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( poly_nat2 @ one_one_poly_nat @ X2 )
% 0.26/0.59 = one_one_nat ) ).
% 0.26/0.59
% 0.26/0.59 % poly_1
% 0.26/0.59 thf(fact_171_pderiv__1,axiom,
% 0.26/0.59 ( ( pderiv_real @ one_one_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_1
% 0.26/0.59 thf(fact_172_pderiv__1,axiom,
% 0.26/0.59 ( ( pderiv_poly_real @ one_on501200385y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_1
% 0.26/0.59 thf(fact_173_pderiv__1,axiom,
% 0.26/0.59 ( ( pderiv_nat @ one_one_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % pderiv_1
% 0.26/0.59 thf(fact_174_lead__coeff__1,axiom,
% 0.26/0.59 ( ( coeff_nat @ one_one_poly_nat @ ( degree_nat @ one_one_poly_nat ) )
% 0.26/0.59 = one_one_nat ) ).
% 0.26/0.59
% 0.26/0.59 % lead_coeff_1
% 0.26/0.59 thf(fact_175_lead__coeff__1,axiom,
% 0.26/0.59 ( ( coeff_real @ one_one_poly_real @ ( degree_real @ one_one_poly_real ) )
% 0.26/0.59 = one_one_real ) ).
% 0.26/0.59
% 0.26/0.59 % lead_coeff_1
% 0.26/0.59 thf(fact_176_one__reorient,axiom,
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( one_one_nat = X2 )
% 0.26/0.59 = ( X2 = one_one_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % one_reorient
% 0.26/0.59 thf(fact_177_Ints__1,axiom,
% 0.26/0.59 member_real @ one_one_real @ ring_1_Ints_real ).
% 0.26/0.59
% 0.26/0.59 % Ints_1
% 0.26/0.59 thf(fact_178_Rats__1,axiom,
% 0.26/0.59 member_real @ one_one_real @ field_1537545994s_real ).
% 0.26/0.59
% 0.26/0.59 % Rats_1
% 0.26/0.59 thf(fact_179_is__unit__iff__degree,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( P != zero_zero_poly_real )
% 0.26/0.59 => ( ( dvd_dvd_poly_real @ P @ one_one_poly_real )
% 0.26/0.59 = ( ( degree_real @ P )
% 0.26/0.59 = zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % is_unit_iff_degree
% 0.26/0.59 thf(fact_180_not__dvd__pderiv,axiom,
% 0.26/0.59 ! [P: poly_real] :
% 0.26/0.59 ( ( ( degree_real @ P )
% 0.26/0.59 != zero_zero_nat )
% 0.26/0.59 => ~ ( dvd_dvd_poly_real @ P @ ( pderiv_real @ P ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_dvd_pderiv
% 0.26/0.59 thf(fact_181_poly__shift__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_real @ N @ one_one_poly_real )
% 0.26/0.59 = one_one_poly_real ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_real @ N @ one_one_poly_real )
% 0.26/0.59 = zero_zero_poly_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_1
% 0.26/0.59 thf(fact_182_poly__shift__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_poly_real @ N @ one_on501200385y_real )
% 0.26/0.59 = one_on501200385y_real ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_poly_real @ N @ one_on501200385y_real )
% 0.26/0.59 = zero_z1423781445y_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_1
% 0.26/0.59 thf(fact_183_poly__shift__1,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ( N = zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_nat @ N @ one_one_poly_nat )
% 0.26/0.59 = one_one_poly_nat ) )
% 0.26/0.59 & ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ( poly_shift_nat @ N @ one_one_poly_nat )
% 0.26/0.59 = zero_zero_poly_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % poly_shift_1
% 0.26/0.59 thf(fact_184_dvd__0__left__iff,axiom,
% 0.26/0.59 ! [A3: real] :
% 0.26/0.59 ( ( dvd_dvd_real @ zero_zero_real @ A3 )
% 0.26/0.59 = ( A3 = zero_zero_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left_iff
% 0.26/0.59 thf(fact_185_dvd__0__left__iff,axiom,
% 0.26/0.59 ! [A3: poly_real] :
% 0.26/0.59 ( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A3 )
% 0.26/0.59 = ( A3 = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left_iff
% 0.26/0.59 thf(fact_186_dvd__0__left__iff,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A3 )
% 0.26/0.59 = ( A3 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left_iff
% 0.26/0.59 thf(fact_187_dvd__0__left__iff,axiom,
% 0.26/0.59 ! [A3: poly_poly_real] :
% 0.26/0.59 ( ( dvd_dv1946063458y_real @ zero_z1423781445y_real @ A3 )
% 0.26/0.59 = ( A3 = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left_iff
% 0.26/0.59 thf(fact_188_dvd__0__left__iff,axiom,
% 0.26/0.59 ! [A3: poly_nat] :
% 0.26/0.59 ( ( dvd_dvd_poly_nat @ zero_zero_poly_nat @ A3 )
% 0.26/0.59 = ( A3 = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left_iff
% 0.26/0.59 thf(fact_189_dvd__0__right,axiom,
% 0.26/0.59 ! [A3: real] : ( dvd_dvd_real @ A3 @ zero_zero_real ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_right
% 0.26/0.59 thf(fact_190_dvd__0__right,axiom,
% 0.26/0.59 ! [A3: poly_real] : ( dvd_dvd_poly_real @ A3 @ zero_zero_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_right
% 0.26/0.59 thf(fact_191_dvd__0__right,axiom,
% 0.26/0.59 ! [A3: nat] : ( dvd_dvd_nat @ A3 @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_right
% 0.26/0.59 thf(fact_192_dvd__0__right,axiom,
% 0.26/0.59 ! [A3: poly_poly_real] : ( dvd_dv1946063458y_real @ A3 @ zero_z1423781445y_real ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_right
% 0.26/0.59 thf(fact_193_dvd__0__right,axiom,
% 0.26/0.59 ! [A3: poly_nat] : ( dvd_dvd_poly_nat @ A3 @ zero_zero_poly_nat ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_right
% 0.26/0.59 thf(fact_194_One__nat__def,axiom,
% 0.26/0.59 ( one_one_nat
% 0.26/0.59 = ( suc @ zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % One_nat_def
% 0.26/0.59 thf(fact_195_not__is__unit__0,axiom,
% 0.26/0.59 ~ ( dvd_dvd_poly_real @ zero_zero_poly_real @ one_one_poly_real ) ).
% 0.26/0.59
% 0.26/0.59 % not_is_unit_0
% 0.26/0.59 thf(fact_196_not__is__unit__0,axiom,
% 0.26/0.59 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.26/0.59
% 0.26/0.59 % not_is_unit_0
% 0.26/0.59 thf(fact_197_not__is__unit__0,axiom,
% 0.26/0.59 ~ ( dvd_dv1946063458y_real @ zero_z1423781445y_real @ one_on501200385y_real ) ).
% 0.26/0.59
% 0.26/0.59 % not_is_unit_0
% 0.26/0.59 thf(fact_198_nat_Oinject,axiom,
% 0.26/0.59 ! [X22: nat,Y22: nat] :
% 0.26/0.59 ( ( ( suc @ X22 )
% 0.26/0.59 = ( suc @ Y22 ) )
% 0.26/0.59 = ( X22 = Y22 ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat.inject
% 0.26/0.59 thf(fact_199_old_Onat_Oinject,axiom,
% 0.26/0.59 ! [Nat: nat,Nat2: nat] :
% 0.26/0.59 ( ( ( suc @ Nat )
% 0.26/0.59 = ( suc @ Nat2 ) )
% 0.26/0.59 = ( Nat = Nat2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % old.nat.inject
% 0.26/0.59 thf(fact_200_nat__dvd__1__iff__1,axiom,
% 0.26/0.59 ! [M: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.26/0.59 = ( M = one_one_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat_dvd_1_iff_1
% 0.26/0.59 thf(fact_201_dvd__1__iff__1,axiom,
% 0.26/0.59 ! [M: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.26/0.59 = ( M
% 0.26/0.59 = ( suc @ zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_1_iff_1
% 0.26/0.59 thf(fact_202_dvd__1__left,axiom,
% 0.26/0.59 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_1_left
% 0.26/0.59 thf(fact_203_dvd__trans,axiom,
% 0.26/0.59 ! [A3: nat,B2: nat,C: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.59 => ( ( dvd_dvd_nat @ B2 @ C )
% 0.26/0.59 => ( dvd_dvd_nat @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_trans
% 0.26/0.59 thf(fact_204_dvd__refl,axiom,
% 0.26/0.59 ! [A3: nat] : ( dvd_dvd_nat @ A3 @ A3 ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_refl
% 0.26/0.59 thf(fact_205_n__not__Suc__n,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( N
% 0.26/0.59 != ( suc @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % n_not_Suc_n
% 0.26/0.59 thf(fact_206_Suc__inject,axiom,
% 0.26/0.59 ! [X2: nat,Y2: nat] :
% 0.26/0.59 ( ( ( suc @ X2 )
% 0.26/0.59 = ( suc @ Y2 ) )
% 0.26/0.59 => ( X2 = Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_inject
% 0.26/0.59 thf(fact_207_zero__neq__one,axiom,
% 0.26/0.59 zero_zero_real != one_one_real ).
% 0.26/0.59
% 0.26/0.59 % zero_neq_one
% 0.26/0.59 thf(fact_208_zero__neq__one,axiom,
% 0.26/0.59 zero_zero_poly_real != one_one_poly_real ).
% 0.26/0.59
% 0.26/0.59 % zero_neq_one
% 0.26/0.59 thf(fact_209_zero__neq__one,axiom,
% 0.26/0.59 zero_zero_nat != one_one_nat ).
% 0.26/0.59
% 0.26/0.59 % zero_neq_one
% 0.26/0.59 thf(fact_210_zero__neq__one,axiom,
% 0.26/0.59 zero_z1423781445y_real != one_on501200385y_real ).
% 0.26/0.59
% 0.26/0.59 % zero_neq_one
% 0.26/0.59 thf(fact_211_zero__neq__one,axiom,
% 0.26/0.59 zero_zero_poly_nat != one_one_poly_nat ).
% 0.26/0.59
% 0.26/0.59 % zero_neq_one
% 0.26/0.59 thf(fact_212_dvd__0__left,axiom,
% 0.26/0.59 ! [A3: real] :
% 0.26/0.59 ( ( dvd_dvd_real @ zero_zero_real @ A3 )
% 0.26/0.59 => ( A3 = zero_zero_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left
% 0.26/0.59 thf(fact_213_dvd__0__left,axiom,
% 0.26/0.59 ! [A3: poly_real] :
% 0.26/0.59 ( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A3 )
% 0.26/0.59 => ( A3 = zero_zero_poly_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left
% 0.26/0.59 thf(fact_214_dvd__0__left,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A3 )
% 0.26/0.59 => ( A3 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left
% 0.26/0.59 thf(fact_215_dvd__0__left,axiom,
% 0.26/0.59 ! [A3: poly_poly_real] :
% 0.26/0.59 ( ( dvd_dv1946063458y_real @ zero_z1423781445y_real @ A3 )
% 0.26/0.59 => ( A3 = zero_z1423781445y_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left
% 0.26/0.59 thf(fact_216_dvd__0__left,axiom,
% 0.26/0.59 ! [A3: poly_nat] :
% 0.26/0.59 ( ( dvd_dvd_poly_nat @ zero_zero_poly_nat @ A3 )
% 0.26/0.59 => ( A3 = zero_zero_poly_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_0_left
% 0.26/0.59 thf(fact_217_dvd__unit__imp__unit,axiom,
% 0.26/0.59 ! [A3: nat,B2: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.59 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 0.26/0.59 => ( dvd_dvd_nat @ A3 @ one_one_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_unit_imp_unit
% 0.26/0.59 thf(fact_218_unit__imp__dvd,axiom,
% 0.26/0.59 ! [B2: nat,A3: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 0.26/0.59 => ( dvd_dvd_nat @ B2 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % unit_imp_dvd
% 0.26/0.59 thf(fact_219_one__dvd,axiom,
% 0.26/0.59 ! [A3: nat] : ( dvd_dvd_nat @ one_one_nat @ A3 ) ).
% 0.26/0.59
% 0.26/0.59 % one_dvd
% 0.26/0.59 thf(fact_220_not0__implies__Suc,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( N != zero_zero_nat )
% 0.26/0.59 => ? [M2: nat] :
% 0.26/0.59 ( N
% 0.26/0.59 = ( suc @ M2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not0_implies_Suc
% 0.26/0.59 thf(fact_221_old_Onat_Oinducts,axiom,
% 0.26/0.59 ! [P2: nat > $o,Nat: nat] :
% 0.26/0.59 ( ( P2 @ zero_zero_nat )
% 0.26/0.59 => ( ! [Nat3: nat] :
% 0.26/0.59 ( ( P2 @ Nat3 )
% 0.26/0.59 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.26/0.59 => ( P2 @ Nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % old.nat.inducts
% 0.26/0.59 thf(fact_222_old_Onat_Oexhaust,axiom,
% 0.26/0.59 ! [Y2: nat] :
% 0.26/0.59 ( ( Y2 != zero_zero_nat )
% 0.26/0.59 => ~ ! [Nat3: nat] :
% 0.26/0.59 ( Y2
% 0.26/0.59 != ( suc @ Nat3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % old.nat.exhaust
% 0.26/0.59 thf(fact_223_Zero__not__Suc,axiom,
% 0.26/0.59 ! [M: nat] :
% 0.26/0.59 ( zero_zero_nat
% 0.26/0.59 != ( suc @ M ) ) ).
% 0.26/0.59
% 0.26/0.59 % Zero_not_Suc
% 0.26/0.59 thf(fact_224_Zero__neq__Suc,axiom,
% 0.26/0.59 ! [M: nat] :
% 0.26/0.59 ( zero_zero_nat
% 0.26/0.59 != ( suc @ M ) ) ).
% 0.26/0.59
% 0.26/0.59 % Zero_neq_Suc
% 0.26/0.59 thf(fact_225_Suc__neq__Zero,axiom,
% 0.26/0.59 ! [M: nat] :
% 0.26/0.59 ( ( suc @ M )
% 0.26/0.59 != zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_neq_Zero
% 0.26/0.59 thf(fact_226_zero__induct,axiom,
% 0.26/0.59 ! [P2: nat > $o,K: nat] :
% 0.26/0.59 ( ( P2 @ K )
% 0.26/0.59 => ( ! [N2: nat] :
% 0.26/0.59 ( ( P2 @ ( suc @ N2 ) )
% 0.26/0.59 => ( P2 @ N2 ) )
% 0.26/0.59 => ( P2 @ zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_induct
% 0.26/0.59 thf(fact_227_diff__induct,axiom,
% 0.26/0.59 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 0.26/0.59 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 0.26/0.59 => ( ! [Y4: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y4 ) )
% 0.26/0.59 => ( ! [X3: nat,Y4: nat] :
% 0.26/0.59 ( ( P2 @ X3 @ Y4 )
% 0.26/0.59 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 0.26/0.59 => ( P2 @ M @ N ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % diff_induct
% 0.26/0.59 thf(fact_228_nat__induct,axiom,
% 0.26/0.59 ! [P2: nat > $o,N: nat] :
% 0.26/0.59 ( ( P2 @ zero_zero_nat )
% 0.26/0.59 => ( ! [N2: nat] :
% 0.26/0.59 ( ( P2 @ N2 )
% 0.26/0.59 => ( P2 @ ( suc @ N2 ) ) )
% 0.26/0.59 => ( P2 @ N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat_induct
% 0.26/0.59 thf(fact_229_nat_OdiscI,axiom,
% 0.26/0.59 ! [Nat: nat,X22: nat] :
% 0.26/0.59 ( ( Nat
% 0.26/0.59 = ( suc @ X22 ) )
% 0.26/0.59 => ( Nat != zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat.discI
% 0.26/0.59 thf(fact_230_old_Onat_Odistinct_I1_J,axiom,
% 0.26/0.59 ! [Nat2: nat] :
% 0.26/0.59 ( zero_zero_nat
% 0.26/0.59 != ( suc @ Nat2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % old.nat.distinct(1)
% 0.26/0.59 thf(fact_231_old_Onat_Odistinct_I2_J,axiom,
% 0.26/0.59 ! [Nat2: nat] :
% 0.26/0.59 ( ( suc @ Nat2 )
% 0.26/0.59 != zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % old.nat.distinct(2)
% 0.26/0.59 thf(fact_232_nat_Odistinct_I1_J,axiom,
% 0.26/0.59 ! [X22: nat] :
% 0.26/0.59 ( zero_zero_nat
% 0.26/0.59 != ( suc @ X22 ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat.distinct(1)
% 0.26/0.59 thf(fact_233_algebraic__int_Oinducts,axiom,
% 0.26/0.59 ! [X2: real,P2: real > $o] :
% 0.26/0.59 ( ( algebraic_int_real @ X2 )
% 0.26/0.59 => ( ! [P4: poly_real,X3: real] :
% 0.26/0.59 ( ( ( coeff_real @ P4 @ ( degree_real @ P4 ) )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 => ( ! [I: nat] : ( member_real @ ( coeff_real @ P4 @ I ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( ( poly_real2 @ P4 @ X3 )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 => ( P2 @ X3 ) ) ) )
% 0.26/0.59 => ( P2 @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int.inducts
% 0.26/0.59 thf(fact_234_algebraic__int_Ointros,axiom,
% 0.26/0.59 ! [P: poly_real,X2: real] :
% 0.26/0.59 ( ( ( coeff_real @ P @ ( degree_real @ P ) )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 => ( ! [I3: nat] : ( member_real @ ( coeff_real @ P @ I3 ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( ( poly_real2 @ P @ X2 )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 => ( algebraic_int_real @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int.intros
% 0.26/0.59 thf(fact_235_algebraic__int_Osimps,axiom,
% 0.26/0.59 ( algebraic_int_real
% 0.26/0.59 = ( ^ [A: real] :
% 0.26/0.59 ? [P3: poly_real,X: real] :
% 0.26/0.59 ( ( A = X )
% 0.26/0.59 & ( ( coeff_real @ P3 @ ( degree_real @ P3 ) )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 & ! [I4: nat] : ( member_real @ ( coeff_real @ P3 @ I4 ) @ ring_1_Ints_real )
% 0.26/0.59 & ( ( poly_real2 @ P3 @ X )
% 0.26/0.59 = zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int.simps
% 0.26/0.59 thf(fact_236_algebraic__int_Ocases,axiom,
% 0.26/0.59 ! [A3: real] :
% 0.26/0.59 ( ( algebraic_int_real @ A3 )
% 0.26/0.59 => ~ ! [P4: poly_real] :
% 0.26/0.59 ( ( ( coeff_real @ P4 @ ( degree_real @ P4 ) )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 => ( ! [I: nat] : ( member_real @ ( coeff_real @ P4 @ I ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( poly_real2 @ P4 @ A3 )
% 0.26/0.59 != zero_zero_real ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int.cases
% 0.26/0.59 thf(fact_237_exists__least__lemma,axiom,
% 0.26/0.59 ! [P2: nat > $o] :
% 0.26/0.59 ( ~ ( P2 @ zero_zero_nat )
% 0.26/0.59 => ( ? [X_12: nat] : ( P2 @ X_12 )
% 0.26/0.59 => ? [N2: nat] :
% 0.26/0.59 ( ~ ( P2 @ N2 )
% 0.26/0.59 & ( P2 @ ( suc @ N2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % exists_least_lemma
% 0.26/0.59 thf(fact_238_algebraic__int__0,axiom,
% 0.26/0.59 algebraic_int_real @ zero_zero_real ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int_0
% 0.26/0.59 thf(fact_239_dvd__antisym,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ M @ N )
% 0.26/0.59 => ( ( dvd_dvd_nat @ N @ M )
% 0.26/0.59 => ( M = N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dvd_antisym
% 0.26/0.59 thf(fact_240_int__imp__algebraic__int,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( member_real @ X2 @ ring_1_Ints_real )
% 0.26/0.59 => ( algebraic_int_real @ X2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % int_imp_algebraic_int
% 0.26/0.59 thf(fact_241_algebraic__int__imp__algebraic,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( algebraic_int_real @ X2 )
% 0.26/0.59 => ( algebraic_real @ X2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int_imp_algebraic
% 0.26/0.59 thf(fact_242_rational__algebraic__int__is__int,axiom,
% 0.26/0.59 ! [X2: real] :
% 0.26/0.59 ( ( algebraic_int_real @ X2 )
% 0.26/0.59 => ( ( member_real @ X2 @ field_1537545994s_real )
% 0.26/0.59 => ( member_real @ X2 @ ring_1_Ints_real ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % rational_algebraic_int_is_int
% 0.26/0.59 thf(fact_243_algebraic__int__inverse,axiom,
% 0.26/0.59 ! [P: poly_real,X2: real] :
% 0.26/0.59 ( ( ( poly_real2 @ P @ X2 )
% 0.26/0.59 = zero_zero_real )
% 0.26/0.59 => ( ! [I3: nat] : ( member_real @ ( coeff_real @ P @ I3 ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( ( coeff_real @ P @ zero_zero_nat )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 => ( algebraic_int_real @ ( inverse_inverse_real @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int_inverse
% 0.26/0.59 thf(fact_244_algebraic__int__root,axiom,
% 0.26/0.59 ! [Y2: real,P: poly_real,X2: real] :
% 0.26/0.59 ( ( algebraic_int_real @ Y2 )
% 0.26/0.59 => ( ( ( poly_real2 @ P @ X2 )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ! [I3: nat] : ( member_real @ ( coeff_real @ P @ I3 ) @ ring_1_Ints_real )
% 0.26/0.59 => ( ( ( coeff_real @ P @ ( degree_real @ P ) )
% 0.26/0.59 = one_one_real )
% 0.26/0.59 => ( ( ord_less_nat @ zero_zero_nat @ ( degree_real @ P ) )
% 0.26/0.59 => ( algebraic_int_real @ X2 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % algebraic_int_root
% 0.26/0.59 thf(fact_245_gcd__nat_Oextremum__uniqueI,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A3 )
% 0.26/0.59 => ( A3 = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % gcd_nat.extremum_uniqueI
% 0.26/0.59 thf(fact_246_gcd__nat_Onot__eq__extremum,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ( ( A3 != zero_zero_nat )
% 0.26/0.59 = ( ( dvd_dvd_nat @ A3 @ zero_zero_nat )
% 0.26/0.59 & ( A3 != zero_zero_nat ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % gcd_nat.not_eq_extremum
% 0.26/0.59 thf(fact_247_finite__Collect__less__nat,axiom,
% 0.26/0.59 ! [K: nat] :
% 0.26/0.59 ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_less_nat
% 0.26/0.59 thf(fact_248_not__gr__zero,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.59 = ( N = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_gr_zero
% 0.26/0.59 thf(fact_249_bot__nat__0_Onot__eq__extremum,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ( ( A3 != zero_zero_nat )
% 0.26/0.59 = ( ord_less_nat @ zero_zero_nat @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % bot_nat_0.not_eq_extremum
% 0.26/0.59 thf(fact_250_less__nat__zero__code,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % less_nat_zero_code
% 0.26/0.59 thf(fact_251_neq0__conv,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( N != zero_zero_nat )
% 0.26/0.59 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % neq0_conv
% 0.26/0.59 thf(fact_252_lessI,axiom,
% 0.26/0.59 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % lessI
% 0.26/0.59 thf(fact_253_Suc__mono,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_mono
% 0.26/0.59 thf(fact_254_Suc__less__eq,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.59 = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_less_eq
% 0.26/0.59 thf(fact_255_zero__less__Suc,axiom,
% 0.26/0.59 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_less_Suc
% 0.26/0.59 thf(fact_256_less__Suc0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.59 = ( N = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_Suc0
% 0.26/0.59 thf(fact_257_less__one,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ N @ one_one_nat )
% 0.26/0.59 = ( N = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_one
% 0.26/0.59 thf(fact_258_zero__less__iff__neq__zero,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.59 = ( N != zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % zero_less_iff_neq_zero
% 0.26/0.59 thf(fact_259_gr__implies__not__zero,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( N != zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % gr_implies_not_zero
% 0.26/0.59 thf(fact_260_not__less__zero,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % not_less_zero
% 0.26/0.59 thf(fact_261_gr__zeroI,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % gr_zeroI
% 0.26/0.59 thf(fact_262_gr0I,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( N != zero_zero_nat )
% 0.26/0.59 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % gr0I
% 0.26/0.59 thf(fact_263_not__gr0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.59 = ( N = zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_gr0
% 0.26/0.59 thf(fact_264_not__less0,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % not_less0
% 0.26/0.59 thf(fact_265_less__zeroE,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % less_zeroE
% 0.26/0.59 thf(fact_266_gr__implies__not0,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( N != zero_zero_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % gr_implies_not0
% 0.26/0.59 thf(fact_267_infinite__descent0,axiom,
% 0.26/0.59 ! [P2: nat > $o,N: nat] :
% 0.26/0.59 ( ( P2 @ zero_zero_nat )
% 0.26/0.59 => ( ! [N2: nat] :
% 0.26/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.59 => ( ~ ( P2 @ N2 )
% 0.26/0.59 => ? [M3: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M3 @ N2 )
% 0.26/0.59 & ~ ( P2 @ M3 ) ) ) )
% 0.26/0.59 => ( P2 @ N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_descent0
% 0.26/0.59 thf(fact_268_bot__nat__0_Oextremum__strict,axiom,
% 0.26/0.59 ! [A3: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ A3 @ zero_zero_nat ) ).
% 0.26/0.59
% 0.26/0.59 % bot_nat_0.extremum_strict
% 0.26/0.59 thf(fact_269_not__less__less__Suc__eq,axiom,
% 0.26/0.59 ! [N: nat,M: nat] :
% 0.26/0.59 ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.59 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.59 = ( N = M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_less_less_Suc_eq
% 0.26/0.59 thf(fact_270_strict__inc__induct,axiom,
% 0.26/0.59 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ J )
% 0.26/0.59 => ( ! [I3: nat] :
% 0.26/0.59 ( ( J
% 0.26/0.59 = ( suc @ I3 ) )
% 0.26/0.59 => ( P2 @ I3 ) )
% 0.26/0.59 => ( ! [I3: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I3 @ J )
% 0.26/0.59 => ( ( P2 @ ( suc @ I3 ) )
% 0.26/0.59 => ( P2 @ I3 ) ) )
% 0.26/0.59 => ( P2 @ I2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % strict_inc_induct
% 0.26/0.59 thf(fact_271_less__Suc__induct,axiom,
% 0.26/0.59 ! [I2: nat,J: nat,P2: nat > nat > $o] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ J )
% 0.26/0.59 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.26/0.59 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I3 @ J2 )
% 0.26/0.59 => ( ( ord_less_nat @ J2 @ K2 )
% 0.26/0.59 => ( ( P2 @ I3 @ J2 )
% 0.26/0.59 => ( ( P2 @ J2 @ K2 )
% 0.26/0.59 => ( P2 @ I3 @ K2 ) ) ) ) )
% 0.26/0.59 => ( P2 @ I2 @ J ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_Suc_induct
% 0.26/0.59 thf(fact_272_less__trans__Suc,axiom,
% 0.26/0.59 ! [I2: nat,J: nat,K: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ J )
% 0.26/0.59 => ( ( ord_less_nat @ J @ K )
% 0.26/0.59 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_trans_Suc
% 0.26/0.59 thf(fact_273_Suc__less__SucD,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.59 => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_less_SucD
% 0.26/0.59 thf(fact_274_less__antisym,axiom,
% 0.26/0.59 ! [N: nat,M: nat] :
% 0.26/0.59 ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.59 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.59 => ( M = N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_antisym
% 0.26/0.59 thf(fact_275_Suc__less__eq2,axiom,
% 0.26/0.59 ! [N: nat,M: nat] :
% 0.26/0.59 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.59 = ( ? [M4: nat] :
% 0.26/0.59 ( ( M
% 0.26/0.59 = ( suc @ M4 ) )
% 0.26/0.59 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_less_eq2
% 0.26/0.59 thf(fact_276_All__less__Suc,axiom,
% 0.26/0.59 ! [N: nat,P2: nat > $o] :
% 0.26/0.59 ( ( ! [I4: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.59 => ( P2 @ I4 ) ) )
% 0.26/0.59 = ( ( P2 @ N )
% 0.26/0.59 & ! [I4: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I4 @ N )
% 0.26/0.59 => ( P2 @ I4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % All_less_Suc
% 0.26/0.59 thf(fact_277_not__less__eq,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.26/0.59 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_less_eq
% 0.26/0.59 thf(fact_278_less__Suc__eq,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.59 = ( ( ord_less_nat @ M @ N )
% 0.26/0.59 | ( M = N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_Suc_eq
% 0.26/0.59 thf(fact_279_Ex__less__Suc,axiom,
% 0.26/0.59 ! [N: nat,P2: nat > $o] :
% 0.26/0.59 ( ( ? [I4: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.59 & ( P2 @ I4 ) ) )
% 0.26/0.59 = ( ( P2 @ N )
% 0.26/0.59 | ? [I4: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I4 @ N )
% 0.26/0.59 & ( P2 @ I4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Ex_less_Suc
% 0.26/0.59 thf(fact_280_less__SucI,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_SucI
% 0.26/0.59 thf(fact_281_less__SucE,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.59 => ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( M = N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_SucE
% 0.26/0.59 thf(fact_282_Suc__lessI,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M @ N )
% 0.26/0.59 => ( ( ( suc @ M )
% 0.26/0.59 != N )
% 0.26/0.59 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_lessI
% 0.26/0.59 thf(fact_283_Suc__lessE,axiom,
% 0.26/0.59 ! [I2: nat,K: nat] :
% 0.26/0.59 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 0.26/0.59 => ~ ! [J2: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ J2 )
% 0.26/0.59 => ( K
% 0.26/0.59 != ( suc @ J2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_lessE
% 0.26/0.59 thf(fact_284_Suc__lessD,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.26/0.59 => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % Suc_lessD
% 0.26/0.59 thf(fact_285_Nat_OlessE,axiom,
% 0.26/0.59 ! [I2: nat,K: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ K )
% 0.26/0.59 => ( ( K
% 0.26/0.59 != ( suc @ I2 ) )
% 0.26/0.59 => ~ ! [J2: nat] :
% 0.26/0.59 ( ( ord_less_nat @ I2 @ J2 )
% 0.26/0.59 => ( K
% 0.26/0.59 != ( suc @ J2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Nat.lessE
% 0.26/0.59 thf(fact_286_Rats__inverse,axiom,
% 0.26/0.59 ! [A3: real] :
% 0.26/0.59 ( ( member_real @ A3 @ field_1537545994s_real )
% 0.26/0.59 => ( member_real @ ( inverse_inverse_real @ A3 ) @ field_1537545994s_real ) ) ).
% 0.26/0.59
% 0.26/0.59 % Rats_inverse
% 0.26/0.59 thf(fact_287_nat__neq__iff,axiom,
% 0.26/0.59 ! [M: nat,N: nat] :
% 0.26/0.59 ( ( M != N )
% 0.26/0.59 = ( ( ord_less_nat @ M @ N )
% 0.26/0.59 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat_neq_iff
% 0.26/0.59 thf(fact_288_less__not__refl,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.59
% 0.26/0.59 % less_not_refl
% 0.26/0.59 thf(fact_289_less__not__refl2,axiom,
% 0.26/0.59 ! [N: nat,M: nat] :
% 0.26/0.59 ( ( ord_less_nat @ N @ M )
% 0.26/0.59 => ( M != N ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_not_refl2
% 0.26/0.59 thf(fact_290_less__not__refl3,axiom,
% 0.26/0.59 ! [S: nat,T: nat] :
% 0.26/0.59 ( ( ord_less_nat @ S @ T )
% 0.26/0.59 => ( S != T ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_not_refl3
% 0.26/0.59 thf(fact_291_less__irrefl__nat,axiom,
% 0.26/0.59 ! [N: nat] :
% 0.26/0.59 ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.59
% 0.26/0.59 % less_irrefl_nat
% 0.26/0.59 thf(fact_292_nat__less__induct,axiom,
% 0.26/0.59 ! [P2: nat > $o,N: nat] :
% 0.26/0.59 ( ! [N2: nat] :
% 0.26/0.59 ( ! [M3: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M3 @ N2 )
% 0.26/0.59 => ( P2 @ M3 ) )
% 0.26/0.59 => ( P2 @ N2 ) )
% 0.26/0.59 => ( P2 @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % nat_less_induct
% 0.26/0.59 thf(fact_293_infinite__descent,axiom,
% 0.26/0.59 ! [P2: nat > $o,N: nat] :
% 0.26/0.59 ( ! [N2: nat] :
% 0.26/0.59 ( ~ ( P2 @ N2 )
% 0.26/0.59 => ? [M3: nat] :
% 0.26/0.59 ( ( ord_less_nat @ M3 @ N2 )
% 0.26/0.59 & ~ ( P2 @ M3 ) ) )
% 0.26/0.59 => ( P2 @ N ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_descent
% 0.26/0.59 thf(fact_294_linorder__neqE__nat,axiom,
% 0.26/0.59 ! [X2: nat,Y2: nat] :
% 0.26/0.59 ( ( X2 != Y2 )
% 0.26/0.59 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.26/0.59 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % linorder_neqE_nat
% 0.26/0.59 thf(fact_295_linorder__neqE__linordered__idom,axiom,
% 0.26/0.59 ! [X2: real,Y2: real] :
% 0.26/0.59 ( ( X2 != Y2 )
% 0.26/0.59 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.26/0.59 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % linorder_neqE_linordered_idom
% 0.26/0.59 thf(fact_296_lift__Suc__mono__less__iff,axiom,
% 0.26/0.59 ! [F: nat > nat,N: nat,M: nat] :
% 0.26/0.59 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.59 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.59 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lift_Suc_mono_less_iff
% 0.26/0.59 thf(fact_297_lift__Suc__mono__less__iff,axiom,
% 0.26/0.59 ! [F: nat > real,N: nat,M: nat] :
% 0.26/0.59 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.59 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.59 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lift_Suc_mono_less_iff
% 0.26/0.59 thf(fact_298_lift__Suc__mono__less,axiom,
% 0.26/0.59 ! [F: nat > nat,N: nat,N4: nat] :
% 0.26/0.59 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.59 => ( ( ord_less_nat @ N @ N4 )
% 0.26/0.59 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lift_Suc_mono_less
% 0.26/0.59 thf(fact_299_lift__Suc__mono__less,axiom,
% 0.26/0.59 ! [F: nat > real,N: nat,N4: nat] :
% 0.26/0.59 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.60 => ( ( ord_less_nat @ N @ N4 )
% 0.26/0.60 => ( ord_less_real @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % lift_Suc_mono_less
% 0.26/0.60 thf(fact_300_dvd__pos__nat,axiom,
% 0.26/0.60 ! [N: nat,M: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.60 => ( ( dvd_dvd_nat @ M @ N )
% 0.26/0.60 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % dvd_pos_nat
% 0.26/0.60 thf(fact_301_finite__divisors__nat,axiom,
% 0.26/0.60 ! [M: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.60 => ( finite_finite_nat
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % finite_divisors_nat
% 0.26/0.60 thf(fact_302_not__one__less__zero,axiom,
% 0.26/0.60 ~ ( ord_less_poly_real @ one_one_poly_real @ zero_zero_poly_real ) ).
% 0.26/0.60
% 0.26/0.60 % not_one_less_zero
% 0.26/0.60 thf(fact_303_not__one__less__zero,axiom,
% 0.26/0.60 ~ ( ord_le38482960y_real @ one_on501200385y_real @ zero_z1423781445y_real ) ).
% 0.26/0.60
% 0.26/0.60 % not_one_less_zero
% 0.26/0.60 thf(fact_304_not__one__less__zero,axiom,
% 0.26/0.60 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.26/0.60
% 0.26/0.60 % not_one_less_zero
% 0.26/0.60 thf(fact_305_not__one__less__zero,axiom,
% 0.26/0.60 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.26/0.60
% 0.26/0.60 % not_one_less_zero
% 0.26/0.60 thf(fact_306_zero__less__one,axiom,
% 0.26/0.60 ord_less_poly_real @ zero_zero_poly_real @ one_one_poly_real ).
% 0.26/0.60
% 0.26/0.60 % zero_less_one
% 0.26/0.60 thf(fact_307_zero__less__one,axiom,
% 0.26/0.60 ord_le38482960y_real @ zero_z1423781445y_real @ one_on501200385y_real ).
% 0.26/0.60
% 0.26/0.60 % zero_less_one
% 0.26/0.60 thf(fact_308_zero__less__one,axiom,
% 0.26/0.60 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.26/0.60
% 0.26/0.60 % zero_less_one
% 0.26/0.60 thf(fact_309_zero__less__one,axiom,
% 0.26/0.60 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.26/0.60
% 0.26/0.60 % zero_less_one
% 0.26/0.60 thf(fact_310_less__Suc__eq__0__disj,axiom,
% 0.26/0.60 ! [M: nat,N: nat] :
% 0.26/0.60 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.60 = ( ( M = zero_zero_nat )
% 0.26/0.60 | ? [J3: nat] :
% 0.26/0.60 ( ( M
% 0.26/0.60 = ( suc @ J3 ) )
% 0.26/0.60 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % less_Suc_eq_0_disj
% 0.26/0.60 thf(fact_311_gr0__implies__Suc,axiom,
% 0.26/0.60 ! [N: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.60 => ? [M2: nat] :
% 0.26/0.60 ( N
% 0.26/0.60 = ( suc @ M2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gr0_implies_Suc
% 0.26/0.60 thf(fact_312_All__less__Suc2,axiom,
% 0.26/0.60 ! [N: nat,P2: nat > $o] :
% 0.26/0.60 ( ( ! [I4: nat] :
% 0.26/0.60 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.60 => ( P2 @ I4 ) ) )
% 0.26/0.60 = ( ( P2 @ zero_zero_nat )
% 0.26/0.60 & ! [I4: nat] :
% 0.26/0.60 ( ( ord_less_nat @ I4 @ N )
% 0.26/0.60 => ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % All_less_Suc2
% 0.26/0.60 thf(fact_313_gr0__conv__Suc,axiom,
% 0.26/0.60 ! [N: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.60 = ( ? [M5: nat] :
% 0.26/0.60 ( N
% 0.26/0.60 = ( suc @ M5 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gr0_conv_Suc
% 0.26/0.60 thf(fact_314_Ex__less__Suc2,axiom,
% 0.26/0.60 ! [N: nat,P2: nat > $o] :
% 0.26/0.60 ( ( ? [I4: nat] :
% 0.26/0.60 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.26/0.60 & ( P2 @ I4 ) ) )
% 0.26/0.60 = ( ( P2 @ zero_zero_nat )
% 0.26/0.60 | ? [I4: nat] :
% 0.26/0.60 ( ( ord_less_nat @ I4 @ N )
% 0.26/0.60 & ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Ex_less_Suc2
% 0.26/0.60 thf(fact_315_nat__dvd__not__less,axiom,
% 0.26/0.60 ! [M: nat,N: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.60 => ( ( ord_less_nat @ M @ N )
% 0.26/0.60 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % nat_dvd_not_less
% 0.26/0.60 thf(fact_316_nat__induct__non__zero,axiom,
% 0.26/0.60 ! [N: nat,P2: nat > $o] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.60 => ( ( P2 @ one_one_nat )
% 0.26/0.60 => ( ! [N2: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.60 => ( ( P2 @ N2 )
% 0.26/0.60 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.26/0.60 => ( P2 @ N ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % nat_induct_non_zero
% 0.26/0.60 thf(fact_317_less__degree__imp,axiom,
% 0.26/0.60 ! [N: nat,P: poly_poly_real] :
% 0.26/0.60 ( ( ord_less_nat @ N @ ( degree_poly_real @ P ) )
% 0.26/0.60 => ? [I3: nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ I3 )
% 0.26/0.60 & ( ( coeff_poly_real @ P @ I3 )
% 0.26/0.60 != zero_zero_poly_real ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % less_degree_imp
% 0.26/0.60 thf(fact_318_less__degree__imp,axiom,
% 0.26/0.60 ! [N: nat,P: poly_nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ ( degree_nat @ P ) )
% 0.26/0.60 => ? [I3: nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ I3 )
% 0.26/0.60 & ( ( coeff_nat @ P @ I3 )
% 0.26/0.60 != zero_zero_nat ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % less_degree_imp
% 0.26/0.60 thf(fact_319_less__degree__imp,axiom,
% 0.26/0.60 ! [N: nat,P: poly_poly_poly_real] :
% 0.26/0.60 ( ( ord_less_nat @ N @ ( degree360860553y_real @ P ) )
% 0.26/0.60 => ? [I3: nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ I3 )
% 0.26/0.60 & ( ( coeff_poly_poly_real @ P @ I3 )
% 0.26/0.60 != zero_z1423781445y_real ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % less_degree_imp
% 0.26/0.60 thf(fact_320_less__degree__imp,axiom,
% 0.26/0.60 ! [N: nat,P: poly_poly_nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ ( degree_poly_nat @ P ) )
% 0.26/0.60 => ? [I3: nat] :
% 0.26/0.60 ( ( ord_less_nat @ N @ I3 )
% 0.26/0.60 & ( ( coeff_poly_nat @ P @ I3 )
% 0.26/0.60 != zero_zero_poly_nat ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % less_degree_imp
% 0.26/0.60 thf(fact_321_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat] :
% 0.26/0.60 ( ( A3 != B2 )
% 0.26/0.60 => ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 => ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.not_eq_order_implies_strict
% 0.26/0.60 thf(fact_322_gcd__nat_Ostrict__implies__not__eq,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) )
% 0.26/0.60 => ( A3 != B2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_implies_not_eq
% 0.26/0.60 thf(fact_323_gcd__nat_Ostrict__implies__order,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) )
% 0.26/0.60 => ( dvd_dvd_nat @ A3 @ B2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_implies_order
% 0.26/0.60 thf(fact_324_gcd__nat_Ostrict__iff__order,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) )
% 0.26/0.60 = ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_iff_order
% 0.26/0.60 thf(fact_325_gcd__nat_Oorder__iff__strict,axiom,
% 0.26/0.60 ( dvd_dvd_nat
% 0.26/0.60 = ( ^ [A: nat,B3: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A @ B3 )
% 0.26/0.60 & ( A != B3 ) )
% 0.26/0.60 | ( A = B3 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.order_iff_strict
% 0.26/0.60 thf(fact_326_gcd__nat_Ostrict__trans2,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat,C: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) )
% 0.26/0.60 => ( ( dvd_dvd_nat @ B2 @ C )
% 0.26/0.60 => ( ( dvd_dvd_nat @ A3 @ C )
% 0.26/0.60 & ( A3 != C ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_trans2
% 0.26/0.60 thf(fact_327_gcd__nat_Ostrict__trans1,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat,C: nat] :
% 0.26/0.60 ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 => ( ( ( dvd_dvd_nat @ B2 @ C )
% 0.26/0.60 & ( B2 != C ) )
% 0.26/0.60 => ( ( dvd_dvd_nat @ A3 @ C )
% 0.26/0.60 & ( A3 != C ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_trans1
% 0.26/0.60 thf(fact_328_gcd__nat_Ostrict__trans,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat,C: nat] :
% 0.26/0.60 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 & ( A3 != B2 ) )
% 0.26/0.60 => ( ( ( dvd_dvd_nat @ B2 @ C )
% 0.26/0.60 & ( B2 != C ) )
% 0.26/0.60 => ( ( dvd_dvd_nat @ A3 @ C )
% 0.26/0.60 & ( A3 != C ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.strict_trans
% 0.26/0.60 thf(fact_329_gcd__nat_Oantisym,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat] :
% 0.26/0.60 ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.60 => ( ( dvd_dvd_nat @ B2 @ A3 )
% 0.26/0.60 => ( A3 = B2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.antisym
% 0.26/0.60 thf(fact_330_gcd__nat_Oirrefl,axiom,
% 0.26/0.60 ! [A3: nat] :
% 0.26/0.60 ~ ( ( dvd_dvd_nat @ A3 @ A3 )
% 0.26/0.60 & ( A3 != A3 ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.irrefl
% 0.26/0.60 thf(fact_331_gcd__nat_Oeq__iff,axiom,
% 0.26/0.60 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.26/0.60 = ( ^ [A: nat,B3: nat] :
% 0.26/0.60 ( ( dvd_dvd_nat @ A @ B3 )
% 0.26/0.60 & ( dvd_dvd_nat @ B3 @ A ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % gcd_nat.eq_iff
% 0.26/0.60 thf(fact_332_gcd__nat_Otrans,axiom,
% 0.26/0.60 ! [A3: nat,B2: nat,C: nat] :
% 0.26/0.65 ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.65 => ( ( dvd_dvd_nat @ B2 @ C )
% 0.26/0.65 => ( dvd_dvd_nat @ A3 @ C ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.trans
% 0.26/0.65 thf(fact_333_gcd__nat_Orefl,axiom,
% 0.26/0.65 ! [A3: nat] : ( dvd_dvd_nat @ A3 @ A3 ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.refl
% 0.26/0.65 thf(fact_334_gcd__nat_Oasym,axiom,
% 0.26/0.65 ! [A3: nat,B2: nat] :
% 0.26/0.65 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 0.26/0.65 & ( A3 != B2 ) )
% 0.26/0.65 => ~ ( ( dvd_dvd_nat @ B2 @ A3 )
% 0.26/0.65 & ( B2 != A3 ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.asym
% 0.26/0.65 thf(fact_335_gcd__nat_Oextremum,axiom,
% 0.26/0.65 ! [A3: nat] : ( dvd_dvd_nat @ A3 @ zero_zero_nat ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.extremum
% 0.26/0.65 thf(fact_336_gcd__nat_Oextremum__strict,axiom,
% 0.26/0.65 ! [A3: nat] :
% 0.26/0.65 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A3 )
% 0.26/0.65 & ( zero_zero_nat != A3 ) ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.extremum_strict
% 0.26/0.65 thf(fact_337_gcd__nat_Oextremum__unique,axiom,
% 0.26/0.65 ! [A3: nat] :
% 0.26/0.65 ( ( dvd_dvd_nat @ zero_zero_nat @ A3 )
% 0.26/0.65 = ( A3 = zero_zero_nat ) ) ).
% 0.26/0.65
% 0.26/0.65 % gcd_nat.extremum_unique
% 0.26/0.65 thf(fact_338_poly__IVT__pos,axiom,
% 0.26/0.65 ! [A3: real,B2: real,P: poly_real] :
% 0.26/0.65 ( ( ord_less_real @ A3 @ B2 )
% 0.26/0.65 => ( ( ord_less_real @ ( poly_real2 @ P @ A3 ) @ zero_zero_real )
% 0.26/0.65 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ B2 ) )
% 0.26/0.65 => ? [X3: real] :
% 0.26/0.65 ( ( ord_less_real @ A3 @ X3 )
% 0.26/0.65 & ( ord_less_real @ X3 @ B2 )
% 0.26/0.65 & ( ( poly_real2 @ P @ X3 )
% 0.26/0.65 = zero_zero_real ) ) ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % poly_IVT_pos
% 0.26/0.65 thf(fact_339_poly__IVT__neg,axiom,
% 0.26/0.65 ! [A3: real,B2: real,P: poly_real] :
% 0.26/0.65 ( ( ord_less_real @ A3 @ B2 )
% 0.26/0.65 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ A3 ) )
% 0.26/0.65 => ( ( ord_less_real @ ( poly_real2 @ P @ B2 ) @ zero_zero_real )
% 0.26/0.65 => ? [X3: real] :
% 0.26/0.65 ( ( ord_less_real @ A3 @ X3 )
% 0.26/0.65 & ( ord_less_real @ X3 @ B2 )
% 0.26/0.65 & ( ( poly_real2 @ P @ X3 )
% 0.26/0.65 = zero_zero_real ) ) ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % poly_IVT_neg
% 0.26/0.65 thf(fact_340_finite__M__bounded__by__nat,axiom,
% 0.26/0.65 ! [P2: nat > $o,I2: nat] :
% 0.26/0.65 ( finite_finite_nat
% 0.26/0.65 @ ( collect_nat
% 0.26/0.65 @ ^ [K3: nat] :
% 0.26/0.65 ( ( P2 @ K3 )
% 0.26/0.65 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % finite_M_bounded_by_nat
% 0.26/0.65 thf(fact_341_Rats__dense__in__real,axiom,
% 0.26/0.65 ! [X2: real,Y2: real] :
% 0.26/0.65 ( ( ord_less_real @ X2 @ Y2 )
% 0.26/0.65 => ? [X3: real] :
% 0.26/0.65 ( ( member_real @ X3 @ field_1537545994s_real )
% 0.26/0.65 & ( ord_less_real @ X2 @ X3 )
% 0.26/0.65 & ( ord_less_real @ X3 @ Y2 ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % Rats_dense_in_real
% 0.26/0.65 thf(fact_342_Rats__no__bot__less,axiom,
% 0.26/0.65 ! [X2: real] :
% 0.26/0.65 ? [X3: real] :
% 0.26/0.65 ( ( member_real @ X3 @ field_1537545994s_real )
% 0.26/0.65 & ( ord_less_real @ X3 @ X2 ) ) ).
% 0.26/0.65
% 0.26/0.65 % Rats_no_bot_less
% 0.26/0.65 thf(fact_343_poly__pinfty__gt__lc,axiom,
% 0.26/0.65 ! [P: poly_real] :
% 0.26/0.65 ( ( ord_less_real @ zero_zero_real @ ( coeff_real @ P @ ( degree_real @ P ) ) )
% 0.26/0.65 => ? [N2: real] :
% 0.26/0.65 ! [X4: real] :
% 0.26/0.65 ( ( ord_less_eq_real @ N2 @ X4 )
% 0.26/0.65 => ( ord_less_eq_real @ ( coeff_real @ P @ ( degree_real @ P ) ) @ ( poly_real2 @ P @ X4 ) ) ) ) ).
% 0.26/0.65
% 0.26/0.65 % poly_pinfty_gt_lc
% 0.26/0.65
% 0.26/0.65 % Conjectures (1)
% 0.26/0.65 thf(conj_0,conjecture,
% 0.26/0.65 ( finite_finite_real
% 0.26/0.65 @ ( collect_real
% 0.26/0.65 @ ^ [X: real] :
% 0.26/0.65 ( ( poly_real2 @ ( pderiv_real @ p ) @ X )
% 0.26/0.65 = zero_zero_real ) ) ) ).
% 0.26/0.65
% 0.26/0.65 %------------------------------------------------------------------------------
% 0.26/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0bLkZR8wfu/cvc5---1.0.5_21144.p...
% 0.26/0.65 (declare-sort $$unsorted 0)
% 0.26/0.65 (declare-sort tptp.poly_poly_poly_real 0)
% 0.26/0.65 (declare-sort tptp.set_poly_poly_real 0)
% 0.26/0.65 (declare-sort tptp.poly_poly_real 0)
% 0.26/0.65 (declare-sort tptp.poly_poly_nat 0)
% 0.26/0.65 (declare-sort tptp.set_poly_real 0)
% 0.26/0.65 (declare-sort tptp.poly_real 0)
% 0.26/0.65 (declare-sort tptp.poly_nat 0)
% 0.26/0.65 (declare-sort tptp.set_real 0)
% 0.26/0.65 (declare-sort tptp.set_nat 0)
% 0.26/0.65 (declare-sort tptp.real 0)
% 0.26/0.65 (declare-sort tptp.nat 0)
% 0.26/0.65 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 0.26/0.65 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 0.26/0.65 (declare-fun tptp.finite1328464339y_real (tptp.set_poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.finite1810960971y_real (tptp.set_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 0.26/0.65 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.26/0.65 (declare-fun tptp.one_one_poly_nat () tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.one_on501200385y_real () tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.one_one_poly_real () tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.one_one_real () tptp.real)
% 0.26/0.65 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.26/0.65 (declare-fun tptp.zero_zero_poly_nat () tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.zero_z1059985641ly_nat () tptp.poly_poly_nat)
% 0.26/0.65 (declare-fun tptp.zero_z935034829y_real () tptp.poly_poly_poly_real)
% 0.26/0.65 (declare-fun tptp.zero_z1423781445y_real () tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.zero_zero_poly_real () tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.zero_zero_real () tptp.real)
% 0.26/0.65 (declare-fun tptp.ring_1897377867y_real () tptp.set_poly_poly_real)
% 0.26/0.65 (declare-fun tptp.ring_1690226883y_real () tptp.set_poly_real)
% 0.26/0.65 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 0.26/0.65 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.26/0.65 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.65 (declare-fun tptp.ord_le38482960y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.ord_less_poly_real (tptp.poly_real tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 0.26/0.65 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.26/0.65 (declare-fun tptp.algebraic_real (tptp.real) Bool)
% 0.26/0.65 (declare-fun tptp.algebraic_int_real (tptp.real) Bool)
% 0.26/0.65 (declare-fun tptp.cr_poly_real ((-> tptp.nat tptp.real) tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.degree_nat (tptp.poly_nat) tptp.nat)
% 0.26/0.65 (declare-fun tptp.degree_poly_nat (tptp.poly_poly_nat) tptp.nat)
% 0.26/0.65 (declare-fun tptp.degree360860553y_real (tptp.poly_poly_poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.degree_poly_real (tptp.poly_poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.degree_real (tptp.poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.divide924636027y_real (tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat) tptp.poly_poly_poly_real)
% 0.26/0.65 (declare-fun tptp.divide1142363123y_real (tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.divide1561404011n_real (tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.is_zero_nat (tptp.poly_nat) Bool)
% 0.26/0.65 (declare-fun tptp.is_zero_poly_real (tptp.poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.is_zero_real (tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.order_poly_poly_real (tptp.poly_poly_real tptp.poly_poly_poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.order_poly_real (tptp.poly_real tptp.poly_poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.order_real (tptp.real tptp.poly_real) tptp.nat)
% 0.26/0.65 (declare-fun tptp.pcr_poly_nat_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) tptp.poly_nat) Bool)
% 0.26/0.65 (declare-fun tptp.pcr_po273983709ly_nat ((-> tptp.poly_nat tptp.poly_nat Bool) (-> tptp.nat tptp.poly_nat) tptp.poly_poly_nat) Bool)
% 0.26/0.65 (declare-fun tptp.pcr_po1200519205y_real ((-> tptp.poly_poly_real tptp.poly_poly_real Bool) (-> tptp.nat tptp.poly_poly_real) tptp.poly_poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.pcr_po1314690837y_real ((-> tptp.poly_real tptp.poly_real Bool) (-> tptp.nat tptp.poly_real) tptp.poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.pcr_poly_real_real ((-> tptp.real tptp.real Bool) (-> tptp.nat tptp.real) tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.pderiv_nat (tptp.poly_nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.pderiv_poly_real (tptp.poly_poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.pderiv_real (tptp.poly_real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.poly_nat2 (tptp.poly_nat tptp.nat) tptp.nat)
% 0.26/0.65 (declare-fun tptp.poly_poly_nat2 (tptp.poly_poly_nat tptp.poly_nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.poly_poly_poly_real2 (tptp.poly_poly_poly_real tptp.poly_poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.poly_poly_real2 (tptp.poly_poly_real tptp.poly_real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.poly_real2 (tptp.poly_real tptp.real) tptp.real)
% 0.26/0.65 (declare-fun tptp.coeff_nat (tptp.poly_nat tptp.nat) tptp.nat)
% 0.26/0.65 (declare-fun tptp.coeff_poly_nat (tptp.poly_poly_nat tptp.nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.coeff_poly_poly_real (tptp.poly_poly_poly_real tptp.nat) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.coeff_poly_real (tptp.poly_poly_real tptp.nat) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.coeff_real (tptp.poly_real tptp.nat) tptp.real)
% 0.26/0.65 (declare-fun tptp.poly_cutoff_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.poly_c1404107022y_real (tptp.nat tptp.poly_poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.poly_cutoff_real (tptp.nat tptp.poly_real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.poly_shift_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.poly_shift_poly_real (tptp.nat tptp.poly_poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.poly_shift_real (tptp.nat tptp.poly_real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.reflect_poly_nat (tptp.poly_nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.reflec781175074ly_nat (tptp.poly_poly_nat) tptp.poly_poly_nat)
% 0.26/0.65 (declare-fun tptp.reflec144234502y_real (tptp.poly_poly_poly_real) tptp.poly_poly_poly_real)
% 0.26/0.65 (declare-fun tptp.reflec1522834046y_real (tptp.poly_poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.reflect_poly_real (tptp.poly_real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.rsquar1555552848y_real (tptp.poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.rsquarefree_real (tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.synthetic_div_nat (tptp.poly_nat tptp.nat) tptp.poly_nat)
% 0.26/0.65 (declare-fun tptp.synthe1498897281y_real (tptp.poly_poly_real tptp.poly_real) tptp.poly_poly_real)
% 0.26/0.65 (declare-fun tptp.synthetic_div_real (tptp.poly_real tptp.real) tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.field_1537545994s_real () tptp.set_real)
% 0.26/0.65 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.65 (declare-fun tptp.dvd_dvd_poly_nat (tptp.poly_nat tptp.poly_nat) Bool)
% 0.26/0.65 (declare-fun tptp.dvd_dv1946063458y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.dvd_dvd_poly_real (tptp.poly_real tptp.poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 0.26/0.65 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.26/0.65 (declare-fun tptp.collec927113489y_real ((-> tptp.poly_poly_real Bool)) tptp.set_poly_poly_real)
% 0.26/0.65 (declare-fun tptp.collect_poly_real ((-> tptp.poly_real Bool)) tptp.set_poly_real)
% 0.26/0.65 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 0.26/0.65 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.26/0.65 (declare-fun tptp.member1159720147y_real (tptp.poly_poly_real tptp.set_poly_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.member_poly_real (tptp.poly_real tptp.set_poly_real) Bool)
% 0.26/0.65 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 0.26/0.65 (declare-fun tptp.n () tptp.nat)
% 0.26/0.65 (declare-fun tptp.p () tptp.poly_real)
% 0.26/0.65 (declare-fun tptp.x () tptp.real)
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (=> (not (= P tptp.zero_z935034829y_real)) (@ tptp.finite1328464339y_real (@ tptp.collec927113489y_real (lambda ((X tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P) X) tptp.zero_z1423781445y_real)))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (=> (not (= P tptp.zero_z1423781445y_real)) (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((X tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P) X) tptp.zero_zero_poly_real)))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= P tptp.zero_zero_poly_real)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ (@ tptp.poly_real2 P) X) tptp.zero_zero_real)))))))
% 0.26/0.65 (assert (not (= tptp.p tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (not (= (@ tptp.pderiv_real tptp.p) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (= (@ (@ tptp.poly_real2 tptp.p) tptp.x) tptp.zero_zero_real))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 tptp.zero_z935034829y_real) X2) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_nat)) (= (@ (@ tptp.poly_poly_nat2 tptp.zero_z1059985641ly_nat) X2) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 tptp.zero_z1423781445y_real) X2) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.poly_nat2 tptp.zero_zero_poly_nat) X2) tptp.zero_zero_nat)))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.poly_real2 tptp.zero_zero_poly_real) X2) tptp.zero_zero_real)))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.poly_real Bool)) (Q (-> tptp.poly_real Bool))) (=> (or (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real P2)) (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real Q))) (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((X tptp.poly_real)) (and (@ P2 X) (@ Q X))))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (or (@ tptp.finite_finite_real (@ tptp.collect_real P2)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ P2 X) (@ Q X))))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P2)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P2 X) (@ Q X))))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.poly_real Bool)) (Q (-> tptp.poly_real Bool))) (= (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((X tptp.poly_real)) (or (@ P2 X) (@ Q X))))) (and (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real P2)) (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real Q))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (or (@ P2 X) (@ Q X))))) (and (@ tptp.finite_finite_real (@ tptp.collect_real P2)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P2 X) (@ Q X))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P2)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (forall ((X tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P) X) tptp.zero_z1423781445y_real)) (= P tptp.zero_z935034829y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (forall ((X tptp.real)) (= (@ (@ tptp.poly_real2 P) X) tptp.zero_zero_real)) (= P tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (forall ((X tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P) X) tptp.zero_zero_poly_real)) (= P tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (= tptp.rsquarefree_real (lambda ((P3 tptp.poly_real)) (forall ((A tptp.real)) (not (and (= (@ (@ tptp.poly_real2 P3) A) tptp.zero_zero_real) (= (@ (@ tptp.poly_real2 (@ tptp.pderiv_real P3)) A) tptp.zero_zero_real)))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P2))) (exists ((X_1 tptp.real)) (@ P2 X_1)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P2))) (exists ((X_1 tptp.nat)) (@ P2 X_1)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.poly_real Bool))) (=> (not (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real P2))) (exists ((X_1 tptp.poly_real)) (@ P2 X_1)))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_real B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A tptp.real)) (and (@ (@ tptp.member_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_real) (B tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A tptp.real)) (and (@ (@ tptp.member_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_real) (B tptp.set_poly_real) (R (-> tptp.real tptp.poly_real Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite1810960971y_real B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.poly_real)) (and (@ (@ tptp.member_poly_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.poly_real)) (and (@ (@ tptp.member_poly_real X3) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A tptp.real)) (and (@ (@ tptp.member_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_nat) (B tptp.set_real) (R (-> tptp.nat tptp.real Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_real B) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A tptp.nat)) (and (@ (@ tptp.member_nat A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A tptp.nat)) (and (@ (@ tptp.member_nat A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_nat) (B tptp.set_poly_real) (R (-> tptp.nat tptp.poly_real Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite1810960971y_real B) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.poly_real)) (and (@ (@ tptp.member_poly_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.poly_real)) (and (@ (@ tptp.member_poly_real X3) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A tptp.nat)) (and (@ (@ tptp.member_nat A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_poly_real) (B tptp.set_real) (R (-> tptp.poly_real tptp.real Bool))) (=> (not (@ tptp.finite1810960971y_real A2)) (=> (@ tptp.finite_finite_real B) (=> (forall ((X3 tptp.poly_real)) (=> (@ (@ tptp.member_poly_real X3) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) B) (not (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((A tptp.poly_real)) (and (@ (@ tptp.member_poly_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_poly_real) (B tptp.set_nat) (R (-> tptp.poly_real tptp.nat Bool))) (=> (not (@ tptp.finite1810960971y_real A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X3 tptp.poly_real)) (=> (@ (@ tptp.member_poly_real X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B) (not (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((A tptp.poly_real)) (and (@ (@ tptp.member_poly_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_poly_real) (B tptp.set_poly_real) (R (-> tptp.poly_real tptp.poly_real Bool))) (=> (not (@ tptp.finite1810960971y_real A2)) (=> (@ tptp.finite1810960971y_real B) (=> (forall ((X3 tptp.poly_real)) (=> (@ (@ tptp.member_poly_real X3) A2) (exists ((Xa tptp.poly_real)) (and (@ (@ tptp.member_poly_real Xa) B) (@ (@ R X3) Xa))))) (exists ((X3 tptp.poly_real)) (and (@ (@ tptp.member_poly_real X3) B) (not (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((A tptp.poly_real)) (and (@ (@ tptp.member_poly_real A) A2) (@ (@ R A) X3)))))))))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (Q2 tptp.poly_real)) (= (= (@ tptp.poly_real2 P) (@ tptp.poly_real2 Q2)) (= P Q2))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real) (Q2 tptp.poly_poly_real)) (= (= (@ tptp.poly_poly_real2 P) (@ tptp.poly_poly_real2 Q2)) (= P Q2))))
% 0.26/0.65 (assert (= tptp.n (@ tptp.degree_real tptp.p)))
% 0.26/0.65 (assert (@ tptp.algebraic_real tptp.x))
% 0.26/0.65 (assert (not (@ (@ tptp.member_real tptp.x) tptp.field_1537545994s_real)))
% 0.26/0.65 (assert (= (@ tptp.degree_real tptp.zero_zero_poly_real) tptp.zero_zero_nat))
% 0.26/0.65 (assert (= (@ tptp.degree_poly_real tptp.zero_z1423781445y_real) tptp.zero_zero_nat))
% 0.26/0.65 (assert (= (@ tptp.degree_nat tptp.zero_zero_poly_nat) tptp.zero_zero_nat))
% 0.26/0.65 (assert (= (@ tptp.pderiv_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.26/0.65 (assert (= (@ tptp.pderiv_poly_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.26/0.65 (assert (= (@ tptp.pderiv_nat tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (= (@ tptp.pderiv_real P) tptp.zero_zero_poly_real) (= (@ tptp.degree_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (= (@ tptp.pderiv_poly_real P) tptp.zero_z1423781445y_real) (= (@ tptp.degree_poly_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (= (@ tptp.pderiv_nat P) tptp.zero_zero_poly_nat) (= (@ tptp.degree_nat P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_real)) (= (= tptp.zero_zero_poly_real X2) (= X2 tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real X2) (= X2 tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_nat)) (= (= tptp.zero_zero_poly_nat X2) (= X2 tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (= tptp.is_zero_real (lambda ((P3 tptp.poly_real)) (= P3 tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (= tptp.is_zero_poly_real (lambda ((P3 tptp.poly_poly_real)) (= P3 tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (= tptp.is_zero_nat (lambda ((P3 tptp.poly_nat)) (= P3 tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_c1404107022y_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (= (@ (@ tptp.poly_real2 (@ tptp.reflect_poly_real P)) tptp.zero_zero_real) tptp.zero_zero_real) (= P tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_real2 (@ tptp.reflec1522834046y_real P)) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (= P tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (= (@ (@ tptp.poly_nat2 (@ tptp.reflect_poly_nat P)) tptp.zero_zero_nat) tptp.zero_zero_nat) (= P tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 (@ tptp.reflec144234502y_real P)) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) (= P tptp.zero_z935034829y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (= (= (@ (@ tptp.poly_poly_nat2 (@ tptp.reflec781175074ly_nat P)) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat) (= P tptp.zero_z1059985641ly_nat))))
% 0.26/0.65 (assert (not (forall ((P4 tptp.poly_real)) (=> (forall ((I tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P4) I)) tptp.ring_1_Ints_real)) (=> (not (= P4 tptp.zero_zero_poly_real)) (not (= (@ (@ tptp.poly_real2 P4) tptp.x) tptp.zero_zero_real)))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (C tptp.real)) (= (= (@ (@ tptp.synthetic_div_real P) C) tptp.zero_zero_poly_real) (= (@ tptp.degree_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real) (C tptp.poly_real)) (= (= (@ (@ tptp.synthe1498897281y_real P) C) tptp.zero_z1423781445y_real) (= (@ tptp.degree_poly_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat) (C tptp.nat)) (= (= (@ (@ tptp.synthetic_div_nat P) C) tptp.zero_zero_poly_nat) (= (@ tptp.degree_nat P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_poly_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (A3 tptp.real)) (= (= (@ (@ tptp.poly_real2 P) A3) tptp.zero_zero_real) (or (= P tptp.zero_zero_poly_real) (not (= (@ (@ tptp.order_real A3) P) tptp.zero_zero_nat))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real) (A3 tptp.poly_real)) (= (= (@ (@ tptp.poly_poly_real2 P) A3) tptp.zero_zero_poly_real) (or (= P tptp.zero_z1423781445y_real) (not (= (@ (@ tptp.order_poly_real A3) P) tptp.zero_zero_nat))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real) (A3 tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 P) A3) tptp.zero_z1423781445y_real) (or (= P tptp.zero_z935034829y_real) (not (= (@ (@ tptp.order_poly_poly_real A3) P) tptp.zero_zero_nat))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (= (@ (@ tptp.coeff_real P) (@ tptp.degree_real P)) tptp.zero_zero_real) (= P tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (= (@ (@ tptp.coeff_poly_real P) (@ tptp.degree_poly_real P)) tptp.zero_zero_poly_real) (= P tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (= (@ (@ tptp.coeff_nat P) (@ tptp.degree_nat P)) tptp.zero_zero_nat) (= P tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (= (@ (@ tptp.coeff_poly_poly_real P) (@ tptp.degree360860553y_real P)) tptp.zero_z1423781445y_real) (= P tptp.zero_z935034829y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (= (= (@ (@ tptp.coeff_poly_nat P) (@ tptp.degree_poly_nat P)) tptp.zero_zero_poly_nat) (= P tptp.zero_z1059985641ly_nat))))
% 0.26/0.65 (assert (forall ((R2 tptp.poly_real) (D tptp.poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1561404011n_real tptp.zero_zero_real) tptp.zero_zero_poly_real) R2) D) Dr) N) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((R2 tptp.poly_poly_real) (D tptp.poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1142363123y_real tptp.zero_zero_poly_real) tptp.zero_z1423781445y_real) R2) D) Dr) N) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((R2 tptp.poly_poly_poly_real) (D tptp.poly_poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide924636027y_real tptp.zero_z1423781445y_real) tptp.zero_z935034829y_real) R2) D) Dr) N) tptp.zero_z935034829y_real)))
% 0.26/0.65 (assert (@ (@ (@ tptp.pcr_poly_real_real (lambda ((Y tptp.real) (Z tptp.real)) (= Y Z))) (lambda ((Uu tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_poly_real))
% 0.26/0.65 (assert (@ (@ (@ tptp.pcr_po1314690837y_real (lambda ((Y tptp.poly_real) (Z tptp.poly_real)) (= Y Z))) (lambda ((Uu tptp.nat)) tptp.zero_zero_poly_real)) tptp.zero_z1423781445y_real))
% 0.26/0.65 (assert (@ (@ (@ tptp.pcr_poly_nat_nat (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z))) (lambda ((Uu tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_poly_nat))
% 0.26/0.65 (assert (@ (@ (@ tptp.pcr_po1200519205y_real (lambda ((Y tptp.poly_poly_real) (Z tptp.poly_poly_real)) (= Y Z))) (lambda ((Uu tptp.nat)) tptp.zero_z1423781445y_real)) tptp.zero_z935034829y_real))
% 0.26/0.65 (assert (@ (@ (@ tptp.pcr_po273983709ly_nat (lambda ((Y tptp.poly_nat) (Z tptp.poly_nat)) (= Y Z))) (lambda ((Uu tptp.nat)) tptp.zero_zero_poly_nat)) tptp.zero_z1059985641ly_nat))
% 0.26/0.65 (assert (forall ((I2 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real tptp.p) I2)) tptp.ring_1_Ints_real)))
% 0.26/0.65 (assert (= (@ tptp.reflect_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.26/0.65 (assert (= (@ tptp.reflec1522834046y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.26/0.65 (assert (= (@ tptp.reflect_poly_nat tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat))
% 0.26/0.65 (assert (forall ((C tptp.real)) (= (@ (@ tptp.synthetic_div_real tptp.zero_zero_poly_real) C) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((C tptp.poly_real)) (= (@ (@ tptp.synthe1498897281y_real tptp.zero_z1423781445y_real) C) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((C tptp.nat)) (= (@ (@ tptp.synthetic_div_nat tptp.zero_zero_poly_nat) C) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.coeff_poly_poly_real tptp.zero_z935034829y_real) N) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.coeff_poly_nat tptp.zero_z1059985641ly_nat) N) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.coeff_real tptp.zero_zero_poly_real) N) tptp.zero_zero_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.coeff_poly_real tptp.zero_z1423781445y_real) N) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.coeff_nat tptp.zero_zero_poly_nat) N) tptp.zero_zero_nat)))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= (@ (@ tptp.coeff_real P) tptp.zero_zero_nat) tptp.zero_zero_real)) (= (@ tptp.reflect_poly_real (@ tptp.reflect_poly_real P)) P))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (=> (not (= (@ (@ tptp.coeff_poly_real P) tptp.zero_zero_nat) tptp.zero_zero_poly_real)) (= (@ tptp.reflec1522834046y_real (@ tptp.reflec1522834046y_real P)) P))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (=> (not (= (@ (@ tptp.coeff_nat P) tptp.zero_zero_nat) tptp.zero_zero_nat)) (= (@ tptp.reflect_poly_nat (@ tptp.reflect_poly_nat P)) P))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (=> (not (= (@ (@ tptp.coeff_poly_poly_real P) tptp.zero_zero_nat) tptp.zero_z1423781445y_real)) (= (@ tptp.reflec144234502y_real (@ tptp.reflec144234502y_real P)) P))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (=> (not (= (@ (@ tptp.coeff_poly_nat P) tptp.zero_zero_nat) tptp.zero_zero_poly_nat)) (= (@ tptp.reflec781175074ly_nat (@ tptp.reflec781175074ly_nat P)) P))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (@ (@ tptp.coeff_real (@ tptp.reflect_poly_real P)) tptp.zero_zero_nat) (@ (@ tptp.coeff_real P) (@ tptp.degree_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (= (@ (@ tptp.coeff_real (@ tptp.reflect_poly_real P)) tptp.zero_zero_nat) tptp.zero_zero_real) (= P tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (= (@ (@ tptp.coeff_poly_real (@ tptp.reflec1522834046y_real P)) tptp.zero_zero_nat) tptp.zero_zero_poly_real) (= P tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (= (@ (@ tptp.coeff_nat (@ tptp.reflect_poly_nat P)) tptp.zero_zero_nat) tptp.zero_zero_nat) (= P tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (= (@ (@ tptp.coeff_poly_poly_real (@ tptp.reflec144234502y_real P)) tptp.zero_zero_nat) tptp.zero_z1423781445y_real) (= P tptp.zero_z935034829y_real))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (= (= (@ (@ tptp.coeff_poly_nat (@ tptp.reflec781175074ly_nat P)) tptp.zero_zero_nat) tptp.zero_zero_poly_nat) (= P tptp.zero_z1059985641ly_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= (@ (@ tptp.coeff_real P) tptp.zero_zero_nat) tptp.zero_zero_real)) (= (@ tptp.degree_real (@ tptp.reflect_poly_real P)) (@ tptp.degree_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (=> (not (= (@ (@ tptp.coeff_poly_real P) tptp.zero_zero_nat) tptp.zero_zero_poly_real)) (= (@ tptp.degree_poly_real (@ tptp.reflec1522834046y_real P)) (@ tptp.degree_poly_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (=> (not (= (@ (@ tptp.coeff_nat P) tptp.zero_zero_nat) tptp.zero_zero_nat)) (= (@ tptp.degree_nat (@ tptp.reflect_poly_nat P)) (@ tptp.degree_nat P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (=> (not (= (@ (@ tptp.coeff_poly_poly_real P) tptp.zero_zero_nat) tptp.zero_z1423781445y_real)) (= (@ tptp.degree360860553y_real (@ tptp.reflec144234502y_real P)) (@ tptp.degree360860553y_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (=> (not (= (@ (@ tptp.coeff_poly_nat P) tptp.zero_zero_nat) tptp.zero_zero_poly_nat)) (= (@ tptp.degree_poly_nat (@ tptp.reflec781175074ly_nat P)) (@ tptp.degree_poly_nat P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (@ (@ tptp.poly_real2 (@ tptp.reflect_poly_real P)) tptp.zero_zero_real) (@ (@ tptp.coeff_real P) (@ tptp.degree_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_real2 (@ tptp.reflec1522834046y_real P)) tptp.zero_zero_poly_real) (@ (@ tptp.coeff_poly_real P) (@ tptp.degree_poly_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (@ (@ tptp.poly_nat2 (@ tptp.reflect_poly_nat P)) tptp.zero_zero_nat) (@ (@ tptp.coeff_nat P) (@ tptp.degree_nat P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 (@ tptp.reflec144234502y_real P)) tptp.zero_z1423781445y_real) (@ (@ tptp.coeff_poly_poly_real P) (@ tptp.degree360860553y_real P)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (= (@ (@ tptp.poly_poly_nat2 (@ tptp.reflec781175074ly_nat P)) tptp.zero_zero_poly_nat) (@ (@ tptp.coeff_poly_nat P) (@ tptp.degree_poly_nat P)))))
% 0.26/0.65 (assert (forall ((A3 tptp.real) (P2 (-> tptp.real Bool))) (= (@ (@ tptp.member_real A3) (@ tptp.collect_real P2)) (@ P2 A3))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A3) (@ tptp.collect_nat P2)) (@ P2 A3))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_real) (P2 (-> tptp.poly_real Bool))) (= (@ (@ tptp.member_poly_real A3) (@ tptp.collect_poly_real P2)) (@ P2 A3))))
% 0.26/0.65 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 0.26/0.65 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A2))) A2)))
% 0.26/0.65 (assert (forall ((A2 tptp.set_poly_real)) (= (@ tptp.collect_poly_real (lambda ((X tptp.poly_real)) (@ (@ tptp.member_poly_real X) A2))) A2)))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_real P2) (@ tptp.collect_real Q)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_nat P2) (@ tptp.collect_nat Q)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.poly_real Bool)) (Q (-> tptp.poly_real Bool))) (=> (forall ((X3 tptp.poly_real)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_poly_real P2) (@ tptp.collect_poly_real Q)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (Q2 tptp.poly_real)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.coeff_real P) N2) (@ (@ tptp.coeff_real Q2) N2))) (= P Q2))))
% 0.26/0.65 (assert (= (lambda ((Y tptp.poly_real) (Z tptp.poly_real)) (= Y Z)) (lambda ((P3 tptp.poly_real) (Q3 tptp.poly_real)) (forall ((N3 tptp.nat)) (= (@ (@ tptp.coeff_real P3) N3) (@ (@ tptp.coeff_real Q3) N3))))))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_real) (Y2 tptp.poly_real)) (= (= (@ tptp.coeff_real X2) (@ tptp.coeff_real Y2)) (= X2 Y2))))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (=> (@ tptp.algebraic_real X2) (not (forall ((P4 tptp.poly_real)) (=> (forall ((I tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P4) I)) tptp.ring_1_Ints_real)) (=> (not (= P4 tptp.zero_zero_poly_real)) (not (= (@ (@ tptp.poly_real2 P4) X2) tptp.zero_zero_real)))))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (X2 tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P) I3)) tptp.ring_1_Ints_real)) (=> (not (= P tptp.zero_zero_poly_real)) (=> (= (@ (@ tptp.poly_real2 P) X2) tptp.zero_zero_real) (@ tptp.algebraic_real X2))))))
% 0.26/0.65 (assert (= tptp.algebraic_real (lambda ((X tptp.real)) (exists ((P3 tptp.poly_real)) (and (forall ((I4 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P3) I4)) tptp.ring_1_Ints_real)) (not (= P3 tptp.zero_zero_poly_real)) (= (@ (@ tptp.poly_real2 P3) X) tptp.zero_zero_real))))))
% 0.26/0.65 (assert (= tptp.algebraic_real (lambda ((X tptp.real)) (exists ((P3 tptp.poly_real)) (and (forall ((I4 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P3) I4)) tptp.field_1537545994s_real)) (not (= P3 tptp.zero_zero_poly_real)) (= (@ (@ tptp.poly_real2 P3) X) tptp.zero_zero_real))))))
% 0.26/0.65 (assert (= (@ tptp.coeff_poly_poly_real tptp.zero_z935034829y_real) (lambda ((Uu tptp.nat)) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (= (@ tptp.coeff_poly_nat tptp.zero_z1059985641ly_nat) (lambda ((Uu tptp.nat)) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (= (@ tptp.coeff_real tptp.zero_zero_poly_real) (lambda ((Uu tptp.nat)) tptp.zero_zero_real)))
% 0.26/0.65 (assert (= (@ tptp.coeff_poly_real tptp.zero_z1423781445y_real) (lambda ((Uu tptp.nat)) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (= (@ tptp.coeff_nat tptp.zero_zero_poly_nat) (lambda ((Uu tptp.nat)) tptp.zero_zero_nat)))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (@ (@ tptp.poly_real2 P) tptp.zero_zero_real) (@ (@ tptp.coeff_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_real2 P) tptp.zero_zero_poly_real) (@ (@ tptp.coeff_poly_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (= (@ (@ tptp.poly_nat2 P) tptp.zero_zero_nat) (@ (@ tptp.coeff_nat P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P) tptp.zero_z1423781445y_real) (@ (@ tptp.coeff_poly_poly_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (= (@ (@ tptp.poly_poly_nat2 P) tptp.zero_zero_poly_nat) (@ (@ tptp.coeff_poly_nat P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (A3 tptp.real)) (=> (not (= (@ (@ tptp.poly_real2 P) A3) tptp.zero_zero_real)) (= (@ (@ tptp.order_real A3) P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real) (A3 tptp.poly_real)) (=> (not (= (@ (@ tptp.poly_poly_real2 P) A3) tptp.zero_zero_poly_real)) (= (@ (@ tptp.order_poly_real A3) P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real) (A3 tptp.poly_poly_real)) (=> (not (= (@ (@ tptp.poly_poly_poly_real2 P) A3) tptp.zero_z1423781445y_real)) (= (@ (@ tptp.order_poly_poly_real A3) P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_poly_real)) (=> (not (= P tptp.zero_z935034829y_real)) (not (= (@ (@ tptp.coeff_poly_poly_real P) (@ tptp.degree360860553y_real P)) tptp.zero_z1423781445y_real)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_nat)) (=> (not (= P tptp.zero_z1059985641ly_nat)) (not (= (@ (@ tptp.coeff_poly_nat P) (@ tptp.degree_poly_nat P)) tptp.zero_zero_poly_nat)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (= (@ (@ tptp.coeff_real P) (@ tptp.degree_real P)) tptp.zero_zero_real)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_poly_real)) (=> (not (= P tptp.zero_z1423781445y_real)) (not (= (@ (@ tptp.coeff_poly_real P) (@ tptp.degree_poly_real P)) tptp.zero_zero_poly_real)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_nat)) (=> (not (= P tptp.zero_zero_poly_nat)) (not (= (@ (@ tptp.coeff_nat P) (@ tptp.degree_nat P)) tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (not (@ tptp.finite_finite_real tptp.field_1537545994s_real)))
% 0.26/0.65 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.field_1537545994s_real))
% 0.26/0.65 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 0.26/0.65 (assert (@ (@ tptp.member_poly_real tptp.zero_zero_poly_real) tptp.ring_1690226883y_real))
% 0.26/0.65 (assert (@ (@ tptp.member1159720147y_real tptp.zero_z1423781445y_real) tptp.ring_1897377867y_real))
% 0.26/0.65 (assert (= tptp.rsquarefree_real (lambda ((P3 tptp.poly_real)) (and (not (= P3 tptp.zero_zero_poly_real)) (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.order_real A) P3))) (or (= _let_1 tptp.zero_zero_nat) (= _let_1 tptp.one_one_nat))))))))
% 0.26/0.65 (assert (= tptp.rsquar1555552848y_real (lambda ((P3 tptp.poly_poly_real)) (and (not (= P3 tptp.zero_z1423781445y_real)) (forall ((A tptp.poly_real)) (let ((_let_1 (@ (@ tptp.order_poly_real A) P3))) (or (= _let_1 tptp.zero_zero_nat) (= _let_1 tptp.one_one_nat))))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_cutoff_real N) tptp.one_one_poly_real))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_poly_real)) (=> (not _let_2) (= _let_1 tptp.one_one_poly_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_c1404107022y_real N) tptp.one_on501200385y_real))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z1423781445y_real)) (=> (not _let_2) (= _let_1 tptp.one_on501200385y_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_cutoff_nat N) tptp.one_one_poly_nat))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_poly_nat)) (=> (not _let_2) (= _let_1 tptp.one_one_poly_nat)))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (A3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.order_real A3))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ tptp.pderiv_real P))) (=> (not (= _let_3 tptp.zero_zero_poly_real)) (=> (not (= _let_2 tptp.zero_zero_nat)) (= (= (@ _let_1 _let_3) N) (= _let_2 (@ tptp.suc N))))))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (A3 tptp.real)) (let ((_let_1 (@ tptp.pderiv_real P))) (let ((_let_2 (@ tptp.order_real A3))) (let ((_let_3 (@ _let_2 P))) (=> (not (= _let_1 tptp.zero_zero_poly_real)) (=> (not (= _let_3 tptp.zero_zero_nat)) (= _let_3 (@ tptp.suc (@ _let_2 _let_1))))))))))
% 0.26/0.65 (assert (= tptp.cr_poly_real (lambda ((X (-> tptp.nat tptp.real)) (Y3 tptp.poly_real)) (= X (@ tptp.coeff_real Y3)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (= (@ (@ tptp.dvd_dvd_poly_real P) (@ tptp.pderiv_real P)) (= (@ tptp.degree_real P) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (= (@ tptp.degree_real tptp.one_one_poly_real) tptp.zero_zero_nat))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.poly_real2 tptp.one_one_poly_real) X2) tptp.one_one_real)))
% 0.26/0.65 (assert (forall ((X2 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 tptp.one_on501200385y_real) X2) tptp.one_one_poly_real)))
% 0.26/0.65 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.poly_nat2 tptp.one_one_poly_nat) X2) tptp.one_one_nat)))
% 0.26/0.65 (assert (= (@ tptp.pderiv_real tptp.one_one_poly_real) tptp.zero_zero_poly_real))
% 0.26/0.65 (assert (= (@ tptp.pderiv_poly_real tptp.one_on501200385y_real) tptp.zero_z1423781445y_real))
% 0.26/0.65 (assert (= (@ tptp.pderiv_nat tptp.one_one_poly_nat) tptp.zero_zero_poly_nat))
% 0.26/0.65 (assert (= (@ (@ tptp.coeff_nat tptp.one_one_poly_nat) (@ tptp.degree_nat tptp.one_one_poly_nat)) tptp.one_one_nat))
% 0.26/0.65 (assert (= (@ (@ tptp.coeff_real tptp.one_one_poly_real) (@ tptp.degree_real tptp.one_one_poly_real)) tptp.one_one_real))
% 0.26/0.65 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 0.26/0.65 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 0.26/0.65 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.field_1537545994s_real))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= P tptp.zero_zero_poly_real)) (= (@ (@ tptp.dvd_dvd_poly_real P) tptp.one_one_poly_real) (= (@ tptp.degree_real P) tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real)) (=> (not (= (@ tptp.degree_real P) tptp.zero_zero_nat)) (not (@ (@ tptp.dvd_dvd_poly_real P) (@ tptp.pderiv_real P))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_shift_real N) tptp.one_one_poly_real))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_poly_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_poly_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_shift_poly_real N) tptp.one_on501200385y_real))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on501200385y_real)) (=> (not _let_2) (= _let_1 tptp.zero_z1423781445y_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.poly_shift_nat N) tptp.one_one_poly_nat))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_poly_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_poly_nat)))))))
% 0.26/0.65 (assert (forall ((A3 tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A3) (= A3 tptp.zero_zero_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_real)) (= (@ (@ tptp.dvd_dvd_poly_real tptp.zero_zero_poly_real) A3) (= A3 tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A3) (= A3 tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_poly_real)) (= (@ (@ tptp.dvd_dv1946063458y_real tptp.zero_z1423781445y_real) A3) (= A3 tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_nat)) (= (@ (@ tptp.dvd_dvd_poly_nat tptp.zero_zero_poly_nat) A3) (= A3 tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.real)) (@ (@ tptp.dvd_dvd_real A3) tptp.zero_zero_real)))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_real)) (@ (@ tptp.dvd_dvd_poly_real A3) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A3) tptp.zero_zero_nat)))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_poly_real)) (@ (@ tptp.dvd_dv1946063458y_real A3) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_nat)) (@ (@ tptp.dvd_dvd_poly_nat A3) tptp.zero_zero_poly_nat)))
% 0.26/0.65 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.26/0.65 (assert (not (@ (@ tptp.dvd_dvd_poly_real tptp.zero_zero_poly_real) tptp.one_one_poly_real)))
% 0.26/0.65 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 0.26/0.65 (assert (not (@ (@ tptp.dvd_dv1946063458y_real tptp.zero_z1423781445y_real) tptp.one_on501200385y_real)))
% 0.26/0.65 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 0.26/0.65 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 0.26/0.65 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A3))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) C) (@ _let_1 C))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A3) A3)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.26/0.65 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 0.26/0.65 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 0.26/0.65 (assert (not (= tptp.zero_zero_poly_real tptp.one_one_poly_real)))
% 0.26/0.65 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 0.26/0.65 (assert (not (= tptp.zero_z1423781445y_real tptp.one_on501200385y_real)))
% 0.26/0.65 (assert (not (= tptp.zero_zero_poly_nat tptp.one_one_poly_nat)))
% 0.26/0.65 (assert (forall ((A3 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A3) (= A3 tptp.zero_zero_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_real)) (=> (@ (@ tptp.dvd_dvd_poly_real tptp.zero_zero_poly_real) A3) (= A3 tptp.zero_zero_poly_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A3) (= A3 tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_poly_real)) (=> (@ (@ tptp.dvd_dv1946063458y_real tptp.zero_z1423781445y_real) A3) (= A3 tptp.zero_z1423781445y_real))))
% 0.26/0.65 (assert (forall ((A3 tptp.poly_nat)) (=> (@ (@ tptp.dvd_dvd_poly_nat tptp.zero_zero_poly_nat) A3) (= A3 tptp.zero_zero_poly_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A3))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 0.26/0.65 (assert (forall ((B2 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B2))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A3)))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A3)))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P2 Nat3) (@ P2 (@ tptp.suc Nat3)))) (@ P2 Nat)))))
% 0.26/0.65 (assert (forall ((Y2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.suc Nat3))))))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P2 K) (=> (forall ((N2 tptp.nat)) (=> (@ P2 (@ tptp.suc N2)) (@ P2 N2))) (@ P2 tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P2 X3) tptp.zero_zero_nat)) (=> (forall ((Y4 tptp.nat)) (@ (@ P2 tptp.zero_zero_nat) (@ tptp.suc Y4))) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ P2 X3) Y4) (@ (@ P2 (@ tptp.suc X3)) (@ tptp.suc Y4)))) (@ (@ P2 M) N))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P2 N2) (@ P2 (@ tptp.suc N2)))) (@ P2 N)))))
% 0.26/0.65 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 0.26/0.65 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 0.26/0.65 (assert (forall ((X2 tptp.real) (P2 (-> tptp.real Bool))) (=> (@ tptp.algebraic_int_real X2) (=> (forall ((P4 tptp.poly_real) (X3 tptp.real)) (=> (= (@ (@ tptp.coeff_real P4) (@ tptp.degree_real P4)) tptp.one_one_real) (=> (forall ((I tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P4) I)) tptp.ring_1_Ints_real)) (=> (= (@ (@ tptp.poly_real2 P4) X3) tptp.zero_zero_real) (@ P2 X3))))) (@ P2 X2)))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (X2 tptp.real)) (=> (= (@ (@ tptp.coeff_real P) (@ tptp.degree_real P)) tptp.one_one_real) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P) I3)) tptp.ring_1_Ints_real)) (=> (= (@ (@ tptp.poly_real2 P) X2) tptp.zero_zero_real) (@ tptp.algebraic_int_real X2))))))
% 0.26/0.65 (assert (= tptp.algebraic_int_real (lambda ((A tptp.real)) (exists ((P3 tptp.poly_real) (X tptp.real)) (and (= A X) (= (@ (@ tptp.coeff_real P3) (@ tptp.degree_real P3)) tptp.one_one_real) (forall ((I4 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P3) I4)) tptp.ring_1_Ints_real)) (= (@ (@ tptp.poly_real2 P3) X) tptp.zero_zero_real))))))
% 0.26/0.65 (assert (forall ((A3 tptp.real)) (=> (@ tptp.algebraic_int_real A3) (not (forall ((P4 tptp.poly_real)) (=> (= (@ (@ tptp.coeff_real P4) (@ tptp.degree_real P4)) tptp.one_one_real) (=> (forall ((I tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P4) I)) tptp.ring_1_Ints_real)) (not (= (@ (@ tptp.poly_real2 P4) A3) tptp.zero_zero_real)))))))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (not (@ P2 tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P2 X_12)) (exists ((N2 tptp.nat)) (and (not (@ P2 N2)) (@ P2 (@ tptp.suc N2))))))))
% 0.26/0.65 (assert (@ tptp.algebraic_int_real tptp.zero_zero_real))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (@ tptp.algebraic_int_real X2))))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (=> (@ tptp.algebraic_int_real X2) (@ tptp.algebraic_real X2))))
% 0.26/0.65 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ tptp.algebraic_int_real X2) (=> (@ _let_1 tptp.field_1537545994s_real) (@ _let_1 tptp.ring_1_Ints_real))))))
% 0.26/0.65 (assert (forall ((P tptp.poly_real) (X2 tptp.real)) (=> (= (@ (@ tptp.poly_real2 P) X2) tptp.zero_zero_real) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P) I3)) tptp.ring_1_Ints_real)) (=> (= (@ (@ tptp.coeff_real P) tptp.zero_zero_nat) tptp.one_one_real) (@ tptp.algebraic_int_real (@ tptp.inverse_inverse_real X2)))))))
% 0.26/0.65 (assert (forall ((Y2 tptp.real) (P tptp.poly_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.degree_real P))) (=> (@ tptp.algebraic_int_real Y2) (=> (= (@ (@ tptp.poly_real2 P) X2) Y2) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.member_real (@ (@ tptp.coeff_real P) I3)) tptp.ring_1_Ints_real)) (=> (= (@ (@ tptp.coeff_real P) _let_1) tptp.one_one_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ tptp.algebraic_int_real X2)))))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A3) (= A3 tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (let ((_let_1 (not (= A3 tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A3) tptp.zero_zero_nat) _let_1)))))
% 0.26/0.65 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) K))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (= (not (= A3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A3))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P2 N2)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (not (@ P2 M3))))))) (@ P2 N)))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (not (@ (@ tptp.ord_less_nat A3) tptp.zero_zero_nat))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 0.26/0.65 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P2 I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P2 (@ tptp.suc I3)) (@ P2 I3)))) (@ P2 I2))))))
% 0.26/0.65 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (@ (@ P2 I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P2 I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P2 J2) K2) (@ _let_1 K2))))))) (@ (@ P2 I2) J))))))
% 0.26/0.65 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N) M4))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P2 I4))) (and (@ P2 N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P2 I4)))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P2 I4))) (or (@ P2 N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P2 I4)))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 0.26/0.65 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.65 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 0.26/0.65 (assert (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) tptp.field_1537545994s_real) (@ (@ tptp.member_real (@ tptp.inverse_inverse_real A3)) tptp.field_1537545994s_real))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.26/0.65 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (@ P2 M3))) (@ P2 N2))) (@ P2 N))))
% 0.26/0.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P2 N2)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (not (@ P2 M3)))))) (@ P2 N))))
% 0.26/0.65 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.26/0.65 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.26/0.65 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.26/0.65 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.26/0.65 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))))
% 0.26/0.65 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_real (@ F N)) (@ F N4))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 0.26/0.65 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 0.26/0.65 (assert (not (@ (@ tptp.ord_less_poly_real tptp.one_one_poly_real) tptp.zero_zero_poly_real)))
% 0.26/0.65 (assert (not (@ (@ tptp.ord_le38482960y_real tptp.one_on501200385y_real) tptp.zero_z1423781445y_real)))
% 0.26/0.65 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 0.26/0.65 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 0.26/0.65 (assert (@ (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real) tptp.one_one_poly_real))
% 0.26/0.65 (assert (@ (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real) tptp.one_on501200385y_real))
% 0.26/0.65 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 0.26/0.65 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P2 I4))) (and (@ P2 tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P2 (@ tptp.suc I4))))))))
% 0.26/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P2 I4))) (or (@ P2 tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P2 (@ tptp.suc I4))))))))
% 0.26/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P2 N2) (@ P2 (@ tptp.suc N2))))) (@ P2 N))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P tptp.poly_poly_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.degree_poly_real P)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N) I3) (not (= (@ (@ tptp.coeff_poly_real P) I3) tptp.zero_zero_poly_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P tptp.poly_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.degree_nat P)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N) I3) (not (= (@ (@ tptp.coeff_nat P) I3) tptp.zero_zero_nat)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P tptp.poly_poly_poly_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.degree360860553y_real P)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N) I3) (not (= (@ (@ tptp.coeff_poly_poly_real P) I3) tptp.zero_z1423781445y_real)))))))
% 0.26/0.65 (assert (forall ((N tptp.nat) (P tptp.poly_poly_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.degree_poly_nat P)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N) I3) (not (= (@ (@ tptp.coeff_poly_nat P) I3) tptp.zero_zero_poly_nat)))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (not (= A3 B2)))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat A3) B2))) (=> _let_1 (=> _let_2 (and _let_2 _let_1)))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (not (= A3 B2)))) (=> (and (@ (@ tptp.dvd_dvd_nat A3) B2) _let_1) _let_1))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A3) B2))) (=> (and _let_1 (not (= A3 B2))) _let_1))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat A3) B2) (not (= A3 B2))))) (= _let_1 _let_1))))
% 0.26/0.65 (assert (= tptp.dvd_dvd_nat (lambda ((A tptp.nat) (B3 tptp.nat)) (let ((_let_1 (= A B3))) (or (and (@ (@ tptp.dvd_dvd_nat A) B3) (not _let_1)) _let_1)))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A3))) (=> (and (@ _let_1 B2) (not (= A3 B2))) (=> (@ (@ tptp.dvd_dvd_nat B2) C) (and (@ _let_1 C) (not (= A3 C))))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A3))) (=> (@ _let_1 B2) (=> (and (@ (@ tptp.dvd_dvd_nat B2) C) (not (= B2 C))) (and (@ _let_1 C) (not (= A3 C))))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A3))) (=> (and (@ _let_1 B2) (not (= A3 B2))) (=> (and (@ (@ tptp.dvd_dvd_nat B2) C) (not (= B2 C))) (and (@ _let_1 C) (not (= A3 C))))))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A3) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A3) (= A3 B2)))))
% 0.26/0.65 (assert (forall ((A3 tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat A3) A3) (not (= A3 A3))))))
% 0.26/0.65 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lam/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 21294 Alarm clock ( read result; case "$result" in
% 299.87/300.20 unsat)
% 299.87/300.20 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.87/300.20 ;;
% 299.87/300.20 sat)
% 299.87/300.20 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.87/300.20 ;;
% 299.87/300.20 esac; exit 1 )
% 299.87/300.21 Alarm clock
% 299.87/300.21 % cvc5---1.0.5 exiting
% 299.87/300.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------