TSTP Solution File: NUM924^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:48:53 EDT 2023
% Result : Theorem 0.21s 0.72s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM924^1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:13:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : NUM924^1 : TPTP v8.1.2. Released v5.3.0.
% 0.21/0.50 % Domain : Number Theory
% 0.21/0.50 % Problem : Sum of two squares line 102, 100 axioms selected
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.21/0.50 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Bla11]
% 0.21/0.50 % Names : s2s_100_thf_l102 [Bla11]
% 0.21/0.50
% 0.21/0.50 % Status : ContradictoryAxioms
% 0.21/0.50 % Rating : 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0
% 0.21/0.50 % Syntax : Number of formulae : 133 ( 50 unt; 26 typ; 0 def)
% 0.21/0.50 % Number of atoms : 184 ( 73 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 7 ( 1 avg)
% 0.21/0.50 % Number of connectives : 814 ( 13 ~; 4 |; 7 &; 724 @)
% 0.21/0.50 % ( 43 <=>; 23 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 13 ( 5 avg)
% 0.21/0.50 % Number of types : 3 ( 2 usr)
% 0.21/0.50 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 25 ( 24 usr; 8 con; 0-2 aty)
% 0.21/0.50 % Number of variables : 160 ( 0 ^; 160 !; 0 ?; 160 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.21/0.50 % 2011-08-09 19:06:31
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Should-be-implicit typings (2)
% 0.21/0.50 thf(ty_ty_tc__Int__Oint,type,
% 0.21/0.50 int: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(ty_ty_tc__Nat__Onat,type,
% 0.21/0.50 nat: $tType ).
% 0.21/0.50
% 0.21/0.50 %----Explicit typings (24)
% 0.21/0.50 thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,
% 0.21/0.50 one_one_int: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.21/0.50 one_one_nat: nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.21/0.50 plus_plus_int: int > int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.21/0.50 plus_plus_nat: nat > nat > nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,type,
% 0.21/0.50 times_times_int: int > int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
% 0.21/0.50 times_times_nat: nat > nat > nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,
% 0.21/0.50 zero_zero_int: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.21/0.50 zero_zero_nat: nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_IntPrimes_Ozprime,type,
% 0.21/0.50 zprime: int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Int_OBit0,type,
% 0.21/0.50 bit0: int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Int_OBit1,type,
% 0.21/0.50 bit1: int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Int_OPls,type,
% 0.21/0.50 pls: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,
% 0.21/0.50 number_number_of_int: int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,
% 0.21/0.50 number_number_of_nat: int > nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,
% 0.21/0.50 ord_less_int: int > int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.21/0.50 ord_less_nat: nat > nat > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint,type,
% 0.21/0.50 ord_less_eq_int: int > int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.21/0.50 ord_less_eq_nat: nat > nat > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Power_Opower__class_Opower_000tc__Int__Oint,type,
% 0.21/0.50 power_power_int: int > nat > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Power_Opower__class_Opower_000tc__Nat__Onat,type,
% 0.21/0.50 power_power_nat: nat > nat > nat ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Ois__sum2sq,type,
% 0.21/0.50 twoSqu1013291560sum2sq: int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_m,type,
% 0.21/0.50 m: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_s____,type,
% 0.21/0.50 s: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_t____,type,
% 0.21/0.50 t: int ).
% 0.21/0.50
% 0.21/0.50 %----Relevant facts (106)
% 0.21/0.50 thf(fact_0__096t_A_060_A0_096,axiom,
% 0.21/0.50 ord_less_int @ t @ zero_zero_int ).
% 0.21/0.50
% 0.21/0.50 thf(fact_1_calculation_I1_J,axiom,
% 0.21/0.50 ord_less_int @ t @ one_one_int ).
% 0.21/0.50
% 0.21/0.50 thf(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
% 0.21/0.50 ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_3_t,axiom,
% 0.21/0.50 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.21/0.50 = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_4_calculation_I2_J,axiom,
% 0.21/0.50 ( ( t = zero_zero_int )
% 0.21/0.50 => ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.21/0.50 = zero_zero_int ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_5__096_126_A1_A_060_061_At_096,axiom,
% 0.21/0.50 ~ ( ord_less_eq_int @ one_one_int @ t ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_6_p0,axiom,
% 0.21/0.50 ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_7_not__sum__power2__lt__zero,axiom,
% 0.21/0.50 ! [X: int,Y: int] :
% 0.21/0.50 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_8_sum__power2__gt__zero__iff,axiom,
% 0.21/0.50 ! [X_10: int,Y_9: int] :
% 0.21/0.50 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_9 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
% 0.21/0.50 <=> ( ( X_10 != zero_zero_int )
% 0.21/0.50 | ( Y_9 != zero_zero_int ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_9_sum__power2__eq__zero__iff,axiom,
% 0.21/0.50 ! [X_9: int,Y_8: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ ( power_power_int @ X_9 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.21/0.50 = zero_zero_int )
% 0.21/0.50 <=> ( ( X_9 = zero_zero_int )
% 0.21/0.50 & ( Y_8 = zero_zero_int ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_10_power2__less__0,axiom,
% 0.21/0.50 ! [A_3: int] :
% 0.21/0.50 ~ ( ord_less_int @ ( power_power_int @ A_3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_11_zero__less__power2,axiom,
% 0.21/0.50 ! [A_2: int] :
% 0.21/0.50 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.21/0.50 <=> ( A_2 != zero_zero_int ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_12_one__power2,axiom,
% 0.21/0.50 ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.21/0.50 = one_one_nat ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_13_one__power2,axiom,
% 0.21/0.50 ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.21/0.50 = one_one_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_14_zero__power2,axiom,
% 0.21/0.50 ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.21/0.50 = zero_zero_nat ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_15_zero__power2,axiom,
% 0.21/0.50 ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.21/0.50 = zero_zero_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_16_zero__eq__power2,axiom,
% 0.21/0.50 ! [A_1: int] :
% 0.21/0.50 ( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.21/0.50 = zero_zero_int )
% 0.21/0.50 <=> ( A_1 = zero_zero_int ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_17_add__special_I2_J,axiom,
% 0.21/0.50 ! [W_7: int] :
% 0.21/0.50 ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_7 ) )
% 0.21/0.50 = ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_7 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_18_add__special_I3_J,axiom,
% 0.21/0.50 ! [V_12: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( number_number_of_int @ V_12 ) @ one_one_int )
% 0.21/0.50 = ( number_number_of_int @ ( plus_plus_int @ V_12 @ ( bit1 @ pls ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_19_t__l__p,axiom,
% 0.21/0.50 ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_20__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
% 0.21/0.50 ~ ! [T: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.21/0.50 != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ T ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_21_p,axiom,
% 0.21/0.50 zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_22_qf1pt,axiom,
% 0.21/0.50 twoSqu1013291560sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_23_zle__refl,axiom,
% 0.21/0.50 ! [W: int] : ( ord_less_eq_int @ W @ W ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_24_number__of__is__id,axiom,
% 0.21/0.50 ! [K: int] :
% 0.21/0.50 ( ( number_number_of_int @ K )
% 0.21/0.50 = K ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_25_zmult__commute,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( times_times_int @ Z @ W )
% 0.21/0.50 = ( times_times_int @ W @ Z ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_26_zle__linear,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ Z @ W )
% 0.21/0.50 | ( ord_less_eq_int @ W @ Z ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_27_times__numeral__code_I5_J,axiom,
% 0.21/0.50 ! [V_2: int,W: int] :
% 0.21/0.50 ( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
% 0.21/0.50 = ( number_number_of_int @ ( times_times_int @ V_2 @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_28_less__eq__number__of__int__code,axiom,
% 0.21/0.50 ! [K: int,L: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_29_le__number__of,axiom,
% 0.21/0.50 ! [X_8: int,Y_7: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( number_number_of_int @ X_8 ) @ ( number_number_of_int @ Y_7 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ X_8 @ Y_7 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_30_zmult__assoc,axiom,
% 0.21/0.50 ! [Z1: int,Z2: int,Z3: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
% 0.21/0.50 = ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_31_zle__trans,axiom,
% 0.21/0.50 ! [K: int,I: int,J: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ I @ J )
% 0.21/0.50 => ( ( ord_less_eq_int @ J @ K )
% 0.21/0.50 => ( ord_less_eq_int @ I @ K ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_32_zle__antisym,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ Z @ W )
% 0.21/0.50 => ( ( ord_less_eq_int @ W @ Z )
% 0.21/0.50 => ( Z = W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_33_zpower__zadd__distrib,axiom,
% 0.21/0.50 ! [X: int,Y: nat,Z: nat] :
% 0.21/0.50 ( ( power_power_int @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.21/0.50 = ( times_times_int @ ( power_power_int @ X @ Y ) @ ( power_power_int @ X @ Z ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_34_less__eq__int__code_I16_J,axiom,
% 0.21/0.50 ! [K1: int,K2: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_35_rel__simps_I34_J,axiom,
% 0.21/0.50 ! [K: int,L: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_36_rel__simps_I19_J,axiom,
% 0.21/0.50 ord_less_eq_int @ pls @ pls ).
% 0.21/0.50
% 0.21/0.50 thf(fact_37_less__eq__int__code_I13_J,axiom,
% 0.21/0.50 ! [K1: int,K2: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_38_rel__simps_I31_J,axiom,
% 0.21/0.50 ! [K: int,L: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_39_zless__le,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( ord_less_int @ Z @ W )
% 0.21/0.50 <=> ( ( ord_less_eq_int @ Z @ W )
% 0.21/0.50 & ( Z != W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_40_zadd__left__mono,axiom,
% 0.21/0.50 ! [K: int,I: int,J: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ I @ J )
% 0.21/0.50 => ( ord_less_eq_int @ ( plus_plus_int @ K @ I ) @ ( plus_plus_int @ K @ J ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_41_eq__number__of__0,axiom,
% 0.21/0.50 ! [V_2: int] :
% 0.21/0.50 ( ( ( number_number_of_nat @ V_2 )
% 0.21/0.50 = zero_zero_nat )
% 0.21/0.50 <=> ( ord_less_eq_int @ V_2 @ pls ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_42_eq__0__number__of,axiom,
% 0.21/0.50 ! [V_2: int] :
% 0.21/0.50 ( ( zero_zero_nat
% 0.21/0.50 = ( number_number_of_nat @ V_2 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ V_2 @ pls ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_43_semiring__mult__number__of,axiom,
% 0.21/0.50 ! [V_11: int,V_10: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ pls @ V_10 )
% 0.21/0.50 => ( ( ord_less_eq_int @ pls @ V_11 )
% 0.21/0.50 => ( ( times_times_nat @ ( number_number_of_nat @ V_10 ) @ ( number_number_of_nat @ V_11 ) )
% 0.21/0.50 = ( number_number_of_nat @ ( times_times_int @ V_10 @ V_11 ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_44_semiring__mult__number__of,axiom,
% 0.21/0.50 ! [V_11: int,V_10: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ pls @ V_10 )
% 0.21/0.50 => ( ( ord_less_eq_int @ pls @ V_11 )
% 0.21/0.50 => ( ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( number_number_of_int @ V_11 ) )
% 0.21/0.50 = ( number_number_of_int @ ( times_times_int @ V_10 @ V_11 ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_45_mult__number__of__left,axiom,
% 0.21/0.50 ! [V_9: int,W_6: int,Z_2: int] :
% 0.21/0.50 ( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( times_times_int @ ( number_number_of_int @ W_6 ) @ Z_2 ) )
% 0.21/0.50 = ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_9 @ W_6 ) ) @ Z_2 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_46_arith__simps_I32_J,axiom,
% 0.21/0.50 ! [V_8: int,W_5: int] :
% 0.21/0.50 ( ( times_times_int @ ( number_number_of_int @ V_8 ) @ ( number_number_of_int @ W_5 ) )
% 0.21/0.50 = ( number_number_of_int @ ( times_times_int @ V_8 @ W_5 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_47_number__of__mult,axiom,
% 0.21/0.50 ! [V_7: int,W_4: int] :
% 0.21/0.50 ( ( number_number_of_int @ ( times_times_int @ V_7 @ W_4 ) )
% 0.21/0.50 = ( times_times_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_4 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_48_sum__squares__le__zero__iff,axiom,
% 0.21/0.50 ! [X_7: int,Y_6: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_7 @ X_7 ) @ ( times_times_int @ Y_6 @ Y_6 ) ) @ zero_zero_int )
% 0.21/0.50 <=> ( ( X_7 = zero_zero_int )
% 0.21/0.50 & ( Y_6 = zero_zero_int ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_49_sum__squares__ge__zero,axiom,
% 0.21/0.50 ! [X_6: int,Y_5: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_6 @ X_6 ) @ ( times_times_int @ Y_5 @ Y_5 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_50_le__special_I3_J,axiom,
% 0.21/0.50 ! [X_5: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( number_number_of_int @ X_5 ) @ zero_zero_int )
% 0.21/0.50 <=> ( ord_less_eq_int @ X_5 @ pls ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_51_le__special_I1_J,axiom,
% 0.21/0.50 ! [Y_4: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_4 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ pls @ Y_4 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_52_less__0__number__of,axiom,
% 0.21/0.50 ! [V_2: int] :
% 0.21/0.51 ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_2 ) )
% 0.21/0.51 <=> ( ord_less_int @ pls @ V_2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_53_le__number__of__eq__not__less,axiom,
% 0.21/0.51 ! [V_6: int,W_3: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( number_number_of_int @ V_6 ) @ ( number_number_of_int @ W_3 ) )
% 0.21/0.51 <=> ~ ( ord_less_int @ ( number_number_of_int @ W_3 ) @ ( number_number_of_int @ V_6 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_54_le__number__of__eq__not__less,axiom,
% 0.21/0.51 ! [V_6: int,W_3: int] :
% 0.21/0.51 ( ( ord_less_eq_nat @ ( number_number_of_nat @ V_6 ) @ ( number_number_of_nat @ W_3 ) )
% 0.21/0.51 <=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_3 ) @ ( number_number_of_nat @ V_6 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_55_rel__simps_I22_J,axiom,
% 0.21/0.51 ! [K: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_56_less__eq__int__code_I14_J,axiom,
% 0.21/0.51 ! [K1: int,K2: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_57_rel__simps_I32_J,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_58_rel__simps_I27_J,axiom,
% 0.21/0.51 ! [K: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
% 0.21/0.51 <=> ( ord_less_eq_int @ K @ pls ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_59_rel__simps_I21_J,axiom,
% 0.21/0.51 ! [K: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_60_zadd__zless__mono,axiom,
% 0.21/0.51 ! [Z_1: int,Z: int,W_2: int,W: int] :
% 0.21/0.51 ( ( ord_less_int @ W_2 @ W )
% 0.21/0.51 => ( ( ord_less_eq_int @ Z_1 @ Z )
% 0.21/0.51 => ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_1 ) @ ( plus_plus_int @ W @ Z ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_61_nat__number__of__Pls,axiom,
% 0.21/0.51 ( ( number_number_of_nat @ pls )
% 0.21/0.51 = zero_zero_nat ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_62_semiring__norm_I113_J,axiom,
% 0.21/0.51 ( zero_zero_nat
% 0.21/0.51 = ( number_number_of_nat @ pls ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_63_le__special_I4_J,axiom,
% 0.21/0.51 ! [X_4: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( number_number_of_int @ X_4 ) @ one_one_int )
% 0.21/0.51 <=> ( ord_less_eq_int @ X_4 @ ( bit1 @ pls ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_64_le__special_I2_J,axiom,
% 0.21/0.51 ! [Y_3: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_3 ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_3 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_65_nat__1__add__1,axiom,
% 0.21/0.51 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.21/0.51 = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_66_mult__Pls,axiom,
% 0.21/0.51 ! [W: int] :
% 0.21/0.51 ( ( times_times_int @ pls @ W )
% 0.21/0.51 = pls ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_67_mult__Bit0,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( times_times_int @ ( bit0 @ K ) @ L )
% 0.21/0.51 = ( bit0 @ ( times_times_int @ K @ L ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_68_less__number__of__int__code,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.21/0.51 <=> ( ord_less_int @ K @ L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_69_zmult__1__right,axiom,
% 0.21/0.51 ! [Z: int] :
% 0.21/0.51 ( ( times_times_int @ Z @ one_one_int )
% 0.21/0.51 = Z ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_70_zmult__1,axiom,
% 0.21/0.51 ! [Z: int] :
% 0.21/0.51 ( ( times_times_int @ one_one_int @ Z )
% 0.21/0.51 = Z ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_71_plus__numeral__code_I9_J,axiom,
% 0.21/0.51 ! [V_2: int,W: int] :
% 0.21/0.51 ( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
% 0.21/0.51 = ( number_number_of_int @ ( plus_plus_int @ V_2 @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_72_zadd__zmult__distrib,axiom,
% 0.21/0.51 ! [Z1: int,Z2: int,W: int] :
% 0.21/0.51 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.21/0.51 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_73_zadd__zmult__distrib2,axiom,
% 0.21/0.51 ! [W: int,Z1: int,Z2: int] :
% 0.21/0.51 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.21/0.51 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_74_rel__simps_I29_J,axiom,
% 0.21/0.51 ! [K: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
% 0.21/0.51 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_75_rel__simps_I5_J,axiom,
% 0.21/0.51 ! [K: int] :
% 0.21/0.51 ( ( ord_less_int @ pls @ ( bit1 @ K ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_76_less__eq__int__code_I15_J,axiom,
% 0.21/0.51 ! [K1: int,K2: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
% 0.21/0.51 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_77_rel__simps_I33_J,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.21/0.51 <=> ( ord_less_int @ K @ L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_78_less__int__code_I14_J,axiom,
% 0.21/0.51 ! [K1: int,K2: int] :
% 0.21/0.51 ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_79_rel__simps_I15_J,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_80_less__nat__number__of,axiom,
% 0.21/0.51 ! [V_2: int,V_3: int] :
% 0.21/0.51 ( ( ord_less_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
% 0.21/0.51 <=> ( ( ( ord_less_int @ V_2 @ V_3 )
% 0.21/0.51 => ( ord_less_int @ pls @ V_3 ) )
% 0.21/0.51 & ( ord_less_int @ V_2 @ V_3 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_81_int__one__le__iff__zero__less,axiom,
% 0.21/0.51 ! [Z: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.21/0.51 <=> ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_82_nat__numeral__1__eq__1,axiom,
% 0.21/0.51 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.21/0.51 = one_one_nat ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_83_Numeral1__eq1__nat,axiom,
% 0.21/0.51 ( one_one_nat
% 0.21/0.51 = ( number_number_of_nat @ ( bit1 @ pls ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_84_zless__imp__add1__zle,axiom,
% 0.21/0.51 ! [W: int,Z: int] :
% 0.21/0.51 ( ( ord_less_int @ W @ Z )
% 0.21/0.51 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_85_add1__zle__eq,axiom,
% 0.21/0.51 ! [W: int,Z: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.21/0.51 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_86_zle__add1__eq__le,axiom,
% 0.21/0.51 ! [W: int,Z: int] :
% 0.21/0.51 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.21/0.51 <=> ( ord_less_eq_int @ W @ Z ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_87_semiring__add__number__of,axiom,
% 0.21/0.51 ! [V_5: int,V_4: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ pls @ V_4 )
% 0.21/0.51 => ( ( ord_less_eq_int @ pls @ V_5 )
% 0.21/0.51 => ( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ V_5 ) )
% 0.21/0.51 = ( number_number_of_int @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_88_semiring__add__number__of,axiom,
% 0.21/0.51 ! [V_5: int,V_4: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ pls @ V_4 )
% 0.21/0.51 => ( ( ord_less_eq_int @ pls @ V_5 )
% 0.21/0.51 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
% 0.21/0.51 = ( number_number_of_nat @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_89_add__nat__number__of,axiom,
% 0.21/0.51 ! [V_3: int,V_2: int] :
% 0.21/0.51 ( ( ( ord_less_int @ V_2 @ pls )
% 0.21/0.51 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
% 0.21/0.51 = ( number_number_of_nat @ V_3 ) ) )
% 0.21/0.51 & ( ~ ( ord_less_int @ V_2 @ pls )
% 0.21/0.51 => ( ( ( ord_less_int @ V_3 @ pls )
% 0.21/0.51 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
% 0.21/0.51 = ( number_number_of_nat @ V_2 ) ) )
% 0.21/0.51 & ( ~ ( ord_less_int @ V_3 @ pls )
% 0.21/0.51 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
% 0.21/0.51 = ( number_number_of_nat @ ( plus_plus_int @ V_2 @ V_3 ) ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_90_le__imp__0__less,axiom,
% 0.21/0.51 ! [Z: int] :
% 0.21/0.51 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.21/0.51 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_91_eq__number__of,axiom,
% 0.21/0.51 ! [X_3: int,Y_2: int] :
% 0.21/0.51 ( ( ( number_number_of_int @ X_3 )
% 0.21/0.51 = ( number_number_of_int @ Y_2 ) )
% 0.21/0.51 <=> ( X_3 = Y_2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_92_number__of__reorient,axiom,
% 0.21/0.51 ! [W_1: int,X_2: nat] :
% 0.21/0.51 ( ( ( number_number_of_nat @ W_1 )
% 0.21/0.51 = X_2 )
% 0.21/0.51 <=> ( X_2
% 0.21/0.51 = ( number_number_of_nat @ W_1 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_93_number__of__reorient,axiom,
% 0.21/0.51 ! [W_1: int,X_2: int] :
% 0.21/0.51 ( ( ( number_number_of_int @ W_1 )
% 0.21/0.51 = X_2 )
% 0.21/0.51 <=> ( X_2
% 0.21/0.51 = ( number_number_of_int @ W_1 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_94_rel__simps_I51_J,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ( bit1 @ K )
% 0.21/0.51 = ( bit1 @ L ) )
% 0.21/0.51 <=> ( K = L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_95_rel__simps_I48_J,axiom,
% 0.21/0.51 ! [K: int,L: int] :
% 0.21/0.51 ( ( ( bit0 @ K )
% 0.21/0.51 = ( bit0 @ L ) )
% 0.21/0.51 <=> ( K = L ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_96_zless__linear,axiom,
% 0.21/0.51 ! [X: int,Y: int] :
% 0.21/0.51 ( ( ord_less_int @ X @ Y )
% 0.21/0.51 | ( X = Y )
% 0.21/0.51 | ( ord_less_int @ Y @ X ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_97_sum__squares__eq__zero__iff,axiom,
% 0.21/0.51 ! [X_1: int,Y_1: int] :
% 0.21/0.51 ( ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
% 0.21/0.51 = zero_zero_int )
% 0.21/0.51 <=> ( ( X_1 = zero_zero_int )
% 0.21/0.51 & ( Y_1 = zero_zero_int ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_98_left__distrib__number__of,axiom,
% 0.21/0.51 ! [A: int,B_1: int,V_1: int] :
% 0.21/0.51 ( ( times_times_int @ ( plus_plus_int @ A @ B_1 ) @ ( number_number_of_int @ V_1 ) )
% 0.21/0.51 = ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_1 @ ( number_number_of_int @ V_1 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_99_left__distrib__number__of,axiom,
% 0.21/0.51 ! [A: nat,B_1: nat,V_1: int] :
% 0.21/0.51 ( ( times_times_nat @ ( plus_plus_nat @ A @ B_1 ) @ ( number_number_of_nat @ V_1 ) )
% 0.21/0.51 = ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ V_1 ) ) @ ( times_times_nat @ B_1 @ ( number_number_of_nat @ V_1 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_100_right__distrib__number__of,axiom,
% 0.21/0.51 ! [V: int,B: int,C: int] :
% 0.21/0.51 ( ( times_times_int @ ( number_number_of_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.21/0.51 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V ) @ B ) @ ( times_times_int @ ( number_number_of_int @ V ) @ C ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_101_right__distrib__number__of,axiom,
% 0.21/0.51 ! [V: int,B: nat,C: nat] :
% 0.21/0.51 ( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.21/0.51 = ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ V ) @ C ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_102_zadd__assoc,axiom,
% 0.21/0.51 ! [Z1: int,Z2: int,Z3: int] :
% 0.21/0.51 ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
% 0.21/0.51 = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_103_zadd__left__commute,axiom,
% 0.21/0.51 ! [X: int,Y: int,Z: int] :
% 0.21/0.51 ( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
% 0.21/0.53 = ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(fact_104_zadd__commute,axiom,
% 0.21/0.53 ! [Z: int,W: int] :
% 0.21/0.53 ( ( plus_plus_int @ Z @ W )
% 0.21/0.53 = ( plus_plus_int @ W @ Z ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(fact_105_zero__is__num__zero,axiom,
% 0.21/0.53 ( zero_zero_int
% 0.21/0.53 = ( number_number_of_int @ pls ) ) ).
% 0.21/0.53
% 0.21/0.53 %----Conjectures (1)
% 0.21/0.53 thf(conj_0,conjecture,
% 0.21/0.53 ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cb7ACoGm3s/cvc5---1.0.5_832.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.int 0)
% 0.21/0.53 (declare-sort tptp.nat 0)
% 0.21/0.53 (declare-fun tptp.one_one_int () tptp.int)
% 0.21/0.53 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.21/0.53 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.21/0.53 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.53 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 0.21/0.53 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.53 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.21/0.53 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.21/0.53 (declare-fun tptp.zprime (tptp.int) Bool)
% 0.21/0.53 (declare-fun tptp.bit0 (tptp.int) tptp.int)
% 0.21/0.53 (declare-fun tptp.bit1 (tptp.int) tptp.int)
% 0.21/0.53 (declare-fun tptp.pls () tptp.int)
% 0.21/0.53 (declare-fun tptp.number_number_of_int (tptp.int) tptp.int)
% 0.21/0.53 (declare-fun tptp.number_number_of_nat (tptp.int) tptp.nat)
% 0.21/0.53 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.21/0.53 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.21/0.53 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.21/0.53 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.21/0.53 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 0.21/0.53 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.53 (declare-fun tptp.twoSqu1013291560sum2sq (tptp.int) Bool)
% 0.21/0.53 (declare-fun tptp.m () tptp.int)
% 0.21/0.53 (declare-fun tptp.s () tptp.int)
% 0.21/0.53 (declare-fun tptp.t () tptp.int)
% 0.21/0.53 (assert (@ (@ tptp.ord_less_int tptp.t) tptp.zero_zero_int))
% 0.21/0.53 (assert (@ (@ tptp.ord_less_int tptp.t) tptp.one_one_int))
% 0.21/0.53 (assert (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))) (@ (@ tptp.ord_less_int (@ _let_1 tptp.t)) (@ _let_1 tptp.zero_zero_int))))
% 0.21/0.53 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) tptp.t))))
% 0.21/0.53 (assert (=> (= tptp.t tptp.zero_zero_int) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.one_one_int) tptp.zero_zero_int)))
% 0.21/0.53 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t)))
% 0.21/0.53 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.21/0.53 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 0.21/0.53 (assert (forall ((X_10 tptp.int) (Y_9 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_10) _let_1)) (@ (@ tptp.power_power_int Y_9) _let_1))) (or (not (= X_10 tptp.zero_zero_int)) (not (= Y_9 tptp.zero_zero_int)))))))
% 0.21/0.53 (assert (forall ((X_9 tptp.int) (Y_8 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_9) _let_1)) (@ (@ tptp.power_power_int Y_8) _let_1)) tptp.zero_zero_int) (and (= X_9 tptp.zero_zero_int) (= Y_8 tptp.zero_zero_int))))))
% 0.21/0.53 (assert (forall ((A_3 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_3) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))))
% 0.21/0.53 (assert (forall ((A_2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_2) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_2 tptp.zero_zero_int)))))
% 0.21/0.53 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_nat))
% 0.21/0.53 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_int))
% 0.21/0.53 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_nat))
% 0.21/0.53 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int))
% 0.21/0.53 (assert (forall ((A_1 tptp.int)) (= (= (@ (@ tptp.power_power_int A_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))))
% 0.21/0.53 (assert (forall ((W_7 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_7)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_7)))))
% 0.21/0.53 (assert (forall ((V_12 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_12)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_12) (@ tptp.bit1 tptp.pls))))))
% 0.21/0.53 (assert (@ (@ tptp.ord_less_int tptp.t) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.21/0.53 (assert (not (forall ((T tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T)))))))
% 0.21/0.53 (assert (@ tptp.zprime (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.21/0.53 (assert (@ tptp.twoSqu1013291560sum2sq (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)) tptp.t)))
% 0.21/0.53 (assert (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)))
% 0.21/0.53 (assert (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)))
% 0.21/0.53 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))
% 0.21/0.53 (assert (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.21/0.53 (assert (forall ((V_2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_2)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_2) W)))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.21/0.53 (assert (forall ((X_8 tptp.int) (Y_7 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_8)) (@ tptp.number_number_of_int Y_7)) (@ (@ tptp.ord_less_eq_int X_8) Y_7))))
% 0.21/0.53 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))))
% 0.21/0.53 (assert (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))))
% 0.21/0.53 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))))
% 0.21/0.53 (assert (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.21/0.53 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.21/0.53 (assert (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls))
% 0.21/0.53 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.21/0.53 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))))
% 0.21/0.53 (assert (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))))
% 0.21/0.53 (assert (forall ((V_2 tptp.int)) (= (= (@ tptp.number_number_of_nat V_2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V_2) tptp.pls))))
% 0.21/0.53 (assert (forall ((V_2 tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V_2)) (@ (@ tptp.ord_less_eq_int V_2) tptp.pls))))
% 0.21/0.53 (assert (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_10) (=> (@ _let_1 V_11) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_10)) (@ tptp.number_number_of_nat V_11)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_10) V_11))))))))
% 0.21/0.53 (assert (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_10) (=> (@ _let_1 V_11) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) V_11))))))))
% 0.21/0.53 (assert (forall ((V_9 tptp.int) (W_6 tptp.int) (Z_2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_9)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_6)) Z_2)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_9) W_6))) Z_2))))
% 0.21/0.53 (assert (forall ((V_8 tptp.int) (W_5 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_8)) (@ tptp.number_number_of_int W_5)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_8) W_5)))))
% 0.21/0.53 (assert (forall ((V_7 tptp.int) (W_4 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_7) W_4)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_7)) (@ tptp.number_number_of_int W_4)))))
% 0.21/0.53 (assert (forall ((X_7 tptp.int) (Y_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_7) X_7)) (@ (@ tptp.times_times_int Y_6) Y_6))) tptp.zero_zero_int) (and (= X_7 tptp.zero_zero_int) (= Y_6 tptp.zero_zero_int)))))
% 0.21/0.53 (assert (forall ((X_6 tptp.int) (Y_5 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_6) X_6)) (@ (@ tptp.times_times_int Y_5) Y_5)))))
% 0.21/0.53 (assert (forall ((X_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_5)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_5) tptp.pls))))
% 0.21/0.53 (assert (forall ((Y_4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_4)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_4))))
% 0.21/0.53 (assert (forall ((V_2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V_2)) (@ (@ tptp.ord_less_int tptp.pls) V_2))))
% 0.21/0.53 (assert (forall ((V_6 tptp.int) (W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_6))) (let ((_let_2 (@ tptp.number_number_of_int W_3))) (= (@ (@ tptp.ord_less_eq_int _let_1) _let_2) (not (@ (@ tptp.ord_less_int _let_2) _let_1)))))))
% 0.21/0.53 (assert (forall ((V_6 tptp.int) (W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_6))) (let ((_let_2 (@ tptp.number_number_of_nat W_3))) (= (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (not (@ (@ tptp.ord_less_nat _let_2) _let_1)))))))
% 0.21/0.53 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.21/0.53 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.21/0.53 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))))
% 0.21/0.53 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.21/0.53 (assert (forall ((Z_1 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_2) W) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_2) Z_1)) (@ (@ tptp.plus_plus_int W) Z))))))
% 0.21/0.53 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.21/0.53 (assert (= tptp.zero_zero_nat (@ tptp.number_number_of_nat tptp.pls)))
% 0.21/0.53 (assert (forall ((X_4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_4) (@ tptp.bit1 tptp.pls)))))
% 0.21/0.53 (assert (forall ((Y_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_3)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_3))))
% 0.21/0.53 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.21/0.53 (assert (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit0 K)) L) (@ tptp.bit0 (@ (@ tptp.times_times_int K) L)))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))))
% 0.21/0.53 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)))
% 0.21/0.53 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)))
% 0.21/0.53 (assert (forall ((V_2 tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_2)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_2) W)))))
% 0.21/0.53 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.21/0.53 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.21/0.53 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.21/0.53 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))))
% 0.21/0.53 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.21/0.53 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.21/0.53 (assert (forall ((V_2 tptp.int) (V_3 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V_2) V_3))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V_2)) (@ tptp.number_number_of_nat V_3)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_3)) _let_1)))))
% 0.21/0.53 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 0.21/0.53 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.21/0.53 (assert (= tptp.one_one_nat (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls))))
% 0.21/0.53 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 0.21/0.53 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 0.21/0.53 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.21/0.53 (assert (forall ((V_5 tptp.int) (V_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_4) (=> (@ _let_1 V_5) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_4)) (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_4) V_5))))))))
% 0.21/0.53 (assert (forall ((V_5 tptp.int) (V_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_4) (=> (@ _let_1 V_5) (= (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_4)) (@ tptp.number_number_of_nat V_5)) (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_4) V_5))))))))
% 0.21/0.53 (assert (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_3))) (let ((_let_2 (@ tptp.number_number_of_nat V_2))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_3) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V_2) tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_2) V_3))))))))))))))
% 0.21/0.53 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 0.21/0.53 (assert (forall ((X_3 tptp.int) (Y_2 tptp.int)) (= (= (@ tptp.number_number_of_int X_3) (@ tptp.number_number_of_int Y_2)) (= X_3 Y_2))))
% 0.21/0.53 (assert (forall ((W_1 tptp.int) (X_2 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))))
% 0.21/0.53 (assert (forall ((W_1 tptp.int) (X_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))))
% 0.21/0.53 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit0 K) (@ tptp.bit0 L)) (= K L))))
% 0.21/0.53 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 0.21/0.53 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_1) X_1)) (@ (@ tptp.times_times_int Y_1) Y_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))))
% 0.21/0.53 (assert (forall ((A tptp.int) (B_1 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B_1)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B_1) _let_1))))))
% 0.21/0.53 (assert (forall ((A tptp.nat) (B_1 tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_1))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B_1)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B_1) _let_1))))))
% 0.21/0.53 (assert (forall ((V tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 0.21/0.53 (assert (forall ((V tptp.int) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 0.21/0.72 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))))
% 0.21/0.72 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.21/0.72 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))))
% 0.21/0.72 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.21/0.72 (assert (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.one_one_int)) tptp.zero_zero_int)))
% 0.21/0.72 (set-info :filename cvc5---1.0.5_832)
% 0.21/0.72 (check-sat-assuming ( true ))
% 0.21/0.72 ------- get file name : TPTP file name is NUM924^1
% 0.21/0.72 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_832.smt2...
% 0.21/0.72 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.72 % SZS status Theorem for NUM924^1
% 0.21/0.72 % SZS output start Proof for NUM924^1
% 0.21/0.72 (
% 0.21/0.72 (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) _let_3)) tptp.one_one_int))) (let ((_let_5 (@ tptp.ord_less_int _let_4))) (let ((_let_6 (not (@ _let_5 tptp.zero_zero_int)))) (let ((_let_7 (@ tptp.number_number_of_int tptp.pls))) (let ((_let_8 (= tptp.zero_zero_int _let_7))) (let ((_let_9 (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))) (let ((_let_10 (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))) (let ((_let_11 (@ tptp.number_number_of_nat _let_1))) (let ((_let_12 (= tptp.one_one_nat _let_11))) (let ((_let_13 (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)))) (let ((_let_14 (@ tptp.number_number_of_nat tptp.pls))) (let ((_let_15 (= tptp.zero_zero_nat _let_14))) (let ((_let_16 (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))) (let ((_let_17 (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)))) (let ((_let_18 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_2))) tptp.m)) tptp.one_one_int))) (let ((_let_19 (@ tptp.times_times_int _let_18))) (let ((_let_20 (@ _let_19 tptp.t))) (let ((_let_21 (@ tptp.ord_less_int tptp.t))) (let ((_let_22 (= _let_4 _let_20))) (let ((_let_23 (@ tptp.ord_less_int _let_20))) (let ((_let_24 (@ _let_23 (@ _let_19 tptp.zero_zero_int)))) (let ((_let_25 (ho_3 k_2 tptp.pls))) (let ((_let_26 (= tptp.pls _let_25))) (let ((_let_27 (ho_3 k_8 (ho_3 k_7 tptp.pls)))) (let ((_let_28 (ho_3 (ho_10 k_11 (ho_3 (ho_10 k_9 (ho_3 k_2 (ho_3 k_8 _let_27))) tptp.m)) tptp.one_one_int))) (let ((_let_29 (ho_10 k_9 _let_28))) (let ((_let_30 (ho_3 _let_29 _let_25))) (let ((_let_31 (= _let_30 (ho_3 (ho_10 k_9 _let_25) _let_28)))) (let ((_let_32 (ho_3 _let_29 tptp.t))) (let ((_let_33 (ho_5 k_17 (ho_3 (ho_10 k_11 _let_32) tptp.one_one_int)))) (let ((_let_34 (ho_6 _let_33 _let_30))) (let ((_let_35 (ho_6 _let_33 _let_25))) (let ((_let_36 (= tptp.pls (ho_3 (ho_10 k_9 tptp.pls) _let_28)))) (let ((_let_37 (forall ((K tptp.int)) (= K (ho_3 k_2 K))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((K tptp.int)) (= K (@ tptp.number_number_of_int K))) _let_37))))))) (let ((_let_39 (forall ((Z tptp.int) (W tptp.int)) (= (ho_3 (ho_10 k_9 W) Z) (ho_3 (ho_10 k_9 Z) W))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_16)) (PREPROCESS :args ((= _let_16 _let_39)))))) (let ((_let_41 (ho_5 k_4 _let_32))) (let ((_let_42 (ho_6 _let_41 _let_30))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_34))) (let ((_let_45 (forall ((W tptp.int) (Z tptp.int)) (or (not (ho_6 (ho_5 k_4 W) Z)) (ho_6 (ho_5 k_17 (ho_3 (ho_10 k_11 W) tptp.one_one_int)) Z))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W tptp.int) (Z tptp.int)) (or (not (@ (@ tptp.ord_less_int W) Z)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))) _let_45))))))) (let ((_let_47 (AND_INTRO (ASSUME :args (_let_8)) (ASSUME :args (_let_12)) (ASSUME :args (_let_15))))) (let ((_let_48 (ho_6 _let_41 _let_25))) (let ((_let_49 (= _let_48 _let_35))) (let ((_let_50 (not _let_35))) (let ((_let_51 (forall ((W tptp.int) (Z tptp.int)) (= (ho_6 (ho_5 k_4 W) Z) (ho_6 (ho_5 k_17 (ho_3 (ho_10 k_11 W) tptp.one_one_int)) Z))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_51)))))) (let ((_let_53 (ho_3 (ho_10 k_11 (ho_16 (ho_15 k_14 tptp.s) (ho_13 k_12 _let_27))) tptp.one_one_int))) (let ((_let_54 (= _let_32 _let_53))) (let ((_let_55 (ho_6 (ho_5 k_4 _let_53) _let_25))) (let ((_let_56 (not _let_48))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_22)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_20 _let_4) _let_54))))))) (let ((_let_58 (not _let_55))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO _let_47 :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (@ _let_5 _let_7)) _let_58))))))) (let ((_let_60 (not _let_54))) (let ((_let_61 (or))) (let ((_let_62 (and _let_54 _let_58))) (let ((_let_63 (APPLY_UF ho_6))) (let ((_let_64 (forall ((W tptp.int)) (= tptp.pls (ho_3 (ho_10 k_9 tptp.pls) W))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W tptp.int)) (= tptp.pls (@ (@ tptp.times_times_int tptp.pls) W))) _let_64))))))) (let ((_let_66 (not _let_36))) (let ((_let_67 (not _let_34))) (let ((_let_68 (not _let_31))) (let ((_let_69 (not _let_26))) (let ((_let_70 (ASSUME :args (_let_50)))) (let ((_let_71 (ASSUME :args (_let_26)))) (let ((_let_72 (SYMM _let_71))) (let ((_let_73 (ASSUME :args (_let_36)))) (let ((_let_74 (ASSUME :args (_let_31)))) (let ((_let_75 (ASSUME :args (_let_34)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_70 _let_71 _let_73 _let_74 _let_75) :args (_let_26 _let_31 _let_34 _let_50 _let_36)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_75)) (CONG (REFL :args (_let_33)) (TRANS (SYMM (SYMM _let_74)) (CONG (CONG (REFL :args (k_9)) _let_72 :args (APPLY_UF ho_10)) (REFL :args (_let_28)) :args (APPLY_UF ho_3)) (SYMM _let_73) (SYMM _let_72)) :args _let_63) (FALSE_INTRO _let_70))) :args (_let_50 _let_26 _let_36 _let_31 _let_34)) :args ((not (and _let_26 _let_31 _let_34 _let_50 _let_36)) SB_LITERAL))) (CONG (REFL :args (_let_69)) (REFL :args (_let_68)) (REFL :args (_let_67)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_35))) (REFL :args (_let_66)) :args _let_61)) :args ((or _let_69 _let_35 _let_68 _let_67 _let_66))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_28 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_64))) _let_65 :args (_let_36 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_49)) :args ((or _let_48 _let_50 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_62)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_59 _let_57) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (k_4)) (SYMM (SYMM _let_57)) :args (APPLY_UF ho_5)) (REFL :args (_let_25)) :args _let_63) (FALSE_INTRO _let_59))) :args (_let_58 _let_54))) :args (_let_54 _let_58))) :args (true _let_62)) (CONG (REFL :args (_let_60)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_55))) (REFL :args (_let_56)) :args _let_61)) :args ((or _let_55 _let_60 _let_56))) _let_59 _let_57 :args (_let_56 true _let_55 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_32 _let_25 QUANTIFIERS_INST_E_MATCHING ((ho_6 (ho_5 k_4 W) Z)))) :args (_let_51))) _let_52 :args (_let_49 false _let_51)) :args (_let_50 true _let_48 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_34 (not _let_44)))) (EQ_RESOLVE (ASSUME :args (_let_24)) (TRANS (MACRO_SR_EQ_INTRO _let_47 :args (_let_24 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ _let_23 (@ _let_19 _let_7)) _let_42))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_32 _let_30 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_6 (ho_5 k_4 W) Z) false))))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_34 false _let_42 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_25 _let_28 QUANTIFIERS_INST_E_MATCHING ((ho_3 (ho_10 k_9 W) Z)))) :args (_let_39))) _let_40 :args (_let_31 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.pls QUANTIFIERS_INST_CBQI_PROP)) :args (_let_37))) _let_38 :args (_let_26 false _let_37)) :args (false false _let_36 true _let_35 false _let_34 false _let_31 false _let_26)) :args ((@ _let_21 tptp.zero_zero_int) (@ _let_21 tptp.one_one_int) _let_24 _let_22 (=> (= tptp.t tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_18) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))) (forall ((X_10 tptp.int) (Y_9 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_10) _let_1)) (@ (@ tptp.power_power_int Y_9) _let_1))) (or (not (= X_10 tptp.zero_zero_int)) (not (= Y_9 tptp.zero_zero_int)))))) (forall ((X_9 tptp.int) (Y_8 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_9) _let_1)) (@ (@ tptp.power_power_int Y_8) _let_1)) tptp.zero_zero_int) (and (= X_9 tptp.zero_zero_int) (= Y_8 tptp.zero_zero_int))))) (forall ((A_3 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_3) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))) (forall ((A_2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_2) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_2 tptp.zero_zero_int)))) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_3) tptp.one_one_nat) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_3) tptp.one_one_int) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_3) tptp.zero_zero_nat) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_3) tptp.zero_zero_int) (forall ((A_1 tptp.int)) (= (= (@ (@ tptp.power_power_int A_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))) (forall ((W_7 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_7)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_7)))) (forall ((V_12 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_12)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_12) (@ tptp.bit1 tptp.pls))))) (@ _let_21 _let_18) (not (forall ((T tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T)))))) (@ tptp.zprime _let_18) (@ tptp.twoSqu1013291560sum2sq _let_20) (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)) _let_17 _let_16 (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((V_2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_2)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_2) W)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((X_8 tptp.int) (Y_7 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_8)) (@ tptp.number_number_of_int Y_7)) (@ (@ tptp.ord_less_eq_int X_8) Y_7))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))) (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))) (forall ((V_2 tptp.int)) (= (= (@ tptp.number_number_of_nat V_2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V_2) tptp.pls))) (forall ((V_2 tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V_2)) (@ (@ tptp.ord_less_eq_int V_2) tptp.pls))) (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_10) (=> (@ _let_1 V_11) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_10)) (@ tptp.number_number_of_nat V_11)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_10) V_11))))))) (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_10) (=> (@ _let_1 V_11) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) V_11))))))) (forall ((V_9 tptp.int) (W_6 tptp.int) (Z_2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_9)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_6)) Z_2)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_9) W_6))) Z_2))) (forall ((V_8 tptp.int) (W_5 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_8)) (@ tptp.number_number_of_int W_5)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_8) W_5)))) (forall ((V_7 tptp.int) (W_4 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_7) W_4)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_7)) (@ tptp.number_number_of_int W_4)))) (forall ((X_7 tptp.int) (Y_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_7) X_7)) (@ (@ tptp.times_times_int Y_6) Y_6))) tptp.zero_zero_int) (and (= X_7 tptp.zero_zero_int) (= Y_6 tptp.zero_zero_int)))) (forall ((X_6 tptp.int) (Y_5 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_6) X_6)) (@ (@ tptp.times_times_int Y_5) Y_5)))) (forall ((X_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_5)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_5) tptp.pls))) (forall ((Y_4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_4)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_4))) (forall ((V_2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V_2)) (@ (@ tptp.ord_less_int tptp.pls) V_2))) (forall ((V_6 tptp.int) (W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_6))) (let ((_let_2 (@ tptp.number_number_of_int W_3))) (= (@ (@ tptp.ord_less_eq_int _let_1) _let_2) (not (@ (@ tptp.ord_less_int _let_2) _let_1)))))) (forall ((V_6 tptp.int) (W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_6))) (let ((_let_2 (@ tptp.number_number_of_nat W_3))) (= (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (not (@ (@ tptp.ord_less_nat _let_2) _let_1)))))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (forall ((Z_1 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_2) W) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_2) Z_1)) (@ (@ tptp.plus_plus_int W) Z))))) (= _let_14 tptp.zero_zero_nat) _let_15 (forall ((X_4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_4) (@ tptp.bit1 tptp.pls)))) (forall ((Y_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_3)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_3))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) _let_3) _let_13 (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit0 K)) L) (@ tptp.bit0 (@ (@ tptp.times_times_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((V_2 tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_2)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_2) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((V_2 tptp.int) (V_3 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V_2) V_3))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V_2)) (@ tptp.number_number_of_nat V_3)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_3)) _let_1)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (= _let_11 tptp.one_one_nat) _let_12 _let_10 _let_9 (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((V_5 tptp.int) (V_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_4) (=> (@ _let_1 V_5) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_4)) (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_4) V_5))))))) (forall ((V_5 tptp.int) (V_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_4) (=> (@ _let_1 V_5) (= (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_4)) (@ tptp.number_number_of_nat V_5)) (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_4) V_5))))))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_3))) (let ((_let_2 (@ tptp.number_number_of_nat V_2))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_3) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V_2) tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_2) V_3))))))))))))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))) (forall ((X_3 tptp.int) (Y_2 tptp.int)) (= (= (@ tptp.number_number_of_int X_3) (@ tptp.number_number_of_int Y_2)) (= X_3 Y_2))) (forall ((W_1 tptp.int) (X_2 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 tptp.int) (X_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))) (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit0 K) (@ tptp.bit0 L)) (= K L))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_1) X_1)) (@ (@ tptp.times_times_int Y_1) Y_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))) (forall ((A tptp.int) (B_1 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B_1)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B_1) _let_1))))) (forall ((A tptp.nat) (B_1 tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_1))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B_1)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B_1) _let_1))))) (forall ((V tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.int) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))) _let_8 _let_6 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.72 )
% 0.21/0.72 % SZS output end Proof for NUM924^1
% 0.21/0.72 % cvc5---1.0.5 exiting
% 0.21/0.72 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------