TSTP Solution File: FLD040-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 : Wed Aug 30 22:27:31 EDT 2023
% Result : Unsatisfiable 2.87s 3.11s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 29
% Syntax : Number of formulae : 103 ( 33 unt; 11 typ; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 201 ( 101 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(sum_3,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(c_0_18,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_2 ).
cnf(c_0_21,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_22,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_24,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_26,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_27,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_28,hypothesis,
sum(multiplicative_inverse(a),additive_inverse(multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(multiplicative_inverse(a)),X2)
| ~ sum(X1,X3,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,hypothesis,
sum(additive_identity,additive_inverse(multiplicative_inverse(a)),additive_inverse(multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_32,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_33,hypothesis,
( sum(X1,additive_inverse(multiplicative_inverse(a)),additive_identity)
| ~ sum(X1,additive_identity,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_35,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X2,additive_identity,multiplicative_inverse(a))
| ~ sum(X1,X2,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
sum_3 ).
cnf(c_0_37,hypothesis,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_38,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,additive_identity,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,hypothesis,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_41,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_42,negated_conjecture,
( sum(X1,multiplicative_inverse(a),a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_43,hypothesis,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_45,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_19]),c_0_20]) ).
cnf(c_0_46,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_47,negated_conjecture,
( sum(multiplicative_inverse(a),X1,a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_48,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,multiplicative_inverse(a))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_49,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_50,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_52,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_53,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_54,negated_conjecture,
( sum(X1,a,a)
| ~ sum(X1,multiplicative_inverse(a),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_34])]) ).
cnf(c_0_55,hypothesis,
( sum(multiplicative_inverse(a),X1,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
cnf(c_0_56,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(a),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_58,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_59,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_60,hypothesis,
sum(multiplicative_inverse(a),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_36])]) ).
cnf(c_0_61,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
distributivity_1 ).
cnf(c_0_62,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_51,c_0_19]) ).
cnf(c_0_63,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
cnf(c_0_65,hypothesis,
( product(multiplicative_inverse(a),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_57]) ).
cnf(c_0_66,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_67,hypothesis,
( sum(X1,X2,multiplicative_inverse(a))
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_68,hypothesis,
sum(a,multiplicative_inverse(a),a),
inference(spm,[status(thm)],[c_0_23,c_0_60]) ).
cnf(c_0_69,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X4,a,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,hypothesis,
( product(multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_71,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_44,c_0_62]) ).
cnf(c_0_72,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_64,c_0_58]) ).
cnf(c_0_73,hypothesis,
( product(a,multiplicative_inverse(a),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_65]) ).
cnf(c_0_74,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_75,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_66]) ).
cnf(c_0_76,hypothesis,
( sum(X1,a,multiplicative_inverse(a))
| ~ sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,hypothesis,
( sum(X1,multiplicative_identity,a)
| ~ product(X2,a,X1)
| ~ sum(X2,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_78,plain,
( sum(multiplicative_identity,X1,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_72]) ).
cnf(c_0_79,hypothesis,
( product(X1,a,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_73]) ).
cnf(c_0_80,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X3,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_40]) ).
cnf(c_0_81,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_75]) ).
cnf(c_0_82,hypothesis,
( sum(a,X1,multiplicative_inverse(a))
| ~ sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_76]) ).
cnf(c_0_83,hypothesis,
( sum(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_43])]) ).
cnf(c_0_84,hypothesis,
( product(X1,a,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_71]) ).
cnf(c_0_85,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_86,hypothesis,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,multiplicative_inverse(a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_78]),c_0_43])]) ).
cnf(c_0_87,hypothesis,
( sum(X1,multiplicative_inverse(a),additive_identity)
| ~ sum(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_66])]) ).
cnf(c_0_88,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_89,hypothesis,
sum(a,multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_90,hypothesis,
~ sum(multiplicative_identity,a,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_91,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_89]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 23:34:54 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.57 start to proof: theBenchmark
% 2.87/3.11 % Version : CSE_E---1.5
% 2.87/3.11 % Problem : theBenchmark.p
% 2.87/3.11 % Proof found
% 2.87/3.11 % SZS status Theorem for theBenchmark.p
% 2.87/3.11 % SZS output start Proof
% See solution above
% 2.87/3.11 % Total time : 2.518000 s
% 2.87/3.11 % SZS output end Proof
% 2.87/3.11 % Total time : 2.521000 s
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