TSTP Solution File: HEN011-5 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : HEN011-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n015.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 01:54:11 EDT 2023
% Result : Unsatisfiable 62.42s 62.46s
% Output : CNFRefutation 62.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 13:43:06 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 62.42/62.45 %-------------------------------------------
% 62.42/62.45 % File :CSE---1.6
% 62.42/62.45 % Problem :theBenchmark
% 62.42/62.45 % Transform :cnf
% 62.42/62.45 % Format :tptp:raw
% 62.42/62.45 % Command :java -jar mcs_scs.jar %d %s
% 62.42/62.45
% 62.42/62.45 % Result :Theorem 61.840000s
% 62.42/62.45 % Output :CNFRefutation 61.840000s
% 62.42/62.45 %-------------------------------------------
% 62.42/62.45 %--------------------------------------------------------------------------
% 62.42/62.45 % File : HEN011-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% 62.42/62.45 % Domain : Henkin Models
% 62.42/62.45 % Problem : This operation is commutative
% 62.42/62.45 % Version : [MOW76] (equality) axioms : Reduced & Augmented > Complete.
% 62.42/62.45 % English : Define & on the set of Z', where Z' = identity/Z,
% 62.42/62.45 % by X' & Y' = X'/(identity/Y'). The operation is commutative.
% 62.42/62.45
% 62.42/62.45 % Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 62.42/62.45 % Source : [ANL]
% 62.42/62.45 % Names : hp11.ver3.in [ANL]
% 62.42/62.45
% 62.42/62.45 % Status : Unsatisfiable
% 62.42/62.45 % Rating : 0.06 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.18 v7.3.0, 0.15 v7.2.0, 0.17 v7.1.0, 0.09 v7.0.0, 0.08 v6.4.0, 0.14 v6.3.0, 0.10 v6.2.0, 0.30 v6.1.0, 0.18 v6.0.0, 0.14 v5.5.0, 0.25 v5.4.0, 0.11 v5.3.0, 0.30 v5.2.0, 0.12 v5.1.0, 0.11 v5.0.0, 0.20 v4.1.0, 0.11 v4.0.1, 0.12 v4.0.0, 0.00 v3.3.0, 0.11 v3.2.0, 0.00 v2.1.0, 0.67 v2.0.0
% 62.42/62.45 % Syntax : Number of clauses : 14 ( 9 unt; 0 nHn; 4 RR)
% 62.42/62.45 % Number of literals : 21 ( 21 equ; 8 neg)
% 62.42/62.46 % Maximal clause size : 3 ( 1 avg)
% 62.42/62.46 % Maximal term depth : 4 ( 2 avg)
% 62.42/62.46 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 62.42/62.46 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% 62.42/62.46 % Number of variables : 25 ( 3 sgn)
% 62.42/62.46 % SPC : CNF_UNS_RFO_PEQ_NUE
% 62.42/62.46
% 62.42/62.46 % Comments : less_equal replaced by divides
% 62.42/62.46 % Bugfixes : v1.2.1 - Clauses identity_divide_a, identity_divide_b,
% 62.42/62.46 % identity_divide_c, identity_divide_d, and prove_commutativity,
% 62.42/62.46 % removed.
% 62.42/62.46 %--------------------------------------------------------------------------
% 62.42/62.46 %----Include Henkin model axioms, for the equality formulation with
% 62.42/62.46 %----less_equals removed.
% 62.42/62.46 include('Axioms/HEN003-0.ax').
% 62.42/62.46 %--------------------------------------------------------------------------
% 62.42/62.46 cnf(x_divide_x_is_zero,axiom,
% 62.42/62.46 divide(X,X) = zero ).
% 62.42/62.46
% 62.42/62.46 cnf(x_divide_zero_is_x,axiom,
% 62.42/62.46 divide(X,zero) = X ).
% 62.42/62.46
% 62.42/62.46 cnf(transitivity_of_divide_to_zero,axiom,
% 62.42/62.46 ( divide(X,Y) != zero
% 62.42/62.46 | divide(Y,Z) != zero
% 62.42/62.46 | divide(X,Z) = zero ) ).
% 62.42/62.46
% 62.42/62.46 cnf(property_of_divide1,axiom,
% 62.42/62.46 ( divide(divide(X,Y),Z) != zero
% 62.42/62.46 | divide(divide(X,Z),Y) = zero ) ).
% 62.42/62.46
% 62.42/62.46 cnf(property_of_divide2,axiom,
% 62.42/62.46 ( divide(X,Y) != zero
% 62.42/62.46 | divide(divide(Z,Y),divide(Z,X)) = zero ) ).
% 62.42/62.46
% 62.42/62.46 cnf(property_of_divide3,axiom,
% 62.42/62.46 ( divide(X,Y) != zero
% 62.42/62.46 | divide(divide(X,Z),divide(Y,Z)) = zero ) ).
% 62.42/62.46
% 62.42/62.46 cnf(one_inversion_equals_three,axiom,
% 62.42/62.46 divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ).
% 62.42/62.46
% 62.42/62.46 cnf(property_of_inversion,axiom,
% 62.42/62.46 divide(divide(identity,X),divide(identity,divide(identity,X))) = divide(identity,X) ).
% 62.42/62.46
% 62.42/62.46 cnf(prove_this,negated_conjecture,
% 62.42/62.46 divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))) ).
% 62.42/62.46
% 62.42/62.46 %----This is an alternate way of writing the theorem
% 62.42/62.46 %input_clause(identity_divide_a,negated_conjecture,
% 62.42/62.46 % [++equal(divide(identity,a),c)]).
% 62.42/62.46 %
% 62.42/62.46 %input_clause(identity_divide_b,negated_conjecture,
% 62.42/62.46 % [++equal(divide(identity,b),d)]).
% 62.42/62.46 %
% 62.42/62.46 %input_clause(identity_divide_c,negated_conjecture,
% 62.42/62.46 % [++equal(divide(identity,c),e)]).
% 62.42/62.46 %
% 62.42/62.46 %input_clause(identity_divide_d,negated_conjecture,
% 62.42/62.46 % [++equal(divide(identity,d),g)]).
% 62.42/62.46 %
% 62.42/62.46 %input_clause(prove_commutativity,negated_conjecture,
% 62.42/62.46 % [--equal(divide(c,g),divide(d,e))]).
% 62.42/62.46 %--------------------------------------------------------------------------
% 62.42/62.46 %-------------------------------------------
% 62.42/62.46 % Proof found
% 62.42/62.46 % SZS status Theorem for theBenchmark
% 62.42/62.46 % SZS output start Proof
% 62.42/62.46 %ClaNum:19(EqnAxiom:5)
% 62.42/62.46 %VarNum:51(SingletonVarNum:25)
% 62.42/62.46 %MaxLitNum:3
% 62.42/62.46 %MaxfuncDepth:3
% 62.42/62.46 %SharedTerms:11
% 62.42/62.46 %goalClause: 14
% 62.42/62.46 %singleGoalClaCount:1
% 62.42/62.46 [14]~E(f2(f2(a1,a3),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(a1,f2(a1,a3))))
% 62.42/62.46 [6]E(f2(x61,a1),a5)
% 62.42/62.46 [7]E(f2(a5,x71),a5)
% 62.42/62.46 [8]E(f2(x81,a5),x81)
% 62.42/62.46 [9]E(f2(x91,x91),a5)
% 62.42/62.46 [11]E(f2(a1,f2(a1,f2(a1,x111))),f2(a1,x111))
% 62.42/62.46 [12]E(f2(f2(a1,x121),f2(a1,f2(a1,x121))),f2(a1,x121))
% 62.42/62.46 [10]E(f2(f2(x101,x102),x101),a5)
% 62.42/62.46 [13]E(f2(f2(f2(x131,x132),f2(x133,x132)),f2(f2(x131,x133),x132)),a5)
% 62.42/62.46 [17]~E(f2(x173,x172),a5)+E(f2(f2(x171,x172),f2(x171,x173)),a5)
% 62.42/62.46 [18]~E(f2(x181,x183),a5)+E(f2(f2(x181,x182),f2(x183,x182)),a5)
% 62.42/62.46 [19]~E(f2(f2(x191,x193),x192),a5)+E(f2(f2(x191,x192),x193),a5)
% 62.42/62.46 [15]E(x151,x152)+~E(f2(x152,x151),a5)+~E(f2(x151,x152),a5)
% 62.42/62.46 [16]~E(f2(x161,x163),a5)+E(f2(x161,x162),a5)+~E(f2(x163,x162),a5)
% 62.42/62.46 %EqnAxiom
% 62.42/62.46 [1]E(x11,x11)
% 62.42/62.46 [2]E(x22,x21)+~E(x21,x22)
% 62.42/62.46 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 62.42/62.46 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 62.42/62.46 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 62.42/62.46
% 62.42/62.46 %-------------------------------------------
% 62.42/62.47 cnf(20,plain,
% 62.42/62.47 (E(x201,f2(x201,a5))),
% 62.42/62.47 inference(scs_inference,[],[8,2])).
% 62.42/62.47 cnf(21,plain,
% 62.42/62.47 (E(f2(f2(x211,x211),a5),a5)),
% 62.42/62.47 inference(scs_inference,[],[8,9,2,3])).
% 62.42/62.47 cnf(22,plain,
% 62.42/62.47 (E(f2(x221,a5),x221)),
% 62.42/62.47 inference(rename_variables,[],[8])).
% 62.42/62.47 cnf(23,plain,
% 62.42/62.47 (E(a5,f2(a5,x231))),
% 62.42/62.47 inference(scs_inference,[],[8,9,7,10,2,3,15])).
% 62.42/62.47 cnf(27,plain,
% 62.42/62.47 (E(f2(x271,f2(x272,a5)),f2(x271,x272))),
% 62.42/62.47 inference(scs_inference,[],[8,22,9,7,10,2,3,15,5])).
% 62.42/62.47 cnf(28,plain,
% 62.42/62.47 (E(f2(f2(x281,a5),x282),f2(x281,x282))),
% 62.42/62.47 inference(scs_inference,[],[8,22,9,7,10,2,3,15,5,4])).
% 62.42/62.47 cnf(29,plain,
% 62.42/62.47 (E(f2(f2(x291,x292),f2(a1,x292)),a5)),
% 62.42/62.47 inference(scs_inference,[],[8,22,9,6,7,10,2,3,15,5,4,18])).
% 62.42/62.47 cnf(31,plain,
% 62.42/62.47 (E(f2(f2(x311,a1),f2(x311,x312)),a5)),
% 62.42/62.47 inference(scs_inference,[],[8,22,9,6,7,10,2,3,15,5,4,18,17])).
% 62.42/62.47 cnf(33,plain,
% 62.42/62.47 (E(f2(f2(x331,f2(x331,x332)),x332),a5)),
% 62.42/62.47 inference(scs_inference,[],[8,22,9,6,7,10,2,3,15,5,4,18,17,19])).
% 62.42/62.47 cnf(36,plain,
% 62.42/62.47 (E(f2(f2(f2(x361,x362),f2(x363,x362)),f2(x361,x363)),a5)),
% 62.42/62.47 inference(scs_inference,[],[13,10,16])).
% 62.42/62.47 cnf(43,plain,
% 62.42/62.47 (~E(f2(f2(a1,a4),f2(a1,f2(a1,a3))),f2(f2(a1,a3),f2(a1,f2(a1,a4))))),
% 62.42/62.47 inference(scs_inference,[],[14,13,10,31,16,15,2])).
% 62.42/62.47 cnf(47,plain,
% 62.42/62.47 (E(a5,f2(x471,a1))),
% 62.42/62.47 inference(scs_inference,[],[6,2])).
% 62.42/62.47 cnf(48,plain,
% 62.42/62.47 (E(f2(f2(x481,x481),x482),a5)),
% 62.42/62.47 inference(scs_inference,[],[7,21,16])).
% 62.42/62.47 cnf(50,plain,
% 62.42/62.47 (E(f2(f2(f2(x501,x502),f2(f2(x501,x503),x502)),f2(x503,x502)),a5)),
% 62.42/62.47 inference(scs_inference,[],[7,21,13,16,19])).
% 62.42/62.47 cnf(52,plain,
% 62.42/62.47 (E(f2(f2(a5,x521),f2(x522,x521)),a5)),
% 62.42/62.47 inference(scs_inference,[],[7,21,13,16,19,18])).
% 62.42/62.47 cnf(54,plain,
% 62.42/62.47 (E(f2(f2(x541,x542),f2(x541,a5)),a5)),
% 62.42/62.47 inference(scs_inference,[],[7,21,13,16,19,18,17])).
% 62.42/62.47 cnf(56,plain,
% 62.42/62.47 (E(f2(x561,f2(a5,x562)),f2(x561,a5))),
% 62.42/62.47 inference(scs_inference,[],[7,21,13,16,19,18,17,5])).
% 62.42/62.47 cnf(57,plain,
% 62.42/62.47 (E(f2(f2(a5,x571),x572),f2(a5,x572))),
% 62.42/62.47 inference(scs_inference,[],[7,21,13,16,19,18,17,5,4])).
% 62.42/62.47 cnf(59,plain,
% 62.42/62.47 (E(f2(a5,x591),f2(a5,a5))),
% 62.42/62.47 inference(scs_inference,[],[7,20,3])).
% 62.42/62.47 cnf(61,plain,
% 62.42/62.47 (E(f2(f2(x611,f2(x611,x612)),f2(x612,f2(x611,x612))),f2(f2(x611,x612),f2(x611,x612)))),
% 62.42/62.47 inference(scs_inference,[],[7,20,13,48,3,15])).
% 62.42/62.47 cnf(65,plain,
% 62.42/62.47 (E(f2(x651,x652),f2(x651,f2(x652,a5)))),
% 62.42/62.47 inference(scs_inference,[],[8,2,5])).
% 62.42/62.47 cnf(66,plain,
% 62.42/62.47 (E(f2(f2(x661,x662),f2(x661,x662)),f2(f2(x661,f2(x661,x662)),f2(x662,f2(x661,x662))))),
% 62.42/62.47 inference(scs_inference,[],[13,48,15])).
% 62.42/62.47 cnf(70,plain,
% 62.42/62.47 (E(f2(a1,x701),f2(f2(a1,x701),f2(a1,f2(a1,x701))))),
% 62.42/62.47 inference(scs_inference,[],[12,13,48,15,2])).
% 62.42/62.47 cnf(71,plain,
% 62.42/62.47 (E(f2(f2(x711,f2(x712,a5)),a5),f2(x711,x712))),
% 62.42/62.47 inference(scs_inference,[],[8,27,12,13,48,15,2,3])).
% 62.42/62.47 cnf(74,plain,
% 62.42/62.47 (E(f2(a5,x741),f2(f2(x742,x742),x741))),
% 62.42/62.47 inference(scs_inference,[],[9,2,4])).
% 62.42/62.47 cnf(75,plain,
% 62.42/62.47 (E(f2(f2(x751,x752),f2(x751,f2(x752,x753))),a5)),
% 62.42/62.47 inference(scs_inference,[],[10,17])).
% 62.42/62.47 cnf(79,plain,
% 62.42/62.47 (~E(f2(f2(f2(a1,a3),a5),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(a1,f2(a1,a3))))),
% 62.42/62.47 inference(scs_inference,[],[28,10,43,17,3,2])).
% 62.42/62.47 cnf(80,plain,
% 62.42/62.47 (E(f2(f2(f2(x801,x802),x803),f2(x801,x803)),a5)),
% 62.42/62.47 inference(scs_inference,[],[28,10,43,17,3,2,18])).
% 62.42/62.47 cnf(82,plain,
% 62.42/62.47 (E(f2(f2(f2(x821,x822),f2(x821,x823)),f2(x823,x822)),a5)),
% 62.42/62.47 inference(scs_inference,[],[28,10,43,36,17,3,2,18,19])).
% 62.42/62.47 cnf(84,plain,
% 62.42/62.47 (E(f2(f2(x841,x841),x842),f2(a5,x842))),
% 62.42/62.47 inference(scs_inference,[],[9,28,10,43,36,17,3,2,18,19,4])).
% 62.42/62.47 cnf(85,plain,
% 62.42/62.47 (E(f2(x851,f2(x852,x852)),f2(x851,a5))),
% 62.42/62.47 inference(scs_inference,[],[9,28,10,43,36,17,3,2,18,19,4,5])).
% 62.42/62.47 cnf(87,plain,
% 62.42/62.47 (E(a5,f2(x871,x871))),
% 62.42/62.47 inference(scs_inference,[],[9,2])).
% 62.42/62.47 cnf(88,plain,
% 62.42/62.47 (E(f2(x881,x881),f2(a5,x882))),
% 62.42/62.47 inference(scs_inference,[],[9,23,2,3])).
% 62.42/62.47 cnf(89,plain,
% 62.42/62.47 (E(f2(x891,a5),f2(x891,f2(f2(x892,x893),x892)))),
% 62.42/62.47 inference(scs_inference,[],[10,2,5])).
% 62.42/62.47 cnf(90,plain,
% 62.42/62.47 (E(f2(f2(x901,x902),x901),f2(a5,a5))),
% 62.42/62.47 inference(scs_inference,[],[10,20,3])).
% 62.42/62.47 cnf(92,plain,
% 62.42/62.47 (E(f2(f2(f2(f2(x921,x922),f2(x923,x922)),x924),f2(f2(x921,x923),x922)),a5)),
% 62.42/62.47 inference(scs_inference,[],[10,20,13,3,16])).
% 62.42/62.47 cnf(95,plain,
% 62.42/62.47 (E(f2(f2(x951,x952),x952),f2(f2(x951,x952),f2(x952,x952)))),
% 62.42/62.47 inference(scs_inference,[],[10,20,13,75,3,16,15])).
% 62.42/62.47 cnf(100,plain,
% 62.42/62.47 (E(f2(f2(f2(x1001,x1002),x1003),f2(a1,x1002)),a5)),
% 62.42/62.47 inference(scs_inference,[],[10,29,16])).
% 62.42/62.47 cnf(107,plain,
% 62.42/62.47 (E(f2(f2(a1,x1071),x1072),f2(f2(a1,f2(a1,f2(a1,x1071))),x1072))),
% 62.42/62.47 inference(scs_inference,[],[11,2,4])).
% 62.42/62.47 cnf(108,plain,
% 62.42/62.47 (E(f2(f2(f2(x1081,x1082),x1083),f2(f2(a1,x1082),x1083)),a5)),
% 62.42/62.47 inference(scs_inference,[],[29,18])).
% 62.42/62.47 cnf(110,plain,
% 62.42/62.47 (E(f2(f2(x1101,f2(a1,x1102)),x1102),a5)),
% 62.42/62.47 inference(scs_inference,[],[29,18,19])).
% 62.42/62.47 cnf(112,plain,
% 62.42/62.47 (E(f2(f2(x1121,f2(a1,x1122)),f2(x1121,f2(x1123,x1122))),a5)),
% 62.42/62.47 inference(scs_inference,[],[29,18,19,17])).
% 62.42/62.47 cnf(115,plain,
% 62.42/62.47 (E(f2(x1151,f2(a1,f2(a1,f2(a1,x1152)))),f2(x1151,f2(a1,x1152)))),
% 62.42/62.47 inference(scs_inference,[],[11,29,18,19,17,2,5])).
% 62.42/62.47 cnf(116,plain,
% 62.42/62.47 (E(f2(f2(a1,f2(a1,f2(a1,x1161))),x1162),f2(f2(a1,x1161),x1162))),
% 62.42/62.47 inference(scs_inference,[],[11,29,18,19,17,2,5,4])).
% 62.42/62.47 cnf(120,plain,
% 62.42/62.47 (E(f2(x1201,f2(a1,x1202)),f2(x1201,f2(f2(a1,x1202),f2(a1,f2(a1,x1202)))))),
% 62.42/62.47 inference(scs_inference,[],[12,2,5])).
% 62.42/62.47 cnf(124,plain,
% 62.42/62.47 (E(a5,f2(f2(f2(x1241,f2(x1241,x1242)),x1243),f2(x1242,x1243)))),
% 62.42/62.47 inference(scs_inference,[],[33,2,18])).
% 62.42/62.47 cnf(127,plain,
% 62.42/62.47 (E(f2(f2(x1271,a1),x1272),a5)),
% 62.42/62.47 inference(scs_inference,[],[28,33,31,14,3,16])).
% 62.42/62.47 cnf(136,plain,
% 62.42/62.47 (E(f2(a5,x1361),f2(f2(f2(f2(x1362,x1363),f2(x1364,x1363)),f2(f2(x1362,x1364),x1363)),x1361))),
% 62.42/62.47 inference(scs_inference,[],[13,2,4])).
% 62.42/62.47 cnf(137,plain,
% 62.42/62.47 (E(f2(f2(f2(f2(x1371,x1372),f2(x1373,x1372)),x1374),f2(f2(x1371,x1373),x1374)),a5)),
% 62.42/62.47 inference(scs_inference,[],[36,18])).
% 62.42/62.47 cnf(139,plain,
% 62.42/62.47 (E(f2(f2(x1391,f2(x1392,x1393)),f2(x1391,f2(f2(x1392,x1394),f2(x1393,x1394)))),a5)),
% 62.42/62.47 inference(scs_inference,[],[36,18,17])).
% 62.42/62.47 cnf(141,plain,
% 62.42/62.47 (E(f2(f2(f2(x1411,f2(x1412,x1413)),f2(x1413,f2(x1412,x1413))),f2(x1411,x1412)),a5)),
% 62.42/62.47 inference(scs_inference,[],[13,36,18,17,16])).
% 62.42/62.47 cnf(142,plain,
% 62.42/62.47 (E(f2(f2(f2(x1421,x1422),f2(x1423,x1422)),f2(f2(x1421,x1423),x1422)),a5)),
% 62.42/62.47 inference(rename_variables,[],[13])).
% 62.42/62.47 cnf(144,plain,
% 62.42/62.47 (E(f2(f2(x1441,x1442),a1),f2(f2(x1441,a1),f2(x1442,a1)))),
% 62.42/62.47 inference(scs_inference,[],[13,142,36,127,18,17,16,15])).
% 62.42/62.47 cnf(145,plain,
% 62.42/62.47 (E(f2(f2(f2(x1451,x1452),f2(x1453,x1452)),f2(f2(x1451,x1453),x1452)),a5)),
% 62.42/62.47 inference(rename_variables,[],[13])).
% 62.42/62.47 cnf(148,plain,
% 62.42/62.47 (E(a5,f2(f2(f2(x1481,x1482),f2(x1483,x1482)),f2(f2(x1481,x1483),x1482)))),
% 62.42/62.47 inference(scs_inference,[],[13,142,145,36,127,18,17,16,15,2])).
% 62.42/62.47 cnf(149,plain,
% 62.42/62.47 (E(f2(f2(f2(f2(x1491,x1492),f2(x1493,x1492)),a5),f2(x1491,x1493)),a5)),
% 62.42/62.47 inference(scs_inference,[],[13,142,145,36,28,127,18,17,16,15,2,3])).
% 62.42/62.47 cnf(155,plain,
% 62.42/62.47 (E(a5,f2(f2(f2(x1551,x1552),f2(f2(x1551,x1553),x1552)),f2(x1553,x1552)))),
% 62.42/62.47 inference(scs_inference,[],[13,2,19])).
% 62.42/62.48 cnf(159,plain,
% 62.42/62.48 (E(a5,f2(f2(x1591,x1592),f2(x1591,f2(x1593,f2(x1593,x1592)))))),
% 62.42/62.48 inference(scs_inference,[],[33,2,17])).
% 62.42/62.48 cnf(160,plain,
% 62.42/62.48 (E(f2(x1601,f2(x1601,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[23,33,2,15])).
% 62.42/62.48 cnf(161,plain,
% 62.42/62.48 (E(f2(f2(x1611,x1612),f2(x1611,f2(x1613,f2(x1613,x1612)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[33,17])).
% 62.42/62.48 cnf(163,plain,
% 62.42/62.48 (E(f2(f2(f2(x1631,f2(x1632,x1633)),f2(x1631,x1632)),f2(x1633,f2(x1632,x1633))),a5)),
% 62.42/62.48 inference(scs_inference,[],[33,141,17,19])).
% 62.42/62.48 cnf(165,plain,
% 62.42/62.48 (E(f2(f2(f2(x1651,f2(x1651,x1652)),x1653),f2(x1652,x1653)),a5)),
% 62.42/62.48 inference(scs_inference,[],[33,141,17,19,18])).
% 62.42/62.48 cnf(167,plain,
% 62.42/62.48 (E(f2(f2(x1671,f2(x1671,f2(f2(x1672,x1673),f2(x1674,x1673)))),f2(x1672,x1674)),a5)),
% 62.42/62.48 inference(scs_inference,[],[33,36,141,17,19,18,16])).
% 62.42/62.48 cnf(168,plain,
% 62.42/62.48 (E(f2(f2(x1681,f2(x1681,x1682)),x1682),a5)),
% 62.42/62.48 inference(rename_variables,[],[33])).
% 62.42/62.48 cnf(170,plain,
% 62.42/62.48 (E(f2(x1701,a5),f2(x1701,f2(a5,x1702)))),
% 62.42/62.48 inference(scs_inference,[],[23,33,36,141,17,19,18,16,5])).
% 62.42/62.48 cnf(171,plain,
% 62.42/62.48 (E(f2(a5,x1711),f2(f2(x1712,a1),x1711))),
% 62.42/62.48 inference(scs_inference,[],[23,47,33,36,141,17,19,18,16,5,4])).
% 62.42/62.48 cnf(172,plain,
% 62.42/62.48 (E(f2(x1721,a1),f2(x1722,f2(x1722,f2(x1721,a1))))),
% 62.42/62.48 inference(scs_inference,[],[23,47,33,168,36,141,127,17,19,18,16,5,4,15])).
% 62.42/62.48 cnf(176,plain,
% 62.42/62.48 (E(a5,f2(f2(f2(x1761,x1762),x1763),f2(f2(a1,x1762),x1763)))),
% 62.42/62.48 inference(scs_inference,[],[29,2,18])).
% 62.42/62.48 cnf(177,plain,
% 62.42/62.48 (E(f2(f2(f2(x1771,x1772),f2(x1773,x1772)),f2(a1,x1773)),a5)),
% 62.42/62.48 inference(scs_inference,[],[29,36,16])).
% 62.42/62.48 cnf(180,plain,
% 62.42/62.48 (E(f2(x1801,f2(x1801,f2(x1801,x1802))),f2(x1801,x1802))),
% 62.42/62.48 inference(scs_inference,[],[29,36,33,161,16,15])).
% 62.42/62.48 cnf(186,plain,
% 62.42/62.48 (E(f2(x1861,f2(x1862,x1863)),f2(x1861,f2(f2(x1862,a5),x1863)))),
% 62.42/62.48 inference(scs_inference,[],[28,2,5])).
% 62.42/62.48 cnf(188,plain,
% 62.42/62.48 (E(f2(f2(x1881,a5),x1882),f2(x1881,x1882))),
% 62.42/62.48 inference(rename_variables,[],[28])).
% 62.42/62.48 cnf(189,plain,
% 62.42/62.48 (E(f2(x1891,x1892),f2(f2(x1891,a5),x1892))),
% 62.42/62.48 inference(scs_inference,[],[28,188,50,3,2])).
% 62.42/62.48 cnf(191,plain,
% 62.42/62.48 (~E(f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))),f2(f2(a1,a3),f2(a1,f2(a1,a4))))),
% 62.42/62.48 inference(scs_inference,[],[43,186,3])).
% 62.42/62.48 cnf(193,plain,
% 62.42/62.48 (~E(f2(f2(a1,a3),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))))),
% 62.42/62.48 inference(scs_inference,[],[43,186,3,2])).
% 62.42/62.48 cnf(194,plain,
% 62.42/62.48 (E(f2(a5,x1941),f2(f2(f2(x1942,x1943),f2(a1,x1943)),x1941))),
% 62.42/62.48 inference(scs_inference,[],[29,2,4])).
% 62.42/62.48 cnf(197,plain,
% 62.42/62.48 (E(f2(f2(x1971,f2(x1972,x1973)),f2(x1971,f2(a5,x1973))),a5)),
% 62.42/62.48 inference(scs_inference,[],[52,18,17])).
% 62.42/62.48 cnf(201,plain,
% 62.42/62.48 (E(f2(f2(a5,f2(x2011,x2012)),x2012),a5)),
% 62.42/62.48 inference(scs_inference,[],[29,52,47,18,17,2,3,19])).
% 62.42/62.48 cnf(206,plain,
% 62.42/62.48 (E(f2(f2(x2061,x2062),f2(f2(x2061,x2062),x2062)),f2(x2062,x2062))),
% 62.42/62.48 inference(scs_inference,[],[50,48,15])).
% 62.42/62.48 cnf(210,plain,
% 62.42/62.48 (E(f2(f2(a1,f2(a1,x2101)),f2(x2101,f2(a1,x2101))),a5)),
% 62.42/62.48 inference(scs_inference,[],[29,50,48,61,15,3])).
% 62.42/62.48 cnf(217,plain,
% 62.42/62.48 (E(f2(f2(x2171,f2(x2171,f2(x2172,x2173))),f2(x2172,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[33,54,16])).
% 62.42/62.48 cnf(218,plain,
% 62.42/62.48 (E(f2(f2(x2181,f2(x2181,x2182)),x2182),a5)),
% 62.42/62.48 inference(rename_variables,[],[33])).
% 62.42/62.48 cnf(220,plain,
% 62.42/62.48 (E(f2(x2201,x2201),f2(x2202,f2(x2202,f2(x2201,x2201))))),
% 62.42/62.48 inference(scs_inference,[],[33,218,54,48,16,15])).
% 62.42/62.48 cnf(226,plain,
% 62.42/62.48 (E(f2(f2(x2261,f2(x2261,a5)),x2262),a5)),
% 62.42/62.48 inference(scs_inference,[],[54,19])).
% 62.42/62.48 cnf(230,plain,
% 62.42/62.48 (E(f2(f2(f2(x2301,x2302),x2303),f2(f2(x2301,a5),x2303)),a5)),
% 62.42/62.48 inference(scs_inference,[],[36,54,19,4,2,18])).
% 62.42/62.48 cnf(237,plain,
% 62.42/62.48 (E(f2(f2(x2371,a5),x2372),f2(f2(x2371,f2(a5,x2373)),x2372))),
% 62.42/62.48 inference(scs_inference,[],[56,2,4])).
% 62.42/62.48 cnf(249,plain,
% 62.42/62.48 (E(f2(f2(f2(x2491,x2492),f2(f2(x2491,a5),x2492)),f2(x2493,x2492)),a5)),
% 62.42/62.48 inference(scs_inference,[],[52,50,16])).
% 62.42/62.48 cnf(253,plain,
% 62.42/62.48 (E(f2(f2(x2531,x2531),x2532),a5)),
% 62.42/62.48 inference(rename_variables,[],[48])).
% 62.42/62.48 cnf(256,plain,
% 62.42/62.48 (E(f2(f2(f2(x2561,x2561),x2562),f2(x2563,x2562)),a5)),
% 62.42/62.48 inference(scs_inference,[],[52,50,48,253,16,15,18])).
% 62.42/62.48 cnf(259,plain,
% 62.42/62.48 (E(f2(f2(x2591,x2592),f2(x2591,f2(x2593,x2593))),a5)),
% 62.42/62.48 inference(scs_inference,[],[48,17])).
% 62.42/62.48 cnf(272,plain,
% 62.42/62.48 (E(f2(f2(f2(x2721,x2722),f2(x2721,x2723)),f2(x2723,x2722)),a5)),
% 62.42/62.48 inference(rename_variables,[],[82])).
% 62.42/62.48 cnf(275,plain,
% 62.42/62.48 (E(f2(f2(f2(x2751,x2752),f2(f2(x2751,x2753),x2752)),f2(x2753,x2752)),f2(x2754,a1))),
% 62.42/62.48 inference(scs_inference,[],[47,50,52,82,15,3])).
% 62.42/62.48 cnf(276,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x2761,x2762),f2(x2761,x2763)),x2764),f2(f2(x2763,x2762),x2764)),a5)),
% 62.42/62.48 inference(scs_inference,[],[47,50,52,82,272,15,3,18])).
% 62.42/62.48 cnf(278,plain,
% 62.42/62.48 (E(f2(f2(f2(x2781,x2782),f2(f2(x2781,x2782),x2782)),x2783),a5)),
% 62.42/62.48 inference(scs_inference,[],[47,50,52,48,82,272,15,3,18,16])).
% 62.42/62.48 cnf(282,plain,
% 62.42/62.48 (E(f2(f2(x2821,f2(f2(x2822,x2823),x2824)),f2(x2821,f2(f2(x2822,x2824),f2(x2823,x2824)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[148,2,17])).
% 62.42/62.48 cnf(283,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x2831,x2832),f2(x2833,x2832)),f2(f2(x2831,x2833),x2834)),x2834),a5)),
% 62.42/62.48 inference(scs_inference,[],[137,19])).
% 62.42/62.48 cnf(285,plain,
% 62.42/62.48 (E(f2(f2(f2(x2851,f2(x2852,x2853)),f2(x2851,x2852)),f2(x2853,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[54,163,137,19,16])).
% 62.42/62.48 cnf(289,plain,
% 62.42/62.48 (E(f2(f2(x2891,x2892),f2(x2891,x2892)),f2(f2(f2(x2891,x2893),f2(x2892,x2893)),f2(x2891,x2892)))),
% 62.42/62.48 inference(scs_inference,[],[48,54,163,137,19,16,15])).
% 62.42/62.48 cnf(293,plain,
% 62.42/62.48 (E(a5,f2(f2(a5,x2931),f2(x2932,x2931)))),
% 62.42/62.48 inference(scs_inference,[],[48,54,52,163,137,19,16,15,2])).
% 62.42/62.48 cnf(294,plain,
% 62.42/62.48 (E(f2(f2(x2941,f2(x2942,x2943)),f2(x2941,f2(f2(x2942,x2944),x2943))),a5)),
% 62.42/62.48 inference(scs_inference,[],[48,54,52,163,137,80,19,16,15,2,17])).
% 62.42/62.48 cnf(301,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x3011,x3012),f2(f2(x3011,x3012),x3012)),x3013),f2(x3014,x3013)),a5)),
% 62.42/62.48 inference(scs_inference,[],[278,18])).
% 62.42/62.48 cnf(304,plain,
% 62.42/62.48 (E(f2(f2(f2(x3041,f2(x3041,x3042)),f2(x3042,x3043)),x3043),a5)),
% 62.42/62.48 inference(scs_inference,[],[124,2,19])).
% 62.42/62.48 cnf(307,plain,
% 62.42/62.48 (E(f2(f2(a5,x3071),f2(x3072,x3071)),a5)),
% 62.42/62.48 inference(rename_variables,[],[52])).
% 62.42/62.48 cnf(312,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x3121,x3122),f2(x3121,x3123)),f2(f2(x3123,x3122),x3124)),x3124),a5)),
% 62.42/62.48 inference(scs_inference,[],[52,66,65,165,276,15,3,19])).
% 62.42/62.48 cnf(316,plain,
% 62.42/62.48 (E(f2(f2(a5,x3161),f2(x3162,x3161)),a5)),
% 62.42/62.48 inference(rename_variables,[],[52])).
% 62.42/62.48 cnf(320,plain,
% 62.42/62.48 (E(f2(f2(x3201,x3202),f2(x3201,f2(f2(x3203,f2(x3203,x3204)),f2(x3204,x3202)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[52,307,316,66,65,289,139,165,276,304,15,3,19,16,4,2,17])).
% 62.42/62.48 cnf(323,plain,
% 62.42/62.48 (E(f2(f2(x3231,f2(x3231,f2(f2(x3232,x3233),f2(x3234,x3233)))),f2(x3232,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[54,167,16])).
% 62.42/62.48 cnf(327,plain,
% 62.42/62.48 (E(f2(x3271,f2(f2(x3272,f2(x3272,x3273)),f2(x3273,a5))),f2(x3271,a5))),
% 62.42/62.48 inference(scs_inference,[],[54,167,320,16,5,15])).
% 62.42/62.48 cnf(333,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x3331,x3331),x3332),x3333),f2(f2(x3334,x3332),x3333)),a5)),
% 62.42/62.48 inference(scs_inference,[],[256,18])).
% 62.42/62.48 cnf(338,plain,
% 62.42/62.48 (E(f2(f2(x3381,f2(x3382,f2(x3383,x3383))),f2(x3381,f2(x3382,x3384))),a5)),
% 62.42/62.48 inference(scs_inference,[],[301,259,19,17])).
% 62.42/62.48 cnf(340,plain,
% 62.42/62.48 (E(f2(f2(x3401,f2(a5,x3402)),x3403),f2(f2(x3401,a5),x3403))),
% 62.42/62.48 inference(scs_inference,[],[56,301,259,19,17,4])).
% 62.42/62.48 cnf(351,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x3511,x3512),f2(x3513,x3512)),f2(f2(x3511,x3513),x3514)),f2(x3514,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[57,74,283,294,197,160,15,3,16])).
% 62.42/62.48 cnf(365,plain,
% 62.42/62.48 (E(f2(f2(f2(x3651,x3652),x3653),f2(f2(x3651,f2(x3652,x3654)),x3653)),a5)),
% 62.42/62.48 inference(scs_inference,[],[75,18])).
% 62.42/62.48 cnf(368,plain,
% 62.42/62.48 (E(f2(f2(x3681,f2(x3681,f2(x3682,x3683))),x3682),a5)),
% 62.42/62.48 inference(scs_inference,[],[75,19])).
% 62.42/62.48 cnf(370,plain,
% 62.42/62.48 (E(f2(f2(x3701,f2(x3702,f2(x3703,x3704))),f2(x3701,f2(x3702,x3703))),a5)),
% 62.42/62.48 inference(scs_inference,[],[75,19,17])).
% 62.42/62.48 cnf(375,plain,
% 62.42/62.48 (E(f2(f2(a1,x3751),x3752),f2(f2(f2(a1,x3751),f2(a1,f2(a1,x3751))),x3752))),
% 62.42/62.48 inference(scs_inference,[],[59,70,5,4])).
% 62.42/62.48 cnf(407,plain,
% 62.42/62.48 (E(f2(f2(x4071,x4072),x4073),f2(f2(x4071,f2(x4072,a5)),x4073))),
% 62.42/62.48 inference(scs_inference,[],[65,5,4])).
% 62.42/62.48 cnf(408,plain,
% 62.42/62.48 (E(f2(x4081,f2(x4082,f2(x4083,a5))),f2(x4081,f2(x4082,x4083)))),
% 62.42/62.48 inference(scs_inference,[],[65,2,5])).
% 62.42/62.48 cnf(413,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x4131,x4132),x4133),x4134),f2(f2(x4131,x4133),x4134)),a5)),
% 62.42/62.48 inference(scs_inference,[],[80,18])).
% 62.42/62.48 cnf(415,plain,
% 62.42/62.48 (E(f2(f2(x4151,x4151),f2(x4151,f2(x4151,x4151))),f2(f2(x4151,x4151),x4151))),
% 62.42/62.48 inference(scs_inference,[],[82,80,75,18,15])).
% 62.42/62.48 cnf(416,plain,
% 62.42/62.48 (E(f2(f2(f2(x4161,x4162),f2(x4161,x4163)),f2(x4163,x4162)),a5)),
% 62.42/62.48 inference(rename_variables,[],[82])).
% 62.42/62.48 cnf(422,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x4221,x4222),x4223),f2(x4221,x4224)),f2(x4224,x4222)),a5)),
% 62.42/62.48 inference(scs_inference,[],[71,70,82,416,80,75,18,15,3,16])).
% 62.42/62.48 cnf(426,plain,
% 62.42/62.48 (E(f2(f2(x4261,f2(x4262,x4263)),f2(x4261,f2(f2(x4264,x4263),f2(x4264,x4262)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,17])).
% 62.42/62.48 cnf(428,plain,
% 62.42/62.48 (E(f2(f2(f2(x4281,x4282),f2(x4281,f2(x4283,x4284))),f2(x4283,x4282)),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,80,17,16])).
% 62.42/62.48 cnf(431,plain,
% 62.42/62.48 (E(f2(f2(f2(x4311,x4312),f2(x4311,x4313)),x4313),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,80,17,16,19])).
% 62.42/62.48 cnf(442,plain,
% 62.42/62.48 (E(f2(f2(x4421,x4422),x4423),f2(f2(f2(x4421,f2(x4422,a5)),a5),x4423))),
% 62.42/62.48 inference(scs_inference,[],[71,2,4])).
% 62.42/62.48 cnf(443,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x4431,x4432),x4433),f2(x4431,x4434)),x4435),f2(f2(x4434,x4432),x4435)),a5)),
% 62.42/62.48 inference(scs_inference,[],[422,18])).
% 62.42/62.48 cnf(455,plain,
% 62.42/62.48 (E(f2(f2(x4551,x4552),f2(x4551,f2(f2(x4553,x4554),f2(x4553,x4552)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[71,84,75,428,431,15,3,17])).
% 62.42/62.48 cnf(457,plain,
% 62.42/62.48 (E(f2(f2(x4571,f2(x4571,f2(f2(x4572,x4573),f2(x4572,x4574)))),f2(x4574,x4573)),a5)),
% 62.42/62.48 inference(scs_inference,[],[71,84,75,426,428,431,15,3,17,19])).
% 62.42/62.48 cnf(464,plain,
% 62.42/62.48 (E(f2(f2(f2(x4641,x4642),x4641),f2(x4643,x4642)),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,75,16])).
% 62.42/62.48 cnf(473,plain,
% 62.42/62.48 (E(f2(x4731,f2(a5,x4732)),f2(x4731,f2(f2(x4733,x4733),x4732)))),
% 62.42/62.48 inference(scs_inference,[],[74,5])).
% 62.42/62.48 cnf(475,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x4751,x4752),x4751),x4753),f2(f2(x4754,x4752),x4753)),a5)),
% 62.42/62.48 inference(scs_inference,[],[464,18])).
% 62.42/62.48 cnf(477,plain,
% 62.42/62.48 (E(f2(x4771,a5),f2(x4771,f2(f2(x4772,x4773),f2(x4772,f2(x4773,x4774)))))),
% 62.42/62.48 inference(scs_inference,[],[75,2,5])).
% 62.42/62.48 cnf(478,plain,
% 62.42/62.48 (E(f2(f2(x4781,f2(a1,x4782)),f2(x4781,f2(f2(x4783,x4784),f2(x4782,x4784)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[177,17])).
% 62.42/62.48 cnf(480,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x4801,x4801),x4802),f2(f2(x4803,x4802),x4804)),x4804),a5)),
% 62.42/62.48 inference(scs_inference,[],[333,177,17,19])).
% 62.42/62.48 cnf(482,plain,
% 62.42/62.48 (E(f2(a5,x4821),f2(x4822,x4822))),
% 62.42/62.48 inference(scs_inference,[],[88,333,177,17,19,2])).
% 62.42/62.48 cnf(483,plain,
% 62.42/62.48 (E(f2(f2(x4831,x4832),f2(x4831,f2(x4832,x4833))),f2(x4834,x4834))),
% 62.42/62.48 inference(scs_inference,[],[75,88,87,333,177,17,19,2,3])).
% 62.42/62.48 cnf(484,plain,
% 62.42/62.48 (E(f2(f2(a5,a5),x4841),f2(f2(f2(x4842,x4843),x4842),x4841))),
% 62.42/62.48 inference(scs_inference,[],[90,2,4])).
% 62.42/62.48 cnf(485,plain,
% 62.42/62.48 (E(f2(f2(f2(x4851,x4852),f2(x4853,x4852)),f2(f2(x4851,x4853),a5)),f2(a5,a5))),
% 62.42/62.48 inference(scs_inference,[],[351,48,15])).
% 62.42/62.48 cnf(490,plain,
% 62.42/62.48 (E(f2(x4901,a5),f2(x4901,f2(f2(x4902,x4903),x4902)))),
% 62.42/62.48 inference(rename_variables,[],[89])).
% 62.42/62.48 cnf(491,plain,
% 62.42/62.48 (E(f2(f2(f2(x4911,f2(x4912,f2(x4913,x4914))),f2(x4911,x4915)),f2(x4915,f2(x4912,x4913))),a5)),
% 62.42/62.48 inference(scs_inference,[],[89,90,82,370,351,48,15,3,16])).
% 62.42/62.48 cnf(495,plain,
% 62.42/62.48 (E(f2(f2(x4951,a5),x4952),f2(f2(x4951,f2(f2(x4953,x4954),x4953)),x4952))),
% 62.42/62.48 inference(scs_inference,[],[89,490,90,82,370,351,48,15,3,16,4])).
% 62.42/62.48 cnf(496,plain,
% 62.42/62.48 (E(f2(x4961,f2(x4962,f2(f2(x4963,x4964),x4963))),f2(x4961,f2(x4962,a5)))),
% 62.42/62.48 inference(scs_inference,[],[89,2,5])).
% 62.42/62.48 cnf(497,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x4971,x4972),x4973),f2(x4971,x4974)),x4975),f2(x4974,x4975)),a5)),
% 62.42/62.48 inference(scs_inference,[],[80,443,16])).
% 62.42/62.48 cnf(500,plain,
% 62.42/62.48 (E(f2(a5,a5),f2(x5001,f2(x5001,f2(f2(a5,x5002),f2(x5003,x5002)))))),
% 62.42/62.48 inference(scs_inference,[],[80,443,323,48,16,15])).
% 62.42/62.48 cnf(516,plain,
% 62.42/62.48 (E(f2(f2(f2(x5161,x5162),f2(x5161,x5163)),f2(x5163,x5162)),f2(x5164,x5164))),
% 62.42/62.48 inference(scs_inference,[],[82,87,4,3])).
% 62.42/62.48 cnf(520,plain,
% 62.42/62.48 (E(f2(f2(f2(x5201,x5202),f2(x5201,x5203)),f2(x5203,x5202)),a5)),
% 62.42/62.48 inference(rename_variables,[],[82])).
% 62.42/62.48 cnf(522,plain,
% 62.42/62.48 (E(f2(f2(f2(x5221,x5222),f2(x5221,f2(x5222,x5223))),a5),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,520,89,161,15,3])).
% 62.42/62.48 cnf(523,plain,
% 62.42/62.48 (E(f2(f2(f2(x5231,x5232),f2(x5231,x5233)),f2(x5233,x5232)),a5)),
% 62.42/62.48 inference(rename_variables,[],[82])).
% 62.42/62.48 cnf(525,plain,
% 62.42/62.48 (E(f2(f2(f2(x5251,x5252),f2(x5251,x5253)),f2(x5253,f2(f2(x5254,x5255),f2(x5254,x5252)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[82,520,523,89,455,161,15,3,16])).
% 62.42/62.48 cnf(529,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x5291,x5292),x5293),f2(x5294,x5292)),x5295),f2(f2(x5291,x5294),x5292)),a5)),
% 62.42/62.48 inference(scs_inference,[],[92,413,16])).
% 62.42/62.48 cnf(547,plain,
% 62.42/62.48 (E(f2(f2(x5471,a5),x5472),f2(f2(x5471,f2(x5473,x5473)),x5472))),
% 62.42/62.48 inference(scs_inference,[],[85,2,4])).
% 62.42/62.48 cnf(555,plain,
% 62.42/62.48 (E(f2(f2(f2(x5551,x5552),x5553),f2(a1,x5552)),a5)),
% 62.42/62.48 inference(rename_variables,[],[100])).
% 62.42/62.48 cnf(559,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x5591,x5592),f2(x5593,x5592)),x5594),f2(a1,x5593)),a5)),
% 62.42/62.48 inference(scs_inference,[],[87,100,555,92,226,18,15,3,16])).
% 62.42/62.48 cnf(565,plain,
% 62.42/62.48 (E(f2(f2(f2(x5651,x5652),f2(a1,x5652)),x5653),a5)),
% 62.42/62.48 inference(scs_inference,[],[100,464,17,19])).
% 62.42/62.48 cnf(617,plain,
% 62.42/62.48 (E(f2(f2(x6171,f2(x6172,a5)),f2(x6171,x6172)),a5)),
% 62.42/62.48 inference(scs_inference,[],[160,17])).
% 62.42/62.48 cnf(635,plain,
% 62.42/62.48 (E(f2(f2(x6351,x6352),x6352),f2(f2(x6351,x6352),f2(x6352,x6352)))),
% 62.42/62.48 inference(rename_variables,[],[95])).
% 62.42/62.48 cnf(636,plain,
% 62.42/62.48 (E(f2(f2(f2(x6361,x6362),x6362),x6363),f2(f2(f2(x6361,x6362),f2(x6362,x6362)),x6363))),
% 62.42/62.48 inference(scs_inference,[],[95,635,107,112,100,16,3,4])).
% 62.42/62.48 cnf(652,plain,
% 62.42/62.48 (E(f2(f2(x6521,f2(x6522,x6523)),f2(x6521,f2(x6522,f2(x6523,a5)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[338,617,19,17])).
% 62.42/62.48 cnf(667,plain,
% 62.42/62.48 (E(f2(f2(f2(x6671,x6672),x6673),f2(a1,f2(a1,f2(a1,x6672)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[100,115,110,16,3])).
% 62.42/62.48 cnf(707,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x7071,f2(x7071,x7072)),f2(x7072,x7073)),x7074),f2(x7073,x7074)),a5)),
% 62.42/62.48 inference(scs_inference,[],[108,116,415,529,304,667,210,16,3,15,18])).
% 62.42/62.48 cnf(710,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x7101,f2(x7101,x7102)),f2(x7102,x7103)),f2(x7103,x7104)),x7104),a5)),
% 62.42/62.48 inference(scs_inference,[],[707,19])).
% 62.42/62.48 cnf(728,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x7281,f2(x7281,x7282)),f2(x7282,x7283)),f2(x7283,x7284)),x7285),f2(x7284,x7285)),a5)),
% 62.42/62.48 inference(scs_inference,[],[710,559,226,15,18])).
% 62.42/62.48 cnf(736,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x7361,f2(x7361,x7362)),f2(x7362,x7363)),f2(x7363,x7364)),x7365),f2(x7364,x7365)),a5)),
% 62.42/62.48 inference(rename_variables,[],[728])).
% 62.42/62.48 cnf(743,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x7431,f2(x7431,x7432)),f2(x7432,x7433)),f2(x7433,x7434)),f2(x7434,x7435)),x7435),a5)),
% 62.42/62.48 inference(scs_inference,[],[112,116,206,728,736,565,16,3,17,19])).
% 62.42/62.48 cnf(756,plain,
% 62.42/62.48 (E(f2(f2(f2(x7561,a1),x7562),f2(x7563,x7562)),a5)),
% 62.42/62.48 inference(scs_inference,[],[127,18])).
% 62.42/62.48 cnf(794,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(f2(x7941,x7942),x7943),f2(x7941,x7944)),f2(x7944,x7945)),x7945),a5)),
% 62.42/62.48 inference(scs_inference,[],[497,756,17,19])).
% 62.42/62.48 cnf(814,plain,
% 62.42/62.48 (E(f2(f2(f2(x8141,x8142),f2(x8141,f2(x8142,x8143))),f2(a5,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[120,137,127,516,522,160,3,15,16])).
% 62.42/62.48 cnf(820,plain,
% 62.42/62.48 (E(f2(f2(f2(x8201,x8202),f2(a5,a5)),f2(x8201,f2(x8202,x8203))),a5)),
% 62.42/62.48 inference(scs_inference,[],[814,794,18,19])).
% 62.42/62.48 cnf(822,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x8221,x8222),f2(f2(x8223,x8224),x8222)),f2(x8224,f2(x8223,x8224))),f2(x8221,x8223)),a5)),
% 62.42/62.48 inference(scs_inference,[],[141,137,814,794,18,19,16])).
% 62.42/62.48 cnf(841,plain,
% 62.42/62.48 (E(f2(f2(f2(x8411,x8412),f2(a5,a5)),f2(x8411,f2(f2(x8412,x8413),f2(x8414,x8413)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[136,139,141,127,220,820,15,3,16])).
% 62.42/62.48 cnf(850,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x8501,x8502),f2(f2(x8503,x8504),x8502)),f2(x8501,x8503)),f2(x8504,f2(x8503,x8504))),a5)),
% 62.42/62.48 inference(scs_inference,[],[144,636,822,743,18,3,19])).
% 62.42/62.48 cnf(931,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x9311,x9312),f2(f2(x9311,x9313),x9312)),x9314),f2(f2(x9313,x9312),x9314)),a5)),
% 62.42/62.48 inference(scs_inference,[],[155,2,18])).
% 62.42/62.48 cnf(939,plain,
% 62.42/62.48 (E(f2(f2(f2(x9391,f2(x9392,a5)),f2(a5,x9392)),f2(x9391,x9392)),a5)),
% 62.42/62.48 inference(scs_inference,[],[141,652,16])).
% 62.42/62.48 cnf(963,plain,
% 62.42/62.48 (~E(f2(f2(a1,f2(a3,a5)),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))))),
% 62.42/62.48 inference(scs_inference,[],[191,407,2,3])).
% 62.42/62.48 cnf(965,plain,
% 62.42/62.48 (~E(f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))),f2(f2(a1,f2(a3,a5)),f2(a1,f2(a1,a4))))),
% 62.42/62.48 inference(scs_inference,[],[483,963,5,2])).
% 62.42/62.48 cnf(970,plain,
% 62.42/62.48 (E(f2(f2(f2(x9701,x9702),f2(x9701,f2(f2(x9702,x9703),f2(x9704,x9703)))),f2(a5,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[193,483,189,963,841,939,5,2,3,18,19])).
% 62.42/62.48 cnf(990,plain,
% 62.42/62.48 (~E(f2(f2(f2(a1,a3),f2(x9901,x9901)),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(a1,f2(a1,a3))))),
% 62.42/62.48 inference(scs_inference,[],[160,79,547,970,48,15,2,3])).
% 62.42/62.48 cnf(1000,plain,
% 62.42/62.48 (E(f2(f2(x10001,x10002),f2(f2(x10001,a5),x10002)),a5)),
% 62.42/62.48 inference(scs_inference,[],[159,160,990,5,2,3,18])).
% 62.42/62.48 cnf(1008,plain,
% 62.42/62.48 (E(f2(f2(x10081,f2(x10082,f2(x10083,f2(x10083,x10084)))),f2(x10081,f2(x10082,x10084))),a5)),
% 62.42/62.48 inference(scs_inference,[],[159,2,17])).
% 62.42/62.48 cnf(1077,plain,
% 62.42/62.48 (E(f2(f2(x10771,f2(x10771,x10772)),f2(x10772,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[171,170,165,160,3,16])).
% 62.42/62.48 cnf(1085,plain,
% 62.42/62.48 (E(f2(f2(f2(x10851,f2(x10852,a5)),f2(x10851,x10852)),a5),a5)),
% 62.42/62.48 inference(scs_inference,[],[170,163,1077,17,3])).
% 62.42/62.48 cnf(1111,plain,
% 62.42/62.48 (E(f2(x11111,f2(x11111,a5)),a5)),
% 62.42/62.48 inference(rename_variables,[],[160])).
% 62.42/62.48 cnf(1115,plain,
% 62.42/62.48 (E(f2(f2(x11151,a5),f2(x11151,f2(f2(x11152,f2(x11153,a5)),f2(x11152,x11153)))),a5)),
% 62.42/62.48 inference(scs_inference,[],[160,1111,172,176,165,1085,16,2,3,17])).
% 62.42/62.48 cnf(1122,plain,
% 62.42/62.48 (E(f2(f2(f2(x11221,x11222),f2(a1,x11223)),f2(x11223,x11222)),a5)),
% 62.42/62.48 inference(scs_inference,[],[177,19])).
% 62.42/62.48 cnf(1223,plain,
% 62.42/62.48 (E(f2(a5,x12231),f2(f2(f2(x12232,x12233),f2(a1,x12233)),x12231))),
% 62.42/62.48 inference(rename_variables,[],[194])).
% 62.42/62.48 cnf(1226,plain,
% 62.42/62.48 (E(f2(x12261,f2(f2(x12262,a5),x12263)),f2(x12261,f2(x12262,x12263)))),
% 62.42/62.48 inference(scs_inference,[],[180,194,1223,186,3,5,2])).
% 62.42/62.48 cnf(1280,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x12801,x12802),f2(f2(x12803,a5),x12802)),f2(x12801,x12803)),a5),a5)),
% 62.42/62.48 inference(scs_inference,[],[201,850,16])).
% 62.42/62.48 cnf(1440,plain,
% 62.42/62.48 (E(f2(f2(f2(x14401,x14402),f2(a1,x14403)),f2(x14403,a5)),a5)),
% 62.42/62.48 inference(scs_inference,[],[217,478,1122,18,16])).
% 62.42/62.48 cnf(1614,plain,
% 62.42/62.48 (E(f2(f2(f2(x16141,x16142),a5),f2(f2(x16141,a5),f2(a5,x16143))),a5)),
% 62.42/62.48 inference(scs_inference,[],[230,249,237,1440,18,2,3])).
% 62.42/62.48 cnf(1722,plain,
% 62.42/62.48 (~E(f2(f2(a1,f2(a3,a5)),f2(a1,f2(a1,a4))),f2(f2(a1,a4),f2(f2(f2(a1,a5),a5),f2(a1,a3))))),
% 62.42/62.48 inference(scs_inference,[],[965,1226,2,3])).
% 62.42/62.48 cnf(1837,plain,
% 62.42/62.48 (E(f2(f2(f2(x18371,x18372),x18373),f2(f2(x18371,x18372),x18372)),a5)),
% 62.42/62.48 inference(scs_inference,[],[278,19])).
% 62.42/62.48 cnf(1869,plain,
% 62.42/62.48 (E(f2(f2(f2(x18691,f2(x18692,x18693)),f2(x18693,a5)),f2(x18691,x18692)),a5)),
% 62.42/62.48 inference(scs_inference,[],[285,19])).
% 62.42/62.48 cnf(1891,plain,
% 62.42/62.48 (E(f2(f2(f2(f2(x18911,f2(x18912,x18913)),f2(x18913,a5)),x18914),f2(f2(x18911,x18912),x18914)),a5)),
% 62.42/62.48 inference(scs_inference,[],[293,289,275,283,1869,1115,16,4,3,18])).
% 62.42/62.48 cnf(1895,plain,
% 62.42/62.48 (E(f2(f2(x18951,x18952),f2(f2(x18951,x18952),x18952)),f2(f2(f2(x18951,x18953),x18952),f2(f2(x18951,x18952),x18952)))),
% 62.42/62.48 inference(scs_inference,[],[278,413,15])).
% 62.42/62.48 cnf(1927,plain,
% 62.42/62.48 (E(f2(f2(f2(x19271,x19272),x19272),f2(f2(f2(x19271,x19272),x19272),x19272)),a5)),
% 62.42/62.48 inference(scs_inference,[],[294,285,276,1895,16,3])).
% 62.42/62.48 cnf(1965,plain,
% 62.42/62.48 (E(f2(f2(x19651,f2(x19652,x19653)),f2(f2(x19652,x19654),x19653)),f2(f2(x19651,f2(x19652,x19653)),f2(x19652,x19653)))),
% 62.42/62.48 inference(scs_inference,[],[294,1837,15])).
% 62.42/62.48 cnf(2013,plain,
% 62.42/62.48 (E(f2(f2(f2(x20131,x20132),f2(f2(x20133,a5),x20132)),f2(x20131,x20133)),a5)),
% 62.42/62.48 inference(scs_inference,[],[304,1891,1280,7,16,15])).
% 62.42/62.48 cnf(2030,plain,
% 62.42/62.48 (E(f2(f2(f2(x20301,x20302),f2(x20301,x20303)),f2(f2(x20303,x20302),a5)),a5)),
% 62.42/62.49 inference(scs_inference,[],[312,7,15])).
% 62.42/62.49 cnf(2111,plain,
% 62.42/62.49 (E(f2(f2(x21111,f2(x21112,a5)),f2(x21111,f2(f2(x21112,x21113),f2(x21114,x21113)))),a5)),
% 62.42/62.49 inference(scs_inference,[],[323,19])).
% 62.42/62.49 cnf(2242,plain,
% 62.42/62.49 (E(f2(f2(f2(x22421,x22421),x22421),x22421),f2(f2(x22421,x22421),x22421))),
% 62.42/62.49 inference(scs_inference,[],[333,1927,15])).
% 62.42/62.49 cnf(2312,plain,
% 62.42/62.49 (E(f2(x23121,f2(f2(x23122,a5),x23123)),f2(x23121,f2(f2(x23122,f2(a5,x23124)),x23123)))),
% 62.42/62.49 inference(scs_inference,[],[340,2,5])).
% 62.42/62.49 cnf(2430,plain,
% 62.42/62.49 (E(f2(f2(f2(x24301,x24302),f2(x24301,a5)),x24303),a5)),
% 62.42/62.49 inference(scs_inference,[],[368,2111,16])).
% 62.42/62.49 cnf(2460,plain,
% 62.42/62.49 (E(f2(f2(a1,x24601),f2(f2(a1,x24601),f2(a1,a1))),a5)),
% 62.42/62.49 inference(scs_inference,[],[375,370,2430,1614,15,3])).
% 62.42/62.49 cnf(2465,plain,
% 62.42/62.49 (E(f2(f2(x24651,f2(f2(a1,x24652),f2(a1,a1))),f2(x24651,f2(a1,x24652))),a5)),
% 62.42/62.49 inference(scs_inference,[],[2460,17])).
% 62.42/62.49 cnf(2472,plain,
% 62.42/62.49 (E(f2(f2(f2(x24721,x24722),f2(f2(a1,x24723),f2(a1,a1))),f2(f2(x24721,f2(x24722,x24724)),f2(a1,x24723))),a5)),
% 62.42/62.49 inference(scs_inference,[],[365,2465,16])).
% 62.42/62.49 cnf(2708,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(f2(x27081,x27082),x27083),f2(x27084,x27082)),x27085),f2(f2(x27081,x27084),x27085)),a5)),
% 62.42/62.49 inference(scs_inference,[],[422,19,18])).
% 62.42/62.49 cnf(2728,plain,
% 62.42/62.49 (E(f2(f2(x27281,f2(x27282,x27283)),x27284),f2(f2(x27281,f2(x27282,f2(x27283,a5))),x27284))),
% 62.42/62.49 inference(scs_inference,[],[408,2,4])).
% 62.42/62.49 cnf(2780,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(f2(x27801,x27802),x27803),f2(x27804,x27802)),f2(x27801,f2(x27805,x27806))),f2(x27805,x27804)),a5)),
% 62.42/62.49 inference(scs_inference,[],[428,2708,16])).
% 62.42/62.49 cnf(2837,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(f2(x28371,x28372),x28373),f2(x28374,x28372)),f2(x28375,x28374)),f2(x28371,f2(x28375,x28376))),a5)),
% 62.42/62.49 inference(scs_inference,[],[2780,19])).
% 62.42/62.49 cnf(2904,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(f2(x29041,x29042),x29043),f2(x29044,x29042)),f2(x29041,x29044)),f2(x29045,x29046)),a5)),
% 62.42/62.49 inference(scs_inference,[],[442,457,455,2837,3,16])).
% 62.42/62.49 cnf(3035,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(x30351,x30352),x30351),f2(x30353,f2(x30352,x30354))),a5),a5)),
% 62.42/62.49 inference(scs_inference,[],[477,475,3])).
% 62.42/62.49 cnf(3064,plain,
% 62.42/62.49 (E(f2(f2(f2(f2(f2(x30641,x30642),x30643),f2(x30644,x30642)),f2(x30645,x30646)),f2(x30641,x30644)),a5)),
% 62.42/62.49 inference(scs_inference,[],[483,473,2242,2904,4,3,19])).
% 62.42/62.49 cnf(3137,plain,
% 62.42/62.49 (E(f2(f2(f2(x31371,x31372),x31371),f2(x31373,f2(x31372,x31374))),a5)),
% 62.42/62.49 inference(scs_inference,[],[496,485,491,2472,3035,7,3,16,15])).
% 62.42/62.49 cnf(3194,plain,
% 62.42/62.49 (~E(f2(f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))),f2(f2(a1,a3),f2(a1,f2(a1,a4)))),a5)),
% 62.42/62.49 inference(scs_inference,[],[480,1722,2728,931,525,193,3,18,19,15])).
% 62.42/62.49 cnf(3197,plain,
% 62.42/62.49 (~E(f2(f2(a1,a4),f2(f2(f2(a1,a5),a5),f2(a1,a3))),f2(f2(a1,f2(a3,a5)),f2(a1,f2(a1,a4))))),
% 62.42/62.49 inference(scs_inference,[],[480,1722,2728,931,525,193,3,18,19,15,2])).
% 62.42/62.49 cnf(3206,plain,
% 62.42/62.49 (~E(f2(f2(f2(a1,a4),f2(f2(a1,a3),a4)),f2(f2(a1,a5),f2(a1,a3))),a5)),
% 62.42/62.49 inference(scs_inference,[],[480,495,3194,1008,3,19,16])).
% 62.42/62.49 cnf(3221,plain,
% 62.42/62.49 (~E(f2(f2(f2(a1,a4),f2(f2(a1,a3),a4)),f2(f2(f2(f2(x32211,x32212),x32213),f2(x32211,f2(a1,a5))),f2(a1,a3))),a5)),
% 62.42/62.49 inference(scs_inference,[],[482,496,497,282,3206,3,19,16])).
% 62.42/62.49 cnf(3238,plain,
% 62.42/62.49 (~E(f2(f2(f2(f2(a1,a4),f2(f2(a1,a3),a4)),f2(f2(a1,a5),f2(a1,a3))),a5),a5)),
% 62.42/62.49 inference(scs_inference,[],[497,3197,2312,3064,3221,3206,7,3,19,16,15])).
% 62.42/62.49 cnf(3245,plain,
% 62.42/62.49 (~E(f2(f2(f2(f2(a1,a4),f2(f2(a1,a3),a4)),a5),f2(f2(a1,a5),f2(a1,a3))),a5)),
% 62.42/62.49 inference(scs_inference,[],[483,500,3238,3,19])).
% 62.42/62.49 cnf(3278,plain,
% 62.42/62.49 (~E(f2(f2(f2(f2(a1,a4),f2(f2(a1,a5),f2(a1,a3))),f2(f2(a1,a3),a4)),a5),a5)),
% 62.42/62.49 inference(scs_inference,[],[484,496,3206,7,3,19,15])).
% 62.42/62.49 cnf(3339,plain,
% 62.42/62.49 (~E(f2(a1,f2(f2(a1,a3),f2(a1,f2(a1,a4)))),a5)),
% 62.42/62.49 inference(scs_inference,[],[6,327,3137,2030,2013,3194,3238,2,5,19,15,16])).
% 62.42/62.49 cnf(3357,plain,
% 62.42/62.49 (~E(f2(f2(a1,f2(f2(a1,a3),f2(a1,f2(a1,a4)))),a5),a5)),
% 62.42/62.49 inference(scs_inference,[],[2030,2460,3278,7,3339,2,19,18,15])).
% 62.42/62.49 cnf(3374,plain,
% 62.42/62.49 ($false),
% 62.42/62.49 inference(scs_inference,[],[160,3137,2013,1965,149,3194,3357,1000,3245,2,19,3,15,16]),
% 62.42/62.49 ['proof']).
% 62.42/62.49 % SZS output end Proof
% 62.42/62.49 % Total time :61.840000s
%------------------------------------------------------------------------------