TSTP Solution File: RNG001-5 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 13:47:36 EDT 2023
% Result : Unsatisfiable 0.56s 0.88s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n023.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 02:47:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.56/0.87 %-------------------------------------------
% 0.56/0.87 % File :CSE---1.6
% 0.56/0.87 % Problem :theBenchmark
% 0.56/0.87 % Transform :cnf
% 0.56/0.87 % Format :tptp:raw
% 0.56/0.87 % Command :java -jar mcs_scs.jar %d %s
% 0.56/0.87
% 0.56/0.87 % Result :Theorem 0.260000s
% 0.56/0.87 % Output :CNFRefutation 0.260000s
% 0.56/0.87 %-------------------------------------------
% 0.56/0.87 %--------------------------------------------------------------------------
% 0.56/0.87 % File : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.56/0.87 % Domain : Ring Theory
% 0.56/0.87 % Problem : X.additive_identity = additive_identity for any X
% 0.56/0.87 % Version : [Wos65] axioms : Reduced > Incomplete.
% 0.56/0.87 % English :
% 0.56/0.87
% 0.56/0.87 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.56/0.87 % : [FL+74] Fleisig et al. (1974), An Implementation of the Model
% 0.56/0.87 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.56/0.87 % Source : [SPRFN]
% 0.56/0.87 % Names : Problem 21 [Wos65]
% 0.56/0.87 % : wos21 [WM76]
% 0.56/0.87
% 0.56/0.87 % Status : Unsatisfiable
% 0.56/0.87 % Rating : 0.14 v8.1.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.1.0, 0.29 v6.0.0, 0.22 v5.5.0, 0.50 v5.3.0, 0.55 v5.2.0, 0.31 v5.1.0, 0.44 v5.0.0, 0.40 v4.0.1, 0.43 v3.4.0, 0.40 v3.3.0, 0.00 v2.7.0, 0.25 v2.6.0, 0.43 v2.5.0, 0.29 v2.4.0, 0.29 v2.3.0, 0.57 v2.2.1, 0.67 v2.1.0, 0.57 v2.0.0
% 0.56/0.87 % Syntax : Number of clauses : 30 ( 8 unt; 0 nHn; 21 RR)
% 0.56/0.87 % Number of literals : 81 ( 0 equ; 52 neg)
% 0.56/0.87 % Maximal clause size : 5 ( 2 avg)
% 0.56/0.87 % Maximal term depth : 2 ( 1 avg)
% 0.56/0.87 % Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% 0.56/0.87 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.56/0.87 % Number of variables : 109 ( 0 sgn)
% 0.56/0.87 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.56/0.87
% 0.56/0.87 % Comments : Omits two equality subsitution axioms.
% 0.56/0.87 % : These are the same axioms as in [MOW76].
% 0.56/0.87 % : I guess this is Example 6c in [FL+74].
% 0.56/0.87 %--------------------------------------------------------------------------
% 0.56/0.87 %----Include ring theory axioms
% 0.56/0.87 %include('Axioms/RNG001-0.ax').
% 0.56/0.87 %--------------------------------------------------------------------------
% 0.56/0.87 cnf(reflexivity,axiom,
% 0.56/0.87 equalish(X,X) ).
% 0.56/0.87
% 0.56/0.87 cnf(symmetry,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | equalish(Y,X) ) ).
% 0.56/0.87
% 0.56/0.87 cnf(transitivity,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | ~ equalish(Y,Z)
% 0.56/0.87 | equalish(X,Z) ) ).
% 0.56/0.87
% 0.56/0.87 %----Equality axioms for additive operator
% 0.56/0.87 cnf(additive_inverse_substitution,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | equalish(additive_inverse(X),additive_inverse(Y)) ) ).
% 0.56/0.87
% 0.56/0.87 cnf(add_substitution1,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | equalish(add(X,W),add(Y,W)) ) ).
% 0.56/0.87
% 0.56/0.87 %----This axiom omited in this version
% 0.56/0.87 %input_clause(add_substitution2,axiom,
% 0.56/0.87 % [--equalish(X,Y),
% 0.56/0.87 % ++equalish(add(W,X),add(W,Y))]).
% 0.56/0.87
% 0.56/0.87 cnf(sum_substitution1,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | ~ sum(X,W,Z)
% 0.56/0.87 | sum(Y,W,Z) ) ).
% 0.56/0.87
% 0.56/0.87 cnf(sum_substitution2,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | ~ sum(W,X,Z)
% 0.56/0.87 | sum(W,Y,Z) ) ).
% 0.56/0.87
% 0.56/0.87 cnf(sum_substitution3,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.87 | ~ sum(W,Z,X)
% 0.56/0.87 | sum(W,Z,Y) ) ).
% 0.56/0.87
% 0.56/0.87 %----Equality axioms for multiplicative operator
% 0.56/0.87 cnf(multiply_substitution1,axiom,
% 0.56/0.87 ( ~ equalish(X,Y)
% 0.56/0.88 | equalish(multiply(X,W),multiply(Y,W)) ) ).
% 0.56/0.88
% 0.56/0.88 %----This axiom omited in this version
% 0.56/0.88 %input_clause(multiply_substitution2,axiom,
% 0.56/0.88 % [--equalish(X,Y),
% 0.56/0.88 % ++equalish(multiply(W,X),multiply(W,Y))]).
% 0.56/0.88
% 0.56/0.88 cnf(product_substitution1,axiom,
% 0.56/0.88 ( ~ equalish(X,Y)
% 0.56/0.88 | ~ product(X,W,Z)
% 0.56/0.88 | product(Y,W,Z) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(product_substitution2,axiom,
% 0.56/0.88 ( ~ equalish(X,Y)
% 0.56/0.88 | ~ product(W,X,Z)
% 0.56/0.88 | product(W,Y,Z) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(product_substitution3,axiom,
% 0.56/0.88 ( ~ equalish(X,Y)
% 0.56/0.88 | ~ product(W,Z,X)
% 0.56/0.88 | product(W,Z,Y) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(additive_identity1,axiom,
% 0.56/0.88 sum(additive_identity,X,X) ).
% 0.56/0.88
% 0.56/0.88 cnf(additive_identity2,axiom,
% 0.56/0.88 sum(X,additive_identity,X) ).
% 0.56/0.88
% 0.56/0.88 cnf(closure_of_multiplication,axiom,
% 0.56/0.88 product(X,Y,multiply(X,Y)) ).
% 0.56/0.88
% 0.56/0.88 cnf(closure_of_addition,axiom,
% 0.56/0.88 sum(X,Y,add(X,Y)) ).
% 0.56/0.88
% 0.56/0.88 cnf(left_inverse,axiom,
% 0.56/0.88 sum(additive_inverse(X),X,additive_identity) ).
% 0.56/0.88
% 0.56/0.88 cnf(right_inverse,axiom,
% 0.56/0.88 sum(X,additive_inverse(X),additive_identity) ).
% 0.56/0.88
% 0.56/0.88 cnf(associativity_of_addition1,axiom,
% 0.56/0.88 ( ~ sum(X,Y,U)
% 0.56/0.88 | ~ sum(Y,Z,V)
% 0.56/0.88 | ~ sum(U,Z,W)
% 0.56/0.88 | sum(X,V,W) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(associativity_of_addition2,axiom,
% 0.56/0.88 ( ~ sum(X,Y,U)
% 0.56/0.88 | ~ sum(Y,Z,V)
% 0.56/0.88 | ~ sum(X,V,W)
% 0.56/0.88 | sum(U,Z,W) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(commutativity_of_addition,axiom,
% 0.56/0.88 ( ~ sum(X,Y,Z)
% 0.56/0.88 | sum(Y,X,Z) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(associativity_of_multiplication1,axiom,
% 0.56/0.88 ( ~ product(X,Y,U)
% 0.56/0.88 | ~ product(Y,Z,V)
% 0.56/0.88 | ~ product(U,Z,W)
% 0.56/0.88 | product(X,V,W) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(associativity_of_multiplication2,axiom,
% 0.56/0.88 ( ~ product(X,Y,U)
% 0.56/0.88 | ~ product(Y,Z,V)
% 0.56/0.88 | ~ product(X,V,W)
% 0.56/0.88 | product(U,Z,W) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(distributivity1,axiom,
% 0.56/0.88 ( ~ product(X,Y,V1)
% 0.56/0.88 | ~ product(X,Z,V2)
% 0.56/0.88 | ~ sum(Y,Z,V3)
% 0.56/0.88 | ~ product(X,V3,V4)
% 0.56/0.88 | sum(V1,V2,V4) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(distributivity2,axiom,
% 0.56/0.88 ( ~ product(X,Y,V1)
% 0.56/0.88 | ~ product(X,Z,V2)
% 0.56/0.88 | ~ sum(Y,Z,V3)
% 0.56/0.88 | ~ sum(V1,V2,V4)
% 0.56/0.88 | product(X,V3,V4) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(distributivity3,axiom,
% 0.56/0.88 ( ~ product(Y,X,V1)
% 0.56/0.88 | ~ product(Z,X,V2)
% 0.56/0.88 | ~ sum(Y,Z,V3)
% 0.56/0.88 | ~ product(V3,X,V4)
% 0.56/0.88 | sum(V1,V2,V4) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(distributivity4,axiom,
% 0.56/0.88 ( ~ product(Y,X,V1)
% 0.56/0.88 | ~ product(Z,X,V2)
% 0.56/0.88 | ~ sum(Y,Z,V3)
% 0.56/0.88 | ~ sum(V1,V2,V4)
% 0.56/0.88 | product(V3,X,V4) ) ).
% 0.56/0.88
% 0.56/0.88 %-----Equality axioms for operators
% 0.56/0.88 cnf(addition_is_well_defined,axiom,
% 0.56/0.88 ( ~ sum(X,Y,U)
% 0.56/0.88 | ~ sum(X,Y,V)
% 0.56/0.88 | equalish(U,V) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(multiplication_is_well_defined,axiom,
% 0.56/0.88 ( ~ product(X,Y,U)
% 0.56/0.88 | ~ product(X,Y,V)
% 0.56/0.88 | equalish(U,V) ) ).
% 0.56/0.88
% 0.56/0.88 cnf(prove_multiplicative_identity_axiom,negated_conjecture,
% 0.56/0.88 ~ product(a,additive_identity,additive_identity) ).
% 0.56/0.88
% 0.56/0.88 %--------------------------------------------------------------------------
% 0.56/0.88 %-------------------------------------------
% 0.56/0.88 % Proof found
% 0.56/0.88 % SZS status Theorem for theBenchmark
% 0.56/0.88 % SZS output start Proof
% 0.56/0.88 %ClaNum:30(EqnAxiom:0)
% 0.56/0.88 %VarNum:222(SingletonVarNum:109)
% 0.56/0.88 %MaxLitNum:5
% 0.56/0.88 %MaxfuncDepth:1
% 0.56/0.88 %SharedTerms:3
% 0.56/0.88 %goalClause: 8
% 0.56/0.88 %singleGoalClaCount:1
% 0.56/0.88 [8]~P3(a3,a1,a1)
% 0.56/0.88 [1]P1(x11,x11)
% 0.56/0.88 [2]P2(x21,a1,x21)
% 0.56/0.88 [3]P2(a1,x31,x31)
% 0.56/0.88 [4]P2(x41,f4(x41),a1)
% 0.56/0.88 [5]P2(f4(x51),x51,a1)
% 0.56/0.88 [6]P2(x61,x62,f2(x61,x62))
% 0.56/0.88 [7]P3(x71,x72,f5(x71,x72))
% 0.56/0.88 [9]~P1(x92,x91)+P1(x91,x92)
% 0.56/0.88 [10]~P1(x101,x102)+P1(f4(x101),f4(x102))
% 0.56/0.88 [14]~P2(x142,x141,x143)+P2(x141,x142,x143)
% 0.56/0.88 [12]~P1(x121,x123)+P1(f2(x121,x122),f2(x123,x122))
% 0.56/0.88 [13]~P1(x131,x133)+P1(f5(x131,x132),f5(x133,x132))
% 0.56/0.88 [11]~P1(x111,x113)+P1(x111,x112)+~P1(x113,x112)
% 0.56/0.88 [15]~P2(x151,x152,x154)+P2(x151,x152,x153)+~P1(x154,x153)
% 0.56/0.88 [16]~P2(x161,x164,x163)+P2(x161,x162,x163)+~P1(x164,x162)
% 0.56/0.88 [17]~P2(x174,x172,x173)+P2(x171,x172,x173)+~P1(x174,x171)
% 0.56/0.88 [18]~P3(x181,x182,x184)+P3(x181,x182,x183)+~P1(x184,x183)
% 0.56/0.88 [19]~P3(x191,x194,x193)+P3(x191,x192,x193)+~P1(x194,x192)
% 0.56/0.88 [20]~P3(x204,x202,x203)+P3(x201,x202,x203)+~P1(x204,x201)
% 0.56/0.88 [21]~P2(x213,x214,x211)+P1(x211,x212)+~P2(x213,x214,x212)
% 0.56/0.88 [22]~P3(x223,x224,x221)+P1(x221,x222)+~P3(x223,x224,x222)
% 0.56/0.88 [23]~P2(x236,x234,x231)+P2(x231,x232,x233)+~P2(x234,x232,x235)+~P2(x236,x235,x233)
% 0.56/0.88 [24]~P2(x241,x246,x244)+P2(x241,x242,x243)+~P2(x244,x245,x243)+~P2(x246,x245,x242)
% 0.56/0.88 [25]~P3(x256,x254,x251)+P3(x251,x252,x253)+~P3(x254,x252,x255)+~P3(x256,x255,x253)
% 0.56/0.88 [26]~P3(x261,x266,x264)+P3(x261,x262,x263)+~P3(x264,x265,x263)+~P3(x266,x265,x262)
% 0.56/0.88 [27]~P3(x277,x275,x272)+~P3(x277,x274,x271)+P2(x271,x272,x273)+~P2(x274,x275,x276)+~P3(x277,x276,x273)
% 0.56/0.88 [28]~P3(x285,x287,x282)+~P3(x284,x287,x281)+P2(x281,x282,x283)+~P2(x284,x285,x286)+~P3(x286,x287,x283)
% 0.56/0.88 [29]~P3(x297,x292,x295)+~P3(x296,x292,x294)+P3(x291,x292,x293)+~P2(x294,x295,x293)+~P2(x296,x297,x291)
% 0.56/0.88 [30]~P3(x301,x307,x305)+~P3(x301,x306,x304)+P3(x301,x302,x303)+~P2(x304,x305,x303)+~P2(x306,x307,x302)
% 0.56/0.88 %EqnAxiom
% 0.56/0.88
% 0.56/0.88 %-------------------------------------------
% 0.56/0.88 cnf(31,plain,
% 0.56/0.88 (P1(x311,f2(x311,a1))),
% 0.56/0.88 inference(scs_inference,[],[2,6,21])).
% 0.56/0.88 cnf(32,plain,
% 0.56/0.88 (P2(x321,x322,f2(x321,x322))),
% 0.56/0.88 inference(rename_variables,[],[6])).
% 0.56/0.88 cnf(33,plain,
% 0.56/0.88 (P3(f2(x331,a1),x332,f5(x331,x332))),
% 0.56/0.88 inference(scs_inference,[],[2,6,7,21,20])).
% 0.56/0.88 cnf(35,plain,
% 0.56/0.88 (P3(x351,f2(x351,a1),f5(x351,x351))),
% 0.56/0.88 inference(scs_inference,[],[2,6,7,21,20,19])).
% 0.56/0.88 cnf(36,plain,
% 0.56/0.88 (P3(x361,x362,f5(x361,x362))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(38,plain,
% 0.56/0.88 (P3(x381,x382,f2(f5(x381,x382),a1))),
% 0.56/0.88 inference(scs_inference,[],[2,6,7,36,21,20,19,18])).
% 0.56/0.88 cnf(41,plain,
% 0.56/0.88 (P2(x411,a1,x411)),
% 0.56/0.88 inference(rename_variables,[],[2])).
% 0.56/0.88 cnf(46,plain,
% 0.56/0.88 (P2(x461,f2(a1,a1),x461)),
% 0.56/0.88 inference(scs_inference,[],[2,41,3,6,32,7,36,21,20,19,18,17,16,24])).
% 0.56/0.88 cnf(47,plain,
% 0.56/0.88 (P2(x471,x472,f2(x471,x472))),
% 0.56/0.88 inference(rename_variables,[],[6])).
% 0.56/0.88 cnf(49,plain,
% 0.56/0.88 (P3(x491,a1,f2(f5(x491,a1),f5(x491,a1)))),
% 0.56/0.88 inference(scs_inference,[],[2,41,3,6,32,47,7,36,21,20,19,18,17,16,24,30])).
% 0.56/0.88 cnf(50,plain,
% 0.56/0.88 (P2(x501,x502,f2(x501,x502))),
% 0.56/0.88 inference(rename_variables,[],[6])).
% 0.56/0.88 cnf(51,plain,
% 0.56/0.88 (P2(x511,a1,x511)),
% 0.56/0.88 inference(rename_variables,[],[2])).
% 0.56/0.88 cnf(53,plain,
% 0.56/0.88 (P3(x531,x532,f5(x531,x532))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(56,plain,
% 0.56/0.88 (P2(x561,x562,f2(x561,x562))),
% 0.56/0.88 inference(rename_variables,[],[6])).
% 0.56/0.88 cnf(57,plain,
% 0.56/0.88 (P2(x571,a1,x571)),
% 0.56/0.88 inference(rename_variables,[],[2])).
% 0.56/0.88 cnf(59,plain,
% 0.56/0.88 (P3(x591,x592,f5(x591,x592))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(64,plain,
% 0.56/0.88 (P3(x641,x642,f5(x641,x642))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(65,plain,
% 0.56/0.88 (P2(x651,a1,x651)),
% 0.56/0.88 inference(rename_variables,[],[2])).
% 0.56/0.88 cnf(67,plain,
% 0.56/0.88 (P2(f5(x671,a1),f5(x671,a1),f5(x671,a1))),
% 0.56/0.88 inference(scs_inference,[],[2,41,51,57,65,3,6,32,47,50,7,36,53,59,64,21,20,19,18,17,16,24,30,29,28,27])).
% 0.56/0.88 cnf(70,plain,
% 0.56/0.88 (P3(x701,x702,f5(x701,x702))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(73,plain,
% 0.56/0.88 (P2(x731,x732,f2(x732,x731))),
% 0.56/0.88 inference(scs_inference,[],[2,41,51,57,65,3,6,32,47,50,56,7,36,53,59,64,21,20,19,18,17,16,24,30,29,28,27,14])).
% 0.56/0.88 cnf(77,plain,
% 0.56/0.88 (P1(f2(f5(x771,a1),f5(x771,a1)),f5(x771,a1))),
% 0.56/0.88 inference(scs_inference,[],[2,41,51,57,65,3,6,32,47,50,56,7,36,53,59,64,70,21,20,19,18,17,16,24,30,29,28,27,14,9,22])).
% 0.56/0.88 cnf(92,plain,
% 0.56/0.88 (P1(f5(x921,x922),f5(f2(x921,a1),x922))),
% 0.56/0.88 inference(scs_inference,[],[31,13])).
% 0.56/0.88 cnf(94,plain,
% 0.56/0.88 (P1(f2(x941,x942),f2(f2(x941,a1),x942))),
% 0.56/0.88 inference(scs_inference,[],[31,13,12])).
% 0.56/0.88 cnf(96,plain,
% 0.56/0.88 (P1(f4(x961),f4(f2(x961,a1)))),
% 0.56/0.88 inference(scs_inference,[],[31,13,12,10])).
% 0.56/0.88 cnf(99,plain,
% 0.56/0.88 (P2(a1,x991,x991)),
% 0.56/0.88 inference(rename_variables,[],[3])).
% 0.56/0.88 cnf(101,plain,
% 0.56/0.88 (~P2(f5(a3,a1),f5(a3,a1),a1)),
% 0.56/0.88 inference(scs_inference,[],[8,3,99,7,77,31,13,12,10,15,30])).
% 0.56/0.88 cnf(102,plain,
% 0.56/0.88 (P2(a1,x1021,x1021)),
% 0.56/0.88 inference(rename_variables,[],[3])).
% 0.56/0.88 cnf(104,plain,
% 0.56/0.88 (P3(x1041,x1042,f5(x1041,x1042))),
% 0.56/0.88 inference(rename_variables,[],[7])).
% 0.56/0.88 cnf(106,plain,
% 0.56/0.88 (P3(f2(x1061,x1061),x1062,f2(f5(x1061,x1062),f5(x1061,x1062)))),
% 0.56/0.88 inference(scs_inference,[],[8,3,99,6,7,104,73,77,31,13,12,10,15,30,29])).
% 0.56/0.88 cnf(107,plain,
% 0.56/0.88 (P2(x1071,x1072,f2(x1071,x1072))),
% 0.56/0.88 inference(rename_variables,[],[6])).
% 0.56/0.88 cnf(110,plain,
% 0.56/0.89 (~P2(f4(f5(a3,a1)),a1,f5(a3,a1))),
% 0.56/0.89 inference(scs_inference,[],[8,4,3,99,102,6,7,104,73,77,31,13,12,10,15,30,29,24])).
% 0.56/0.89 cnf(111,plain,
% 0.56/0.89 (P2(x1111,f4(x1111),a1)),
% 0.56/0.89 inference(rename_variables,[],[4])).
% 0.56/0.89 cnf(112,plain,
% 0.56/0.89 (P2(a1,x1121,x1121)),
% 0.56/0.89 inference(rename_variables,[],[3])).
% 0.56/0.89 cnf(114,plain,
% 0.56/0.89 (~P2(a1,f4(f5(a3,a1)),f5(a3,a1))),
% 0.56/0.89 inference(scs_inference,[],[8,4,5,3,99,102,112,6,7,104,73,77,31,13,12,10,15,30,29,24,23])).
% 0.56/0.89 cnf(115,plain,
% 0.56/0.89 (P2(f4(x1151),x1151,a1)),
% 0.56/0.89 inference(rename_variables,[],[5])).
% 0.56/0.89 cnf(116,plain,
% 0.56/0.89 (P2(a1,x1161,x1161)),
% 0.56/0.89 inference(rename_variables,[],[3])).
% 0.56/0.89 cnf(118,plain,
% 0.56/0.89 (~P3(f2(a3,a3),a1,a1)),
% 0.56/0.89 inference(scs_inference,[],[8,4,5,3,99,102,112,6,107,7,104,73,77,31,13,12,10,15,30,29,24,23,28])).
% 0.56/0.89 cnf(120,plain,
% 0.56/0.89 (P3(x1201,x1202,f5(x1201,x1202))),
% 0.56/0.89 inference(rename_variables,[],[7])).
% 0.56/0.89 cnf(123,plain,
% 0.56/0.89 (P1(f4(a1),a1)),
% 0.56/0.89 inference(scs_inference,[],[8,4,111,5,3,99,102,112,116,6,107,7,104,73,77,31,13,12,10,15,30,29,24,23,28,21])).
% 0.56/0.89 cnf(124,plain,
% 0.56/0.89 (P2(a1,x1241,x1241)),
% 0.56/0.89 inference(rename_variables,[],[3])).
% 0.56/0.89 cnf(127,plain,
% 0.56/0.89 (~P1(f5(a3,a1),a1)),
% 0.56/0.89 inference(scs_inference,[],[8,4,111,5,3,99,102,112,116,6,107,7,104,120,73,77,31,13,12,10,15,30,29,24,23,28,21,18])).
% 0.56/0.89 cnf(130,plain,
% 0.56/0.89 (~P1(f4(f5(a3,a1)),f5(a3,a1))),
% 0.56/0.89 inference(scs_inference,[],[8,4,111,5,115,3,99,102,112,116,6,107,7,104,120,73,77,31,13,12,10,15,30,29,24,23,28,21,18,17])).
% 0.56/0.89 cnf(136,plain,
% 0.56/0.89 (~P1(f2(f5(a3,a1),a1),a1)),
% 0.56/0.89 inference(scs_inference,[],[8,4,111,5,115,3,99,102,112,116,124,6,107,7,104,120,73,77,31,13,12,10,15,30,29,24,23,28,21,18,17,16,11])).
% 0.56/0.89 cnf(139,plain,
% 0.56/0.89 (~P1(a1,f5(a3,a1))),
% 0.56/0.89 inference(scs_inference,[],[8,4,111,5,115,3,99,102,112,116,124,6,107,7,104,120,73,77,31,13,12,10,15,30,29,24,23,28,21,18,17,16,11,9])).
% 0.56/0.89 cnf(162,plain,
% 0.56/0.89 (P2(a1,x1621,x1621)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(164,plain,
% 0.87/0.89 (~P3(a3,a1,f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[2,3,7,130,114,24,22])).
% 0.87/0.89 cnf(165,plain,
% 0.87/0.89 (P3(x1651,x1652,f5(x1651,x1652))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(170,plain,
% 0.87/0.89 (P2(x1701,x1702,f2(x1701,x1702))),
% 0.87/0.89 inference(rename_variables,[],[6])).
% 0.87/0.89 cnf(172,plain,
% 0.87/0.89 (P1(f2(x1721,a1),x1721)),
% 0.87/0.89 inference(scs_inference,[],[5,2,3,6,31,7,130,114,24,22,23,9])).
% 0.87/0.89 cnf(174,plain,
% 0.87/0.89 (~P2(f5(a1,a1),f2(f5(a3,a1),f5(a3,a1)),a1)),
% 0.87/0.89 inference(scs_inference,[],[5,2,3,162,6,31,7,165,106,130,114,118,24,22,23,9,29])).
% 0.87/0.89 cnf(179,plain,
% 0.87/0.89 (~P2(x1791,f4(x1791),f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[4,5,2,3,162,6,31,7,165,106,130,114,118,127,24,22,23,9,29,21])).
% 0.87/0.89 cnf(181,plain,
% 0.87/0.89 (~P2(a1,f5(a3,a1),f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[4,5,2,3,162,6,31,7,165,106,130,114,118,127,24,22,23,9,29,21,14])).
% 0.87/0.89 cnf(183,plain,
% 0.87/0.89 (~P1(f5(a3,a1),f4(a1))),
% 0.87/0.89 inference(scs_inference,[],[4,5,2,3,162,6,31,7,165,106,130,114,118,127,123,24,22,23,9,29,21,14,11])).
% 0.87/0.89 cnf(185,plain,
% 0.87/0.89 (~P1(f2(f5(a3,a1),f5(a3,a1)),a1)),
% 0.87/0.89 inference(scs_inference,[],[4,5,2,3,162,6,170,31,7,165,106,130,114,118,127,101,123,24,22,23,9,29,21,14,11,15])).
% 0.87/0.89 cnf(210,plain,
% 0.87/0.89 (P2(f2(a1,a1),x2101,x2101)),
% 0.87/0.89 inference(scs_inference,[],[46,14])).
% 0.87/0.89 cnf(212,plain,
% 0.87/0.89 (~P2(a1,f4(f5(a3,a1)),a1)),
% 0.87/0.89 inference(scs_inference,[],[2,179,46,14,23])).
% 0.87/0.89 cnf(214,plain,
% 0.87/0.89 (P2(x2141,a1,x2141)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(215,plain,
% 0.87/0.89 (~P2(x2151,f4(x2151),f5(a3,a1))),
% 0.87/0.89 inference(rename_variables,[],[179])).
% 0.87/0.89 cnf(217,plain,
% 0.87/0.89 (P3(x2171,f2(x2171,a1),f2(f5(x2171,a1),f5(x2171,x2171)))),
% 0.87/0.89 inference(scs_inference,[],[2,3,6,7,179,46,35,14,23,30])).
% 0.87/0.89 cnf(218,plain,
% 0.87/0.89 (P3(x2181,f2(x2181,a1),f5(x2181,x2181))),
% 0.87/0.89 inference(rename_variables,[],[35])).
% 0.87/0.89 cnf(219,plain,
% 0.87/0.89 (P3(x2191,x2192,f5(x2191,x2192))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(223,plain,
% 0.87/0.89 (~P3(a1,a1,f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[2,214,3,6,7,219,179,215,46,35,14,23,30,28])).
% 0.87/0.89 cnf(226,plain,
% 0.87/0.89 (P3(x2261,x2262,f5(x2261,x2262))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(227,plain,
% 0.87/0.89 (P2(x2271,a1,x2271)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(230,plain,
% 0.87/0.89 (P3(x2301,f2(x2301,a1),f5(x2301,x2301))),
% 0.87/0.89 inference(rename_variables,[],[35])).
% 0.87/0.89 cnf(231,plain,
% 0.87/0.89 (P3(x2311,x2312,f5(x2311,x2312))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(232,plain,
% 0.87/0.89 (P3(x2321,x2322,f5(x2321,x2322))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(234,plain,
% 0.87/0.89 (P1(f5(x2341,x2341),f5(x2341,f2(x2341,a1)))),
% 0.87/0.89 inference(scs_inference,[],[2,214,3,6,7,219,226,232,179,215,46,35,218,230,14,23,30,28,27,22])).
% 0.87/0.89 cnf(236,plain,
% 0.87/0.89 (P3(x2361,x2362,f5(x2361,x2362))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(238,plain,
% 0.87/0.89 (~P1(f4(a1),f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[2,214,3,6,7,219,226,232,179,215,46,183,35,218,230,14,23,30,28,27,22,9])).
% 0.87/0.89 cnf(241,plain,
% 0.87/0.89 (P3(x2411,x2412,f5(x2411,x2412))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(242,plain,
% 0.87/0.89 (P3(x2421,x2422,f5(x2421,x2422))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(245,plain,
% 0.87/0.89 (~P2(f5(a3,a1),f5(a1,a1),f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[2,214,227,3,6,7,219,226,232,236,242,241,231,179,215,164,46,183,35,218,230,14,23,30,28,27,22,9,26,29])).
% 0.87/0.89 cnf(247,plain,
% 0.87/0.89 (P2(x2471,a1,x2471)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(250,plain,
% 0.87/0.89 (P1(x2501,f2(a1,x2501))),
% 0.87/0.89 inference(scs_inference,[],[2,214,227,247,3,6,7,219,226,232,236,242,241,231,179,215,164,46,183,35,218,230,73,14,23,30,28,27,22,9,26,29,21])).
% 0.87/0.89 cnf(255,plain,
% 0.87/0.89 (P3(f2(x2551,a1),f2(x2552,a1),f5(x2551,x2552))),
% 0.87/0.89 inference(scs_inference,[],[33,31,19])).
% 0.87/0.89 cnf(256,plain,
% 0.87/0.89 (P3(f2(x2561,a1),x2562,f5(x2561,x2562))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(258,plain,
% 0.87/0.89 (~P1(f2(f4(a1),a1),f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[33,31,238,19,11])).
% 0.87/0.89 cnf(259,plain,
% 0.87/0.89 (P1(x2591,f2(x2591,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(262,plain,
% 0.87/0.89 (P1(f2(x2621,a1),x2621)),
% 0.87/0.89 inference(rename_variables,[],[172])).
% 0.87/0.89 cnf(265,plain,
% 0.87/0.89 (P1(f2(x2651,a1),x2651)),
% 0.87/0.89 inference(rename_variables,[],[172])).
% 0.87/0.89 cnf(267,plain,
% 0.87/0.89 (~P2(f2(a1,a1),f5(a3,a1),f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[33,31,172,262,265,223,238,181,118,19,11,20,18,17])).
% 0.87/0.89 cnf(268,plain,
% 0.87/0.89 (P1(f2(x2681,a1),x2681)),
% 0.87/0.89 inference(rename_variables,[],[172])).
% 0.87/0.89 cnf(270,plain,
% 0.87/0.89 (~P2(f4(f5(a3,a1)),f2(a1,a1),f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[33,31,110,172,262,265,268,223,238,181,118,19,11,20,18,17,16])).
% 0.87/0.89 cnf(273,plain,
% 0.87/0.89 (P2(x2731,f4(x2731),f2(a1,a1))),
% 0.87/0.89 inference(scs_inference,[],[33,4,31,259,110,172,262,265,268,223,238,181,118,19,11,20,18,17,16,15])).
% 0.87/0.89 cnf(276,plain,
% 0.87/0.89 (~P2(f5(a1,a1),f5(a3,a1),f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[33,4,31,259,110,245,172,262,265,268,223,238,181,118,19,11,20,18,17,16,15,14])).
% 0.87/0.89 cnf(280,plain,
% 0.87/0.89 (P3(f2(x2801,a1),x2802,f5(x2801,x2802))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(281,plain,
% 0.87/0.89 (P3(x2811,x2812,f5(x2811,x2812))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(284,plain,
% 0.87/0.89 (P2(f4(x2841),x2841,a1)),
% 0.87/0.89 inference(rename_variables,[],[5])).
% 0.87/0.89 cnf(287,plain,
% 0.87/0.89 (P1(f5(x2871,f2(x2871,a1)),f5(x2871,x2871))),
% 0.87/0.89 inference(scs_inference,[],[33,256,4,5,3,31,259,7,110,245,234,172,262,265,268,223,238,181,35,118,19,11,20,18,17,16,15,14,25,23,9])).
% 0.87/0.89 cnf(289,plain,
% 0.87/0.89 (P3(x2891,f5(x2892,x2893),f5(f5(x2891,x2892),x2893))),
% 0.87/0.89 inference(scs_inference,[],[33,256,280,4,5,3,31,259,7,281,110,245,234,172,262,265,268,223,238,181,38,35,118,19,11,20,18,17,16,15,14,25,23,9,26])).
% 0.87/0.89 cnf(291,plain,
% 0.87/0.89 (P3(f2(x2911,a1),x2912,f5(x2911,x2912))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(296,plain,
% 0.87/0.89 (P3(f2(x2961,a1),x2962,f5(x2961,x2962))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(299,plain,
% 0.87/0.89 (~P3(f2(a3,a1),a1,f4(a1))),
% 0.87/0.89 inference(scs_inference,[],[2,33,256,280,291,296,4,5,3,31,259,7,281,110,245,234,172,262,265,268,223,238,181,38,179,35,118,19,11,20,18,17,16,15,14,25,23,9,26,27,22])).
% 0.87/0.89 cnf(302,plain,
% 0.87/0.89 (~P2(f4(x3021),x3021,f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[2,33,256,280,291,296,4,5,284,3,31,259,7,281,110,245,234,172,262,265,268,223,238,181,139,38,179,35,118,19,11,20,18,17,16,15,14,25,23,9,26,27,22,21])).
% 0.87/0.89 cnf(317,plain,
% 0.87/0.89 (P1(x3171,f2(x3171,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(319,plain,
% 0.87/0.89 (P3(f2(x3191,a1),f2(a1,x3192),f5(x3191,x3192))),
% 0.87/0.89 inference(scs_inference,[],[33,31,250,20,19])).
% 0.87/0.89 cnf(320,plain,
% 0.87/0.89 (P1(x3201,f2(a1,x3201))),
% 0.87/0.89 inference(rename_variables,[],[250])).
% 0.87/0.89 cnf(323,plain,
% 0.87/0.89 (P1(x3231,f2(x3231,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(328,plain,
% 0.87/0.89 (P2(x3281,x3282,f2(x3281,x3282))),
% 0.87/0.89 inference(rename_variables,[],[6])).
% 0.87/0.89 cnf(331,plain,
% 0.87/0.89 (P2(x3311,a1,x3311)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(334,plain,
% 0.87/0.89 (P1(x3341,f2(x3341,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(339,plain,
% 0.87/0.89 (P2(x3391,x3392,f2(x3391,f2(x3392,a1)))),
% 0.87/0.89 inference(scs_inference,[],[2,331,33,6,328,4,31,317,323,334,287,94,250,172,20,19,11,24,15,18,17,16])).
% 0.87/0.89 cnf(342,plain,
% 0.87/0.89 (P2(f4(x3421),x3421,f2(a1,a1))),
% 0.87/0.89 inference(scs_inference,[],[2,331,33,6,328,4,31,317,323,334,273,287,94,250,172,20,19,11,24,15,18,17,16,14])).
% 0.87/0.89 cnf(346,plain,
% 0.87/0.89 (P3(f2(x3461,a1),x3462,f5(x3461,x3462))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(348,plain,
% 0.87/0.89 (~P1(f5(a3,a1),f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[2,331,33,6,328,4,31,317,323,334,273,258,287,94,250,255,172,20,19,11,24,15,18,17,16,14,25,9])).
% 0.87/0.89 cnf(350,plain,
% 0.87/0.89 (P2(f5(a1,x3501),f5(x3502,x3501),f5(x3502,x3501))),
% 0.87/0.89 inference(scs_inference,[],[2,331,33,346,6,328,3,4,31,317,323,334,7,273,258,287,94,250,255,172,20,19,11,24,15,18,17,16,14,25,9,28])).
% 0.87/0.89 cnf(352,plain,
% 0.87/0.89 (P3(f2(x3521,a1),x3522,f5(x3521,x3522))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(353,plain,
% 0.87/0.89 (P2(a1,x3531,x3531)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(354,plain,
% 0.87/0.89 (P3(x3541,x3542,f5(x3541,x3542))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(359,plain,
% 0.87/0.89 (P2(x3591,a1,x3591)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(360,plain,
% 0.87/0.89 (P3(f2(x3601,a1),x3602,f5(x3601,x3602))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(362,plain,
% 0.87/0.89 (~P2(a1,f5(a3,a1),f4(a1))),
% 0.87/0.89 inference(scs_inference,[],[2,331,359,33,346,352,6,328,3,353,4,31,317,323,334,7,354,302,273,258,287,94,250,255,172,20,19,11,24,15,18,17,16,14,25,9,28,27,23])).
% 0.87/0.89 cnf(364,plain,
% 0.87/0.89 (P2(x3641,a1,x3641)),
% 0.87/0.89 inference(rename_variables,[],[2])).
% 0.87/0.89 cnf(367,plain,
% 0.87/0.89 (~P3(f2(a3,a1),a1,f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[2,331,359,33,346,352,360,6,328,3,353,4,31,317,323,334,7,354,302,273,258,287,94,250,255,172,20,19,11,24,15,18,17,16,14,25,9,28,27,23,22])).
% 0.87/0.89 cnf(370,plain,
% 0.87/0.89 (~P2(f5(a3,a1),a1,f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[2,331,359,364,33,346,352,360,6,328,3,353,4,31,317,323,334,7,354,302,273,258,287,94,250,255,172,20,19,11,24,15,18,17,16,14,25,9,28,27,23,22,21])).
% 0.87/0.89 cnf(375,plain,
% 0.87/0.89 (P1(f5(x3751,x3752),f5(f2(a1,x3751),x3752))),
% 0.87/0.89 inference(scs_inference,[],[2,331,359,364,33,346,352,360,6,328,3,353,4,31,317,323,334,7,354,302,273,258,287,94,250,320,255,172,20,19,11,24,15,18,17,16,14,25,9,28,27,23,22,21,10,13])).
% 0.87/0.89 cnf(377,plain,
% 0.87/0.89 (P1(f2(x3771,x3772),f2(f2(a1,x3771),x3772))),
% 0.87/0.89 inference(scs_inference,[],[2,331,359,364,33,346,352,360,6,328,3,353,4,31,317,323,334,7,354,302,273,258,287,94,250,320,255,172,20,19,11,24,15,18,17,16,14,25,9,28,27,23,22,21,10,13,12])).
% 0.87/0.89 cnf(393,plain,
% 0.87/0.89 (~P3(a3,a1,f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[31,377,367,11,20])).
% 0.87/0.89 cnf(394,plain,
% 0.87/0.89 (P1(x3941,f2(x3941,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(396,plain,
% 0.87/0.89 (~P1(a1,f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[3,31,377,367,302,11,20,17])).
% 0.87/0.89 cnf(397,plain,
% 0.87/0.89 (P2(a1,x3971,x3971)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(400,plain,
% 0.87/0.89 (P2(x4001,f2(x4002,a1),f2(x4001,x4002))),
% 0.87/0.89 inference(scs_inference,[],[3,6,31,394,377,367,302,11,20,17,16])).
% 0.87/0.89 cnf(401,plain,
% 0.87/0.89 (P2(x4011,x4012,f2(x4011,x4012))),
% 0.87/0.89 inference(rename_variables,[],[6])).
% 0.87/0.89 cnf(403,plain,
% 0.87/0.89 (P2(a1,a1,f2(f4(x4031),x4031))),
% 0.87/0.89 inference(scs_inference,[],[3,397,6,401,5,31,394,377,367,302,11,20,17,16,24])).
% 0.87/0.89 cnf(404,plain,
% 0.87/0.89 (P2(f4(x4041),x4041,a1)),
% 0.87/0.89 inference(rename_variables,[],[5])).
% 0.87/0.89 cnf(405,plain,
% 0.87/0.89 (P2(a1,x4051,x4051)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(406,plain,
% 0.87/0.89 (P2(x4061,x4062,f2(x4061,x4062))),
% 0.87/0.89 inference(rename_variables,[],[6])).
% 0.87/0.89 cnf(410,plain,
% 0.87/0.89 (~P1(f4(f5(a3,a1)),a1)),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,6,401,5,31,394,270,377,367,212,302,11,20,17,16,24,14,15])).
% 0.87/0.89 cnf(411,plain,
% 0.87/0.89 (P2(a1,x4111,x4111)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(416,plain,
% 0.87/0.89 (P1(f5(f2(x4161,a1),x4162),f5(x4161,x4162))),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,35,6,401,5,31,394,270,92,377,367,212,302,11,20,17,16,24,14,15,18,9])).
% 0.87/0.89 cnf(418,plain,
% 0.87/0.89 (~P2(f5(a3,a1),f5(a3,a1),f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,411,35,6,401,5,33,31,394,270,92,377,367,212,302,11,20,17,16,24,14,15,18,9,30])).
% 0.87/0.89 cnf(419,plain,
% 0.87/0.89 (P2(a1,x4191,x4191)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(421,plain,
% 0.87/0.89 (P3(f2(x4211,a1),x4212,f5(x4211,x4212))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(423,plain,
% 0.87/0.89 (P2(f5(a1,a1),f5(a1,f2(a1,a1)),f5(a1,a1))),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,411,419,35,6,401,5,33,31,394,7,270,92,377,367,212,302,11,20,17,16,24,14,15,18,9,30,28])).
% 0.87/0.89 cnf(424,plain,
% 0.87/0.89 (P3(x4241,x4242,f5(x4241,x4242))),
% 0.87/0.89 inference(rename_variables,[],[7])).
% 0.87/0.89 cnf(425,plain,
% 0.87/0.89 (P2(a1,x4251,x4251)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(427,plain,
% 0.87/0.89 (P3(x4271,f2(x4271,a1),f5(x4271,x4271))),
% 0.87/0.89 inference(rename_variables,[],[35])).
% 0.87/0.89 cnf(429,plain,
% 0.87/0.89 (~P3(f2(a3,a1),a1,a1)),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,411,419,425,35,6,401,5,33,421,31,394,7,270,92,377,367,212,302,101,11,20,17,16,24,14,15,18,9,30,28,27])).
% 0.87/0.89 cnf(431,plain,
% 0.87/0.89 (P2(a1,x4311,x4311)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(435,plain,
% 0.87/0.89 (P2(x4351,x4352,f2(x4351,x4352))),
% 0.87/0.89 inference(rename_variables,[],[6])).
% 0.87/0.89 cnf(444,plain,
% 0.87/0.89 (P1(f2(f4(x4441),x4441),a1)),
% 0.87/0.89 inference(scs_inference,[],[3,397,405,411,419,425,431,35,427,6,401,406,435,5,404,33,421,31,394,7,424,270,92,377,217,319,367,212,302,101,11,20,17,16,24,14,15,18,9,30,28,27,23,26,22,21])).
% 0.87/0.89 cnf(458,plain,
% 0.87/0.89 (~P2(f2(f4(x4581),x4581),f5(a3,a1),f4(a1))),
% 0.87/0.89 inference(scs_inference,[],[362,444,17])).
% 0.87/0.89 cnf(461,plain,
% 0.87/0.89 (P1(x4611,f2(x4611,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(463,plain,
% 0.87/0.89 (P3(x4631,f2(f2(x4631,a1),a1),f5(x4631,x4631))),
% 0.87/0.89 inference(scs_inference,[],[35,31,461,362,444,396,17,11,19])).
% 0.87/0.89 cnf(464,plain,
% 0.87/0.89 (P1(x4641,f2(x4641,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(467,plain,
% 0.87/0.89 (P1(x4671,f2(x4671,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(477,plain,
% 0.87/0.89 (~P2(f2(a1,a1),f4(a1),f5(a3,a1))),
% 0.87/0.89 inference(scs_inference,[],[3,35,6,31,461,464,467,429,210,416,362,444,396,299,17,11,19,15,20,18,16,24])).
% 0.87/0.89 cnf(478,plain,
% 0.87/0.89 (P2(a1,x4781,x4781)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(485,plain,
% 0.87/0.89 (~P3(f2(a3,a1),f2(a1,a1),f4(f5(a3,a1)))),
% 0.87/0.89 inference(scs_inference,[],[3,478,35,6,31,461,464,467,429,210,339,276,416,362,444,185,396,299,255,17,11,19,15,20,18,16,24,14,9,28])).
% 0.87/0.89 cnf(486,plain,
% 0.87/0.89 (P2(a1,x4861,x4861)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(487,plain,
% 0.87/0.89 (P3(x4871,f2(x4871,a1),f5(x4871,x4871))),
% 0.87/0.89 inference(rename_variables,[],[35])).
% 0.87/0.89 cnf(488,plain,
% 0.87/0.89 (P3(f2(x4881,a1),f2(x4882,a1),f5(x4881,x4882))),
% 0.87/0.89 inference(rename_variables,[],[255])).
% 0.87/0.89 cnf(490,plain,
% 0.87/0.89 (~P2(f5(a1,a1),f2(f5(a3,a1),f5(a3,a1)),f4(a1))),
% 0.87/0.89 inference(scs_inference,[],[3,478,486,35,6,4,31,461,464,467,429,210,339,276,416,362,444,185,396,299,255,174,17,11,19,15,20,18,16,24,14,9,28,23])).
% 0.87/0.89 cnf(492,plain,
% 0.87/0.89 (P2(a1,x4921,x4921)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(494,plain,
% 0.87/0.89 (P1(f5(x4941,x4941),f2(f5(x4941,a1),f5(x4941,x4941)))),
% 0.87/0.89 inference(scs_inference,[],[3,478,486,35,487,6,4,31,461,464,467,429,210,339,276,416,362,444,185,396,299,217,255,174,17,11,19,15,20,18,16,24,14,9,28,23,22])).
% 0.87/0.89 cnf(497,plain,
% 0.87/0.89 (~P2(a1,f5(a3,a1),f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[3,478,486,492,35,487,6,4,31,461,464,467,429,210,339,276,348,416,362,444,185,396,299,217,255,174,17,11,19,15,20,18,16,24,14,9,28,23,22,21])).
% 0.87/0.89 cnf(498,plain,
% 0.87/0.89 (P2(a1,x4981,x4981)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(502,plain,
% 0.87/0.89 (~P2(f2(f5(a1,a1),f5(a1,a1)),f5(a3,a1),a1)),
% 0.87/0.89 inference(scs_inference,[],[3,478,486,492,498,35,487,6,4,33,31,461,464,467,429,210,339,276,348,416,362,444,185,396,299,217,255,174,49,17,11,19,15,20,18,16,24,14,9,28,23,22,21,25,29])).
% 0.87/0.89 cnf(504,plain,
% 0.87/0.89 (P3(f2(x5041,a1),x5042,f5(x5041,x5042))),
% 0.87/0.89 inference(rename_variables,[],[33])).
% 0.87/0.89 cnf(505,plain,
% 0.87/0.89 (P2(a1,x5051,x5051)),
% 0.87/0.89 inference(rename_variables,[],[3])).
% 0.87/0.89 cnf(507,plain,
% 0.87/0.89 (~P3(f2(a3,a1),f2(a1,a1),f2(f4(a1),a1))),
% 0.87/0.89 inference(scs_inference,[],[3,478,486,492,498,505,35,487,6,4,33,504,31,461,464,467,429,210,418,339,276,348,416,362,444,185,396,299,217,255,488,174,49,17,11,19,15,20,18,16,24,14,9,28,23,22,21,25,29,27])).
% 0.87/0.89 cnf(525,plain,
% 0.87/0.89 (P1(x5251,f2(x5251,a1))),
% 0.87/0.89 inference(rename_variables,[],[31])).
% 0.87/0.89 cnf(528,plain,
% 0.87/0.89 (P1(x5281,f2(x5281,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(530,plain,
% 0.87/0.90 (P1(f4(a1),f2(a1,a1))),
% 0.87/0.90 inference(scs_inference,[],[4,31,525,528,393,123,19,17,16,11])).
% 0.87/0.90 cnf(531,plain,
% 0.87/0.90 (P1(x5311,f2(x5311,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(533,plain,
% 0.87/0.90 (~P2(f5(a1,a1),f5(a3,a1),f4(a1))),
% 0.87/0.90 inference(scs_inference,[],[4,31,525,528,393,350,477,210,123,19,17,16,11,24])).
% 0.87/0.90 cnf(540,plain,
% 0.87/0.90 (P1(x5401,f2(x5401,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(546,plain,
% 0.87/0.90 (P1(f5(x5461,x5462),f5(f2(a1,x5461),x5462))),
% 0.87/0.90 inference(rename_variables,[],[375])).
% 0.87/0.90 cnf(551,plain,
% 0.87/0.90 (P2(x5511,x5512,f2(x5511,x5512))),
% 0.87/0.90 inference(rename_variables,[],[6])).
% 0.87/0.90 cnf(557,plain,
% 0.87/0.90 (P1(f5(f2(a1,x5571),x5572),f5(x5571,x5572))),
% 0.87/0.90 inference(scs_inference,[],[4,35,6,551,33,31,525,528,531,540,289,393,267,375,546,350,458,477,490,370,403,106,210,123,19,17,16,11,24,14,15,20,18,28,23,9])).
% 0.87/0.90 cnf(559,plain,
% 0.87/0.90 (~P2(x5591,f4(x5591),f4(f5(a3,a1)))),
% 0.87/0.90 inference(scs_inference,[],[4,35,6,551,33,31,525,528,531,540,289,393,267,375,546,350,458,477,490,370,410,403,106,210,123,19,17,16,11,24,14,15,20,18,28,23,9,21])).
% 0.87/0.90 cnf(575,plain,
% 0.87/0.90 (P2(f4(x5751),x5751,a1)),
% 0.87/0.90 inference(rename_variables,[],[5])).
% 0.87/0.90 cnf(578,plain,
% 0.87/0.90 (P2(x5781,x5782,f2(x5781,x5782))),
% 0.87/0.90 inference(rename_variables,[],[6])).
% 0.87/0.90 cnf(580,plain,
% 0.87/0.90 (~P3(a3,f2(a1,a1),f2(f4(a1),a1))),
% 0.87/0.90 inference(scs_inference,[],[5,6,31,507,533,16,15,20])).
% 0.87/0.90 cnf(581,plain,
% 0.87/0.90 (P1(x5811,f2(x5811,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(589,plain,
% 0.87/0.90 (P2(x5891,x5892,f2(x5891,x5892))),
% 0.87/0.90 inference(rename_variables,[],[6])).
% 0.87/0.90 cnf(591,plain,
% 0.87/0.90 (P1(f5(f2(a1,x5911),f2(x5911,a1)),f5(x5911,x5911))),
% 0.87/0.90 inference(scs_inference,[],[5,6,578,7,31,581,342,507,557,533,287,101,16,15,20,17,27,11])).
% 0.87/0.90 cnf(596,plain,
% 0.87/0.90 (P2(x5961,f2(x5962,a1),f2(x5961,x5962))),
% 0.87/0.90 inference(rename_variables,[],[400])).
% 0.87/0.90 cnf(597,plain,
% 0.87/0.90 (P2(f4(x5971),x5971,a1)),
% 0.87/0.90 inference(rename_variables,[],[5])).
% 0.87/0.90 cnf(604,plain,
% 0.87/0.90 (P2(f2(x6041,a1),x6042,f2(x6042,x6041))),
% 0.87/0.90 inference(scs_inference,[],[4,5,575,597,6,578,589,7,31,581,342,507,557,400,596,533,497,287,101,16,15,20,17,27,11,24,23,14])).
% 0.87/0.90 cnf(606,plain,
% 0.87/0.90 (~P1(a1,f2(f5(a3,a1),a1))),
% 0.87/0.90 inference(scs_inference,[],[4,5,575,597,6,578,589,7,31,581,342,507,557,400,596,533,497,136,287,101,16,15,20,17,27,11,24,23,14,9])).
% 0.87/0.90 cnf(629,plain,
% 0.87/0.90 (P1(x6291,f2(x6291,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(632,plain,
% 0.87/0.90 (~P2(x6321,f4(x6321),f4(f5(a3,a1)))),
% 0.87/0.90 inference(rename_variables,[],[559])).
% 0.87/0.90 cnf(636,plain,
% 0.87/0.90 (P2(f4(x6361),x6361,a1)),
% 0.87/0.90 inference(rename_variables,[],[5])).
% 0.87/0.90 cnf(639,plain,
% 0.87/0.90 (P2(f2(x6391,a1),x6392,f2(x6392,x6391))),
% 0.87/0.90 inference(rename_variables,[],[604])).
% 0.87/0.90 cnf(640,plain,
% 0.87/0.90 (P2(f4(x6401),x6401,a1)),
% 0.87/0.90 inference(rename_variables,[],[5])).
% 0.87/0.90 cnf(646,plain,
% 0.87/0.90 (P1(x6461,f2(x6461,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(656,plain,
% 0.87/0.90 (~P2(f4(x6561),x6561,f2(f5(a3,a1),a1))),
% 0.87/0.90 inference(scs_inference,[],[5,636,640,31,629,646,559,632,494,591,96,604,639,423,502,606,485,302,20,16,23,24,14,15,17,11,9,21])).
% 0.87/0.90 cnf(668,plain,
% 0.87/0.90 (P1(x6681,f2(x6681,a1))),
% 0.87/0.90 inference(rename_variables,[],[31])).
% 0.87/0.90 cnf(683,plain,
% 0.87/0.90 (P2(f4(x6831),x6831,a1)),
% 0.87/0.90 inference(rename_variables,[],[5])).
% 0.87/0.90 cnf(685,plain,
% 0.87/0.90 ($false),
% 0.87/0.90 inference(scs_inference,[],[5,683,38,35,33,31,668,656,580,463,530,67,212,73,18,23,20,26,17,16,24]),
% 0.87/0.90 ['proof']).
% 0.87/0.90 % SZS output end Proof
% 0.87/0.90 % Total time :0.260000s
%------------------------------------------------------------------------------