TSTP Solution File: GEO039-2 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO039-2 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:42:35 EDT 2023
% Result : Unsatisfiable 1.69s 1.79s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 21:36:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 1.69/1.79 %-------------------------------------------
% 1.69/1.79 % File :CSE---1.6
% 1.69/1.79 % Problem :theBenchmark
% 1.69/1.79 % Transform :cnf
% 1.69/1.79 % Format :tptp:raw
% 1.69/1.79 % Command :java -jar mcs_scs.jar %d %s
% 1.69/1.79
% 1.69/1.79 % Result :Theorem 1.170000s
% 1.69/1.79 % Output :CNFRefutation 1.170000s
% 1.69/1.79 %-------------------------------------------
% 1.69/1.79 %--------------------------------------------------------------------------
% 1.69/1.79 % File : GEO039-2 : TPTP v8.1.2. Released v1.0.0.
% 1.69/1.79 % Domain : Geometry
% 1.69/1.79 % Problem : Corollary the identity axiom for betweenness
% 1.69/1.79 % Version : [Qua89] axioms.
% 1.69/1.79 % English :
% 1.69/1.79
% 1.69/1.79 % Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% 1.69/1.79 % : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% 1.69/1.79 % Source : [TPTP]
% 1.69/1.79 % Names :
% 1.69/1.79
% 1.69/1.79 % Status : Unsatisfiable
% 1.69/1.79 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.29 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.13 v6.3.0, 0.18 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.20 v5.5.0, 0.30 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.27 v3.7.0, 0.10 v3.5.0, 0.18 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0, 0.15 v3.1.0, 0.18 v2.7.0, 0.17 v2.6.0, 0.10 v2.5.0, 0.08 v2.4.0, 0.00 v2.2.0, 0.22 v2.1.0, 0.22 v2.0.0
% 1.69/1.79 % Syntax : Number of clauses : 21 ( 9 unt; 5 nHn; 18 RR)
% 1.69/1.79 % Number of literals : 59 ( 8 equ; 35 neg)
% 1.69/1.79 % Maximal clause size : 8 ( 2 avg)
% 1.69/1.79 % Maximal term depth : 2 ( 1 avg)
% 1.69/1.79 % Number of predicates : 3 ( 2 usr; 0 prp; 2-4 aty)
% 1.69/1.79 % Number of functors : 12 ( 12 usr; 7 con; 0-6 aty)
% 1.69/1.79 % Number of variables : 71 ( 3 sgn)
% 1.69/1.79 % SPC : CNF_UNS_RFO_SEQ_NHN
% 1.69/1.79
% 1.69/1.79 % Comments : Proving corollaries from axioms is not usual.
% 1.69/1.79 %--------------------------------------------------------------------------
% 1.69/1.79 %----Include Tarski geometry axioms
% 1.69/1.79 include('Axioms/GEO002-0.ax').
% 1.69/1.79 %--------------------------------------------------------------------------
% 1.69/1.79 cnf(w_between_u_and_x,hypothesis,
% 1.69/1.79 between(u,w,x) ).
% 1.69/1.79
% 1.69/1.79 cnf(u_is_x,hypothesis,
% 1.69/1.79 u = x ).
% 1.69/1.79
% 1.69/1.79 cnf(prove_corollary,negated_conjecture,
% 1.69/1.79 ~ between(v,w,x) ).
% 1.69/1.79
% 1.69/1.79 %--------------------------------------------------------------------------
% 1.69/1.79 %-------------------------------------------
% 1.69/1.79 % Proof found
% 1.69/1.79 % SZS status Theorem for theBenchmark
% 1.69/1.79 % SZS output start Proof
% 1.69/1.80 %ClaNum:56(EqnAxiom:35)
% 1.69/1.80 %VarNum:211(SingletonVarNum:71)
% 1.69/1.80 %MaxLitNum:8
% 1.69/1.80 %MaxfuncDepth:1
% 1.69/1.80 %SharedTerms:13
% 1.69/1.80 %goalClause: 44
% 1.69/1.80 %singleGoalClaCount:1
% 1.69/1.80 [36]E(a1,a2)
% 1.69/1.80 [37]P1(a2,a11,a1)
% 1.69/1.80 [41]~P1(a7,a9,a10)
% 1.69/1.80 [42]~P1(a9,a10,a7)
% 1.69/1.80 [43]~P1(a10,a7,a9)
% 1.69/1.80 [44]~P1(a12,a11,a1)
% 1.69/1.80 [38]P2(x381,x382,x382,x381)
% 1.69/1.80 [39]P1(x391,x392,f3(x391,x392,x393,x394))
% 1.69/1.80 [40]P2(x401,f3(x402,x401,x403,x404),x403,x404)
% 1.69/1.80 [45]~P1(x451,x452,x451)+E(x451,x452)
% 1.69/1.80 [46]~P2(x461,x462,x463,x463)+E(x461,x462)
% 1.69/1.80 [50]~P1(x505,x501,x504)+~P1(x502,x503,x504)+P1(x501,f8(x502,x503,x504,x501,x505),x502)
% 1.69/1.80 [51]~P1(x515,x514,x513)+~P1(x512,x511,x513)+P1(x511,f8(x512,x511,x513,x514,x515),x515)
% 1.69/1.80 [47]~P2(x475,x476,x471,x472)+P2(x471,x472,x473,x474)+~P2(x475,x476,x473,x474)
% 1.69/1.80 [52]~P1(x524,x522,x523)+~P1(x521,x522,x525)+E(x521,x522)+P1(x521,x523,f4(x521,x524,x522,x523,x525))
% 1.69/1.80 [53]~P1(x533,x532,x534)+~P1(x531,x532,x535)+E(x531,x532)+P1(x531,x533,f5(x531,x533,x532,x534,x535))
% 1.69/1.80 [54]~P1(x543,x542,x544)+~P1(x541,x542,x545)+E(x541,x542)+P1(f5(x541,x543,x542,x544,x545),x545,f4(x541,x543,x542,x544,x545))
% 1.69/1.80 [55]~P1(x553,x554,x555)+~P1(x552,x553,x555)+~P2(x552,x555,x552,x556)+~P2(x552,x553,x552,x551)+P1(x551,f6(x552,x553,x551,x554,x555,x556),x556)
% 1.69/1.80 [56]~P1(x563,x562,x565)+~P1(x561,x563,x565)+~P2(x561,x565,x561,x566)+~P2(x561,x563,x561,x564)+P2(x561,x562,x561,f6(x561,x563,x564,x562,x565,x566))
% 1.69/1.80 [48]P1(x485,x483,x484)+P1(x484,x485,x483)+~P2(x483,x481,x483,x482)+~P2(x485,x481,x485,x482)+~P2(x484,x481,x484,x482)+E(x481,x482)+P1(x483,x484,x485)
% 1.69/1.80 [49]~P1(x491,x492,x493)+~P2(x492,x494,x498,x496)+~P2(x492,x493,x498,x495)+~P2(x491,x494,x497,x496)+~P2(x491,x492,x497,x498)+E(x491,x492)+P2(x493,x494,x495,x496)+~P1(x497,x498,x495)
% 1.69/1.80 %EqnAxiom
% 1.69/1.80 [1]E(x11,x11)
% 1.69/1.80 [2]E(x22,x21)+~E(x21,x22)
% 1.69/1.80 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.69/1.80 [4]~E(x41,x42)+E(f3(x41,x43,x44,x45),f3(x42,x43,x44,x45))
% 1.69/1.80 [5]~E(x51,x52)+E(f3(x53,x51,x54,x55),f3(x53,x52,x54,x55))
% 1.69/1.80 [6]~E(x61,x62)+E(f3(x63,x64,x61,x65),f3(x63,x64,x62,x65))
% 1.69/1.80 [7]~E(x71,x72)+E(f3(x73,x74,x75,x71),f3(x73,x74,x75,x72))
% 1.69/1.80 [8]~E(x81,x82)+E(f6(x81,x83,x84,x85,x86,x87),f6(x82,x83,x84,x85,x86,x87))
% 1.69/1.80 [9]~E(x91,x92)+E(f6(x93,x91,x94,x95,x96,x97),f6(x93,x92,x94,x95,x96,x97))
% 1.69/1.80 [10]~E(x101,x102)+E(f6(x103,x104,x101,x105,x106,x107),f6(x103,x104,x102,x105,x106,x107))
% 1.69/1.80 [11]~E(x111,x112)+E(f6(x113,x114,x115,x111,x116,x117),f6(x113,x114,x115,x112,x116,x117))
% 1.69/1.80 [12]~E(x121,x122)+E(f6(x123,x124,x125,x126,x121,x127),f6(x123,x124,x125,x126,x122,x127))
% 1.69/1.80 [13]~E(x131,x132)+E(f6(x133,x134,x135,x136,x137,x131),f6(x133,x134,x135,x136,x137,x132))
% 1.69/1.80 [14]~E(x141,x142)+E(f8(x141,x143,x144,x145,x146),f8(x142,x143,x144,x145,x146))
% 1.69/1.80 [15]~E(x151,x152)+E(f8(x153,x151,x154,x155,x156),f8(x153,x152,x154,x155,x156))
% 1.69/1.80 [16]~E(x161,x162)+E(f8(x163,x164,x161,x165,x166),f8(x163,x164,x162,x165,x166))
% 1.69/1.80 [17]~E(x171,x172)+E(f8(x173,x174,x175,x171,x176),f8(x173,x174,x175,x172,x176))
% 1.69/1.80 [18]~E(x181,x182)+E(f8(x183,x184,x185,x186,x181),f8(x183,x184,x185,x186,x182))
% 1.69/1.80 [19]~E(x191,x192)+E(f4(x191,x193,x194,x195,x196),f4(x192,x193,x194,x195,x196))
% 1.69/1.80 [20]~E(x201,x202)+E(f4(x203,x201,x204,x205,x206),f4(x203,x202,x204,x205,x206))
% 1.69/1.80 [21]~E(x211,x212)+E(f4(x213,x214,x211,x215,x216),f4(x213,x214,x212,x215,x216))
% 1.69/1.80 [22]~E(x221,x222)+E(f4(x223,x224,x225,x221,x226),f4(x223,x224,x225,x222,x226))
% 1.69/1.80 [23]~E(x231,x232)+E(f4(x233,x234,x235,x236,x231),f4(x233,x234,x235,x236,x232))
% 1.69/1.80 [24]~E(x241,x242)+E(f5(x241,x243,x244,x245,x246),f5(x242,x243,x244,x245,x246))
% 1.69/1.80 [25]~E(x251,x252)+E(f5(x253,x251,x254,x255,x256),f5(x253,x252,x254,x255,x256))
% 1.69/1.80 [26]~E(x261,x262)+E(f5(x263,x264,x261,x265,x266),f5(x263,x264,x262,x265,x266))
% 1.69/1.80 [27]~E(x271,x272)+E(f5(x273,x274,x275,x271,x276),f5(x273,x274,x275,x272,x276))
% 1.69/1.80 [28]~E(x281,x282)+E(f5(x283,x284,x285,x286,x281),f5(x283,x284,x285,x286,x282))
% 1.69/1.80 [29]P1(x292,x293,x294)+~E(x291,x292)+~P1(x291,x293,x294)
% 1.69/1.80 [30]P1(x303,x302,x304)+~E(x301,x302)+~P1(x303,x301,x304)
% 1.69/1.80 [31]P1(x313,x314,x312)+~E(x311,x312)+~P1(x313,x314,x311)
% 1.69/1.80 [32]P2(x322,x323,x324,x325)+~E(x321,x322)+~P2(x321,x323,x324,x325)
% 1.69/1.80 [33]P2(x333,x332,x334,x335)+~E(x331,x332)+~P2(x333,x331,x334,x335)
% 1.69/1.80 [34]P2(x343,x344,x342,x345)+~E(x341,x342)+~P2(x343,x344,x341,x345)
% 1.69/1.80 [35]P2(x353,x354,x355,x352)+~E(x351,x352)+~P2(x353,x354,x355,x351)
% 1.69/1.80
% 1.69/1.80 %-------------------------------------------
% 1.69/1.80 cnf(57,plain,
% 1.69/1.80 (E(a2,a1)),
% 1.69/1.80 inference(scs_inference,[],[36,2])).
% 1.69/1.80 cnf(58,plain,
% 1.69/1.80 (P2(a1,x581,x581,a2)),
% 1.69/1.80 inference(scs_inference,[],[38,36,2,35])).
% 1.69/1.80 cnf(59,plain,
% 1.69/1.80 (P2(x591,x592,x592,x591)),
% 1.69/1.80 inference(rename_variables,[],[38])).
% 1.69/1.80 cnf(60,plain,
% 1.69/1.80 (P2(x601,a1,a2,x601)),
% 1.69/1.80 inference(scs_inference,[],[38,59,36,2,35,34])).
% 1.69/1.80 cnf(61,plain,
% 1.69/1.80 (P2(x611,x612,x612,x611)),
% 1.69/1.80 inference(rename_variables,[],[38])).
% 1.69/1.80 cnf(62,plain,
% 1.69/1.80 (P2(x621,a2,a1,x621)),
% 1.69/1.80 inference(scs_inference,[],[38,59,61,36,2,35,34,33])).
% 1.69/1.80 cnf(63,plain,
% 1.69/1.80 (P2(x631,x632,x632,x631)),
% 1.69/1.80 inference(rename_variables,[],[38])).
% 1.69/1.80 cnf(64,plain,
% 1.69/1.80 (P2(a2,x641,x641,a1)),
% 1.69/1.80 inference(scs_inference,[],[38,59,61,63,36,2,35,34,33,32])).
% 1.69/1.80 cnf(65,plain,
% 1.69/1.80 (P2(x651,x652,x652,x651)),
% 1.69/1.80 inference(rename_variables,[],[38])).
% 1.69/1.80 cnf(66,plain,
% 1.69/1.80 (P1(a2,a11,a2)),
% 1.69/1.80 inference(scs_inference,[],[38,59,61,63,36,37,2,35,34,33,32,31])).
% 1.69/1.80 cnf(67,plain,
% 1.69/1.80 (P1(x671,a2,f3(x671,a1,x672,x673))),
% 1.69/1.80 inference(scs_inference,[],[38,59,61,63,36,37,39,2,35,34,33,32,31,30])).
% 1.69/1.80 cnf(68,plain,
% 1.69/1.80 (P1(x681,x682,f3(x681,x682,x683,x684))),
% 1.69/1.80 inference(rename_variables,[],[39])).
% 1.69/1.80 cnf(69,plain,
% 1.69/1.80 (~E(a2,a12)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,36,37,39,2,35,34,33,32,31,30,29])).
% 1.69/1.80 cnf(70,plain,
% 1.69/1.80 (P2(x701,x702,x701,x702)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,39,2,35,34,33,32,31,30,29,47])).
% 1.69/1.80 cnf(72,plain,
% 1.69/1.80 (E(x721,f3(x722,x721,x723,x723))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46])).
% 1.69/1.80 cnf(75,plain,
% 1.69/1.80 (E(a2,a11)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45])).
% 1.69/1.80 cnf(92,plain,
% 1.69/1.80 (E(f6(x921,x922,x923,x924,x925,a1),f6(x921,x922,x923,x924,x925,a2))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13])).
% 1.69/1.80 cnf(93,plain,
% 1.69/1.80 (E(f6(x931,x932,x933,x934,a1,x935),f6(x931,x932,x933,x934,a2,x935))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12])).
% 1.69/1.80 cnf(94,plain,
% 1.69/1.80 (E(f6(x941,x942,x943,a1,x944,x945),f6(x941,x942,x943,a2,x944,x945))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11])).
% 1.69/1.80 cnf(95,plain,
% 1.69/1.80 (E(f6(x951,x952,a1,x953,x954,x955),f6(x951,x952,a2,x953,x954,x955))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10])).
% 1.69/1.80 cnf(96,plain,
% 1.69/1.80 (E(f6(x961,a1,x962,x963,x964,x965),f6(x961,a2,x962,x963,x964,x965))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9])).
% 1.69/1.80 cnf(98,plain,
% 1.69/1.80 (E(f3(x981,x982,x983,a1),f3(x981,x982,x983,a2))),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7])).
% 1.69/1.80 cnf(102,plain,
% 1.69/1.80 (~E(a1,a12)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3])).
% 1.69/1.80 cnf(103,plain,
% 1.69/1.80 (P1(a11,f8(a2,a11,a1,a11,a2),a2)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,51])).
% 1.69/1.80 cnf(105,plain,
% 1.69/1.80 (P1(x1051,f8(x1052,x1051,f3(x1052,x1051,x1053,x1054),x1051,x1052),x1052)),
% 1.69/1.80 inference(scs_inference,[],[44,38,59,61,63,65,36,37,40,39,68,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,51,50])).
% 1.69/1.80 cnf(109,plain,
% 1.69/1.80 (P1(x1091,x1092,f3(x1091,x1092,x1093,x1094))),
% 1.69/1.80 inference(rename_variables,[],[39])).
% 1.69/1.80 cnf(116,plain,
% 1.69/1.80 (P2(x1161,x1162,x1162,x1161)),
% 1.69/1.80 inference(rename_variables,[],[38])).
% 1.69/1.80 cnf(118,plain,
% 1.69/1.80 (~P2(a2,a11,a2,x1181)+P1(x1181,f6(a2,a11,x1181,f8(a2,a11,a1,a11,a2),a2,a2),a2)),
% 1.69/1.81 inference(scs_inference,[],[44,38,59,61,63,65,116,36,37,40,39,68,109,2,35,34,33,32,31,30,29,47,46,45,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,51,50,53,52,56,55])).
% 1.69/1.81 cnf(124,plain,
% 1.69/1.81 (P1(a11,f6(a2,a11,a11,f8(a2,a11,a1,a11,a2),a2,a2),a2)),
% 1.69/1.81 inference(scs_inference,[],[70,118])).
% 1.69/1.81 cnf(128,plain,
% 1.69/1.81 (P2(x1281,f3(x1282,x1281,x1283,x1284),x1283,x1284)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(129,plain,
% 1.69/1.81 (P2(x1291,x1292,x1292,x1291)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(131,plain,
% 1.69/1.81 (P1(x1311,f6(x1311,x1311,x1311,x1311,f3(x1311,x1311,x1311,x1312),x1312),x1312)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,70,118,47,55])).
% 1.69/1.81 cnf(132,plain,
% 1.69/1.81 (P1(x1321,x1322,f3(x1321,x1322,x1323,x1324))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(133,plain,
% 1.69/1.81 (P2(x1331,x1332,x1332,x1331)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(134,plain,
% 1.69/1.81 (P1(x1341,x1342,f3(x1341,x1342,x1343,x1344))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(135,plain,
% 1.69/1.81 (P2(x1351,f3(x1352,x1351,x1353,x1354),x1353,x1354)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(137,plain,
% 1.69/1.81 (P1(f8(a2,a11,a1,a11,a2),f8(a11,f8(a2,a11,a1,a11,a2),a2,f8(a2,a11,a1,a11,a2),a11),a11)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,70,103,118,47,55,50])).
% 1.69/1.81 cnf(139,plain,
% 1.69/1.81 (~P2(a2,a12,x1391,x1391)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,70,103,69,118,47,55,50,46])).
% 1.69/1.81 cnf(141,plain,
% 1.69/1.81 (~P1(a2,a12,a2)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,70,103,69,118,47,55,50,46,45])).
% 1.69/1.81 cnf(143,plain,
% 1.69/1.81 (~P2(a2,a12,a2,a1)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,36,70,103,69,118,47,55,50,46,45,35])).
% 1.69/1.81 cnf(144,plain,
% 1.69/1.81 (~P2(a2,a12,a1,a2)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,36,70,103,69,118,47,55,50,46,45,35,34])).
% 1.69/1.81 cnf(147,plain,
% 1.69/1.81 (E(a1,f3(x1471,a2,x1472,x1472))),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,36,70,72,103,69,118,47,55,50,46,45,35,34,32,29,3])).
% 1.69/1.81 cnf(149,plain,
% 1.69/1.81 (P1(a2,f8(x1491,a2,f3(x1491,a1,x1492,x1493),a1,x1491),x1491)),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,134,36,70,72,103,67,69,118,47,55,50,46,45,35,34,32,29,3,51])).
% 1.69/1.81 cnf(151,plain,
% 1.69/1.81 (P1(x1511,x1512,f3(x1511,x1512,x1513,x1514))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(153,plain,
% 1.69/1.81 (P1(a2,x1531,f5(a2,x1531,a12,f3(x1531,a12,x1532,x1533),f3(a2,a12,x1534,x1535)))),
% 1.69/1.81 inference(scs_inference,[],[38,129,40,128,39,134,151,132,36,70,72,103,67,69,118,47,55,50,46,45,35,34,32,29,3,51,53])).
% 1.69/1.81 cnf(154,plain,
% 1.69/1.81 (P1(x1541,x1542,f3(x1541,x1542,x1543,x1544))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(155,plain,
% 1.69/1.81 (P1(x1551,x1552,f3(x1551,x1552,x1553,x1554))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(159,plain,
% 1.69/1.81 (P1(x1591,x1592,f3(x1591,x1592,x1593,x1594))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(162,plain,
% 1.69/1.81 (P2(x1621,f3(x1622,x1621,x1623,x1624),x1623,x1624)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(167,plain,
% 1.69/1.81 (~E(a12,a2)),
% 1.69/1.81 inference(scs_inference,[],[38,129,133,40,128,135,39,134,151,155,159,132,154,36,70,72,103,67,69,118,47,55,50,46,45,35,34,32,29,3,51,53,52,56,2])).
% 1.69/1.81 cnf(168,plain,
% 1.69/1.81 (~E(f3(x1681,a2,a2,a1),a12)),
% 1.69/1.81 inference(scs_inference,[],[38,129,133,40,128,135,162,39,134,151,155,159,132,154,36,70,72,103,67,69,118,47,55,50,46,45,35,34,32,29,3,51,53,52,56,2,33])).
% 1.69/1.81 cnf(170,plain,
% 1.69/1.81 (~P1(a12,a2,a1)),
% 1.69/1.81 inference(scs_inference,[],[44,38,129,133,40,128,135,162,39,134,151,155,159,132,154,36,70,72,75,103,67,69,118,47,55,50,46,45,35,34,32,29,3,51,53,52,56,2,33,30])).
% 1.69/1.81 cnf(179,plain,
% 1.69/1.81 (P2(a1,x1791,x1791,a2)),
% 1.69/1.81 inference(rename_variables,[],[58])).
% 1.69/1.81 cnf(180,plain,
% 1.69/1.81 (P1(x1801,x1802,f3(x1801,x1802,x1803,x1804))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(181,plain,
% 1.69/1.81 (P2(x1811,f3(x1812,x1811,x1813,x1814),x1813,x1814)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(182,plain,
% 1.69/1.81 (P1(x1821,x1822,f3(x1821,x1822,x1823,x1824))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(184,plain,
% 1.69/1.81 (~P2(x1841,x1841,a2,a12)),
% 1.69/1.81 inference(scs_inference,[],[38,40,39,58,139,55,47])).
% 1.69/1.81 cnf(186,plain,
% 1.69/1.81 (P2(x1861,x1862,x1862,x1861)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(189,plain,
% 1.69/1.81 (P1(x1891,a2,f3(x1891,a1,x1892,x1893))),
% 1.69/1.81 inference(rename_variables,[],[67])).
% 1.69/1.81 cnf(192,plain,
% 1.69/1.81 (P1(x1921,a2,f3(x1921,a1,x1922,x1923))),
% 1.69/1.81 inference(rename_variables,[],[67])).
% 1.69/1.81 cnf(194,plain,
% 1.69/1.81 (E(x1941,f6(x1941,x1941,x1941,x1941,f3(x1941,x1941,x1941,x1941),x1941))),
% 1.69/1.81 inference(scs_inference,[],[38,40,39,131,58,139,167,67,189,55,47,53,52,45])).
% 1.69/1.81 cnf(195,plain,
% 1.69/1.81 (P1(x1951,f6(x1951,x1951,x1951,x1951,f3(x1951,x1951,x1951,x1952),x1952),x1952)),
% 1.69/1.81 inference(rename_variables,[],[131])).
% 1.69/1.81 cnf(197,plain,
% 1.69/1.81 (P2(x1971,f6(x1972,x1973,x1974,x1975,x1976,a1),f6(x1972,x1973,x1974,x1975,x1976,a2),x1971)),
% 1.69/1.81 inference(scs_inference,[],[38,186,40,39,131,92,58,139,167,67,189,55,47,53,52,45,34])).
% 1.69/1.81 cnf(198,plain,
% 1.69/1.81 (P2(x1981,x1982,x1982,x1981)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(199,plain,
% 1.69/1.81 (P2(f6(x1991,x1992,x1993,x1994,x1995,a2),x1996,x1996,f6(x1991,x1992,x1993,x1994,x1995,a1))),
% 1.69/1.81 inference(scs_inference,[],[38,186,198,40,39,131,92,58,139,167,67,189,55,47,53,52,45,34,32])).
% 1.69/1.81 cnf(200,plain,
% 1.69/1.81 (P2(x2001,x2002,x2002,x2001)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(203,plain,
% 1.69/1.81 (P2(x2031,x2032,x2032,x2031)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(206,plain,
% 1.69/1.81 (P2(f6(x2061,x2062,x2063,x2064,x2065,a1),x2066,x2066,f6(x2061,x2062,x2063,x2064,x2065,a2))),
% 1.69/1.81 inference(scs_inference,[],[38,186,198,200,203,40,39,131,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35])).
% 1.69/1.81 cnf(207,plain,
% 1.69/1.81 (P2(x2071,x2072,x2072,x2071)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(208,plain,
% 1.69/1.81 (P1(x2081,a1,f3(x2081,a2,x2082,x2083))),
% 1.69/1.81 inference(scs_inference,[],[57,38,186,198,200,203,40,39,182,131,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30])).
% 1.69/1.81 cnf(209,plain,
% 1.69/1.81 (P1(x2091,x2092,f3(x2091,x2092,x2093,x2094))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(210,plain,
% 1.69/1.81 (~E(a12,a1)),
% 1.69/1.81 inference(scs_inference,[],[36,57,38,186,198,200,203,40,39,182,131,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30,3])).
% 1.69/1.81 cnf(211,plain,
% 1.69/1.81 (P2(x2111,f6(x2112,x2113,x2114,x2115,x2116,a2),f6(x2112,x2113,x2114,x2115,x2116,a1),x2111)),
% 1.69/1.81 inference(scs_inference,[],[36,57,38,186,198,200,203,207,40,39,182,131,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30,3,33])).
% 1.69/1.81 cnf(212,plain,
% 1.69/1.81 (P2(x2121,x2122,x2122,x2121)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(213,plain,
% 1.69/1.81 (P1(a2,x2131,f3(a1,x2131,x2132,x2133))),
% 1.69/1.81 inference(scs_inference,[],[36,57,38,186,198,200,203,207,40,39,182,209,131,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30,3,33,29])).
% 1.69/1.81 cnf(214,plain,
% 1.69/1.81 (P1(x2141,x2142,f3(x2141,x2142,x2143,x2144))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(216,plain,
% 1.69/1.81 (P1(x2161,f6(x2161,x2161,x2161,x2161,f3(x2161,x2161,x2161,a2),a2),a1)),
% 1.69/1.81 inference(scs_inference,[],[36,57,38,186,198,200,203,207,40,39,182,209,131,195,92,58,139,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30,3,33,29,2,31])).
% 1.69/1.81 cnf(225,plain,
% 1.69/1.81 (~P2(f3(x2251,a2,a2,a1),a12,x2252,x2252)),
% 1.69/1.81 inference(scs_inference,[],[36,57,38,186,198,200,203,207,212,40,181,39,182,209,214,180,131,195,92,58,179,139,168,102,167,70,67,189,192,55,47,53,52,45,34,32,56,35,30,3,33,29,2,31,49,46])).
% 1.69/1.81 cnf(229,plain,
% 1.69/1.81 (P2(f3(x2291,x2292,x2293,x2294),x2292,x2293,x2294)),
% 1.69/1.81 inference(scs_inference,[],[38,40,47])).
% 1.69/1.81 cnf(230,plain,
% 1.69/1.81 (P2(x2301,f3(x2302,x2301,x2303,x2304),x2303,x2304)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(231,plain,
% 1.69/1.81 (P2(x2311,x2312,x2312,x2311)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(233,plain,
% 1.69/1.81 (E(f3(x2331,x2332,x2333,x2333),x2332)),
% 1.69/1.81 inference(scs_inference,[],[38,40,47,46])).
% 1.69/1.81 cnf(240,plain,
% 1.69/1.81 (P2(x2401,f3(x2402,x2401,x2403,x2404),x2403,x2404)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(243,plain,
% 1.69/1.81 (P1(a2,f8(x2431,a1,f3(x2431,a1,x2432,x2433),a1,x2431),x2431)),
% 1.69/1.81 inference(scs_inference,[],[36,38,40,230,39,105,210,58,47,46,45,56,29])).
% 1.69/1.81 cnf(245,plain,
% 1.69/1.81 (P2(x2451,f3(x2452,x2451,x2453,a1),x2453,a2)),
% 1.69/1.81 inference(scs_inference,[],[36,38,40,230,240,39,105,210,58,47,46,45,56,29,35])).
% 1.69/1.81 cnf(246,plain,
% 1.69/1.81 (P2(x2461,f3(x2462,x2461,x2463,x2464),x2463,x2464)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(247,plain,
% 1.69/1.81 (~E(a12,f3(x2471,a2,a2,a1))),
% 1.69/1.81 inference(scs_inference,[],[36,38,231,40,230,240,39,105,225,210,58,47,46,45,56,29,35,34])).
% 1.69/1.81 cnf(249,plain,
% 1.69/1.81 (~P2(f3(x2491,a2,a2,a1),a12,x2492,x2492)),
% 1.69/1.81 inference(rename_variables,[],[225])).
% 1.69/1.81 cnf(250,plain,
% 1.69/1.81 (~E(x2501,f3(x2502,x2501,a2,a12))),
% 1.69/1.81 inference(scs_inference,[],[36,38,231,40,230,240,246,39,105,225,184,210,58,47,46,45,56,29,35,34,32])).
% 1.69/1.81 cnf(251,plain,
% 1.69/1.81 (P2(x2511,f3(x2512,x2511,x2513,x2514),x2513,x2514)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(254,plain,
% 1.69/1.81 (E(x2541,f6(x2541,x2541,x2541,x2541,f3(x2541,x2541,x2541,x2541),x2541))),
% 1.69/1.81 inference(rename_variables,[],[194])).
% 1.69/1.81 cnf(257,plain,
% 1.69/1.81 (~E(f3(x2571,x2572,a2,a12),x2572)),
% 1.69/1.81 inference(scs_inference,[],[36,38,231,40,230,240,246,37,39,194,254,105,225,184,210,58,47,46,45,56,29,35,34,32,3,30,2])).
% 1.69/1.81 cnf(258,plain,
% 1.69/1.81 (~E(f3(x2581,f3(x2582,a2,a2,a1),x2583,x2583),a12)),
% 1.69/1.81 inference(scs_inference,[],[36,38,231,40,230,240,246,251,37,39,194,254,105,225,249,184,210,58,47,46,45,56,29,35,34,32,3,30,2,33])).
% 1.69/1.81 cnf(276,plain,
% 1.69/1.81 (~P2(x2761,f3(x2762,x2761,a2,a12),x2763,x2763)),
% 1.69/1.81 inference(scs_inference,[],[58,250,184,47,46])).
% 1.69/1.81 cnf(278,plain,
% 1.69/1.81 (E(a1,f6(a1,a1,a1,a1,f3(a1,a1,a1,a2),a2))),
% 1.69/1.81 inference(scs_inference,[],[58,250,216,184,47,46,45])).
% 1.69/1.81 cnf(282,plain,
% 1.69/1.81 (E(f3(x2821,x2822,x2823,x2823),x2822)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(284,plain,
% 1.69/1.81 (E(f3(x2841,x2842,x2843,x2843),x2842)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(285,plain,
% 1.69/1.81 (E(f3(x2851,a2,x2852,x2852),a1)),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,250,216,143,184,47,46,45,32,29,3])).
% 1.69/1.81 cnf(286,plain,
% 1.69/1.81 (E(f3(x2861,x2862,x2863,x2863),x2862)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(287,plain,
% 1.69/1.81 (~P2(a2,a12,f3(x2871,a2,x2872,x2872),a1)),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,250,216,143,184,47,46,45,32,29,3,34])).
% 1.69/1.81 cnf(288,plain,
% 1.69/1.81 (E(f3(x2881,x2882,x2883,x2883),x2882)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(289,plain,
% 1.69/1.81 (~P2(a2,a12,a1,f3(x2891,a2,x2892,x2892))),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,288,250,216,143,144,184,47,46,45,32,29,3,34,35])).
% 1.69/1.81 cnf(290,plain,
% 1.69/1.81 (E(f3(x2901,x2902,x2903,x2903),x2902)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(292,plain,
% 1.69/1.81 (E(f3(x2921,x2922,x2923,x2923),x2922)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(293,plain,
% 1.69/1.81 (~P1(a9,a10,f3(x2931,a7,x2932,x2932))),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,288,290,292,250,216,143,144,184,47,46,45,32,29,3,34,35,30,31])).
% 1.69/1.81 cnf(294,plain,
% 1.69/1.81 (E(f3(x2941,x2942,x2943,x2943),x2942)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(296,plain,
% 1.69/1.81 (E(f3(x2961,x2962,x2963,x2963),x2962)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(302,plain,
% 1.69/1.81 (E(f8(x3021,x3022,x3023,x3024,a2),f8(x3021,x3022,x3023,x3024,a1))),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,288,290,292,294,93,250,216,143,144,184,47,46,45,32,29,3,34,35,30,31,33,2,27,26,23,22,18])).
% 1.69/1.81 cnf(316,plain,
% 1.69/1.81 (E(f6(x3161,x3162,x3163,x3164,x3165,f3(x3166,x3167,x3168,x3168)),f6(x3161,x3162,x3163,x3164,x3165,x3167))),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,288,290,292,294,296,93,250,216,143,144,184,47,46,45,32,29,3,34,35,30,31,33,2,27,26,23,22,18,16,15,14,11,9,5,28,25,24,21,20,19,17,13])).
% 1.69/1.81 cnf(317,plain,
% 1.69/1.81 (E(f6(x3171,x3172,x3173,x3174,f3(x3175,x3176,x3177,x3177),x3178),f6(x3171,x3172,x3173,x3174,x3176,x3178))),
% 1.69/1.81 inference(scs_inference,[],[42,58,57,233,282,284,286,288,290,292,294,296,93,250,216,143,144,184,47,46,45,32,29,3,34,35,30,31,33,2,27,26,23,22,18,16,15,14,11,9,5,28,25,24,21,20,19,17,13,12])).
% 1.69/1.81 cnf(330,plain,
% 1.69/1.81 (E(x3301,f3(x3302,x3301,a2,a1))),
% 1.69/1.81 inference(scs_inference,[],[245,46])).
% 1.69/1.81 cnf(333,plain,
% 1.69/1.81 (~P1(f3(x3331,x3332,a2,a12),x3332,f3(x3331,x3332,a2,a12))),
% 1.69/1.81 inference(scs_inference,[],[257,245,46,45])).
% 1.69/1.81 cnf(335,plain,
% 1.69/1.81 (~P2(a1,a2,x3351,f3(x3352,x3351,a2,a12))),
% 1.69/1.81 inference(scs_inference,[],[58,276,257,245,46,45,47])).
% 1.69/1.81 cnf(337,plain,
% 1.69/1.81 (P2(a1,x3371,x3371,a2)),
% 1.69/1.81 inference(rename_variables,[],[58])).
% 1.69/1.81 cnf(339,plain,
% 1.69/1.81 (P1(a1,a11,a1)),
% 1.69/1.81 inference(scs_inference,[],[37,58,57,276,257,245,46,45,47,29])).
% 1.69/1.81 cnf(340,plain,
% 1.69/1.81 (P2(x3401,f3(x3402,x3401,x3403,f6(x3404,x3405,x3406,a1,x3407,x3408)),x3403,f6(x3404,x3405,x3406,a2,x3407,x3408))),
% 1.69/1.81 inference(scs_inference,[],[37,58,40,57,276,94,257,245,46,45,47,29,35])).
% 1.69/1.81 cnf(341,plain,
% 1.69/1.81 (P2(x3411,f3(x3412,x3411,x3413,x3414),x3413,x3414)),
% 1.69/1.81 inference(rename_variables,[],[40])).
% 1.69/1.81 cnf(342,plain,
% 1.69/1.81 (P2(a1,f3(x3421,a2,x3422,x3423),x3422,x3423)),
% 1.69/1.81 inference(scs_inference,[],[37,58,40,341,57,276,94,257,245,46,45,47,29,35,32])).
% 1.69/1.81 cnf(344,plain,
% 1.69/1.81 (P1(x3441,f6(x3442,x3443,x3444,a2,x3445,x3446),f3(x3441,f6(x3442,x3443,x3444,a1,x3445,x3446),x3447,x3448))),
% 1.69/1.81 inference(scs_inference,[],[37,58,40,341,39,57,276,94,257,245,46,45,47,29,35,32,30])).
% 1.69/1.81 cnf(345,plain,
% 1.69/1.81 (P1(x3451,x3452,f3(x3451,x3452,x3453,x3454))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(349,plain,
% 1.69/1.81 (P2(a1,x3491,x3491,a2)),
% 1.69/1.81 inference(rename_variables,[],[58])).
% 1.69/1.81 cnf(354,plain,
% 1.69/1.81 (~E(a12,f3(x3541,f3(x3542,a2,a2,a1),x3543,x3543))),
% 1.69/1.81 inference(scs_inference,[],[37,58,337,349,40,341,39,57,316,276,94,257,245,149,258,46,45,47,29,35,32,30,3,34,31,33,2])).
% 1.69/1.81 cnf(355,plain,
% 1.69/1.81 (P1(a1,f8(x3551,a2,f3(x3551,a2,x3552,x3553),a1,x3551),x3551)),
% 1.69/1.81 inference(scs_inference,[],[37,58,337,349,40,341,39,345,57,316,276,94,257,245,208,149,258,46,45,47,29,35,32,30,3,34,31,33,2,50])).
% 1.69/1.81 cnf(356,plain,
% 1.69/1.81 (P1(x3561,a1,f3(x3561,a2,x3562,x3563))),
% 1.69/1.81 inference(rename_variables,[],[208])).
% 1.69/1.81 cnf(357,plain,
% 1.69/1.81 (P1(x3571,x3572,f3(x3571,x3572,x3573,x3574))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(359,plain,
% 1.69/1.81 (P1(a2,f8(x3591,a2,f3(x3591,a2,x3592,x3593),a1,x3591),x3591)),
% 1.69/1.81 inference(scs_inference,[],[37,58,337,349,40,341,39,345,357,57,316,276,94,257,245,208,356,149,258,46,45,47,29,35,32,30,3,34,31,33,2,50,51])).
% 1.69/1.81 cnf(371,plain,
% 1.69/1.81 (P1(a11,f8(a1,a11,a1,a11,a1),a1)),
% 1.69/1.81 inference(scs_inference,[],[339,50])).
% 1.69/1.81 cnf(373,plain,
% 1.69/1.81 (P1(x3731,f8(a2,x3731,f3(a1,x3731,x3732,x3733),x3731,a1),a1)),
% 1.69/1.81 inference(scs_inference,[],[39,339,213,50,51])).
% 1.69/1.81 cnf(375,plain,
% 1.69/1.81 (P1(x3751,x3752,f3(x3751,x3752,x3753,x3754))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(382,plain,
% 1.69/1.81 (P2(x3821,x3822,x3822,x3821)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(384,plain,
% 1.69/1.81 (~P2(a12,f3(x3841,f3(x3842,a2,a2,a1),x3843,x3843),x3844,x3844)),
% 1.69/1.81 inference(scs_inference,[],[38,60,39,243,354,339,213,50,51,45,47,46])).
% 1.69/1.81 cnf(386,plain,
% 1.69/1.81 (~E(x3861,f3(x3861,x3862,a2,a12))),
% 1.69/1.81 inference(scs_inference,[],[38,60,39,375,333,243,354,339,213,50,51,45,47,46,29])).
% 1.69/1.81 cnf(387,plain,
% 1.69/1.81 (P1(x3871,x3872,f3(x3871,x3872,x3873,x3874))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(389,plain,
% 1.69/1.81 (P2(x3891,x3892,x3892,x3891)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(390,plain,
% 1.69/1.81 (~P2(a1,a2,x3901,f3(x3902,x3901,a2,a12))),
% 1.69/1.81 inference(rename_variables,[],[335])).
% 1.69/1.81 cnf(391,plain,
% 1.69/1.81 (~E(f3(x3911,a12,a2,a1),f3(x3912,f3(x3913,a2,a2,a1),x3914,x3914))),
% 1.69/1.81 inference(scs_inference,[],[38,382,60,39,375,333,330,243,354,335,339,213,50,51,45,47,46,29,35,3])).
% 1.69/1.81 cnf(393,plain,
% 1.69/1.81 (P2(f3(x3931,x3932,a2,x3933),x3932,a1,x3933)),
% 1.69/1.81 inference(scs_inference,[],[38,382,60,39,375,57,229,333,330,243,354,335,339,213,50,51,45,47,46,29,35,3,34])).
% 1.69/1.81 cnf(397,plain,
% 1.69/1.81 (~P2(a1,a2,x3971,f3(x3972,x3971,a2,a12))),
% 1.69/1.81 inference(rename_variables,[],[335])).
% 1.69/1.81 cnf(399,plain,
% 1.69/1.81 (P1(x3991,x3992,f3(x3991,x3992,x3993,x3994))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(401,plain,
% 1.69/1.81 (~E(f3(a10,a7,x4011,x4012),a9)),
% 1.69/1.81 inference(scs_inference,[],[38,382,389,60,43,39,375,387,399,57,229,333,330,243,354,335,390,293,339,213,50,51,45,47,46,29,35,3,34,32,30,31])).
% 1.69/1.81 cnf(403,plain,
% 1.69/1.81 (~E(f3(x4031,a1,x4032,f3(x4033,x4032,a2,a12)),a2)),
% 1.69/1.81 inference(scs_inference,[],[38,382,389,60,43,40,39,375,387,399,57,229,333,330,243,354,335,390,397,293,339,213,50,51,45,47,46,29,35,3,34,32,30,31,33])).
% 1.69/1.81 cnf(405,plain,
% 1.69/1.81 (E(f6(x4051,x4052,x4053,x4054,x4055,x4056),f6(x4051,x4052,x4053,x4054,f3(x4057,x4055,x4058,x4058),x4056))),
% 1.69/1.81 inference(scs_inference,[],[38,382,389,60,43,40,39,375,387,399,57,317,229,333,330,243,354,335,390,397,293,339,213,50,51,45,47,46,29,35,3,34,32,30,31,33,2])).
% 1.69/1.81 cnf(426,plain,
% 1.69/1.81 (P1(x4261,f6(x4261,x4261,x4261,x4261,f3(x4261,x4261,x4261,a1),a2),a2)),
% 1.69/1.81 inference(scs_inference,[],[38,39,245,55])).
% 1.69/1.81 cnf(429,plain,
% 1.69/1.81 (P2(x4291,x4292,x4292,x4291)),
% 1.69/1.81 inference(rename_variables,[],[38])).
% 1.69/1.81 cnf(432,plain,
% 1.69/1.81 (~P1(x4321,f3(x4321,x4322,a2,a12),x4321)),
% 1.69/1.81 inference(scs_inference,[],[38,39,386,245,55,45])).
% 1.69/1.81 cnf(434,plain,
% 1.69/1.81 (E(x4341,f3(x4342,x4341,f6(x4343,x4344,x4345,a2,x4346,x4347),f6(x4343,x4344,x4345,a1,x4346,x4347)))),
% 1.69/1.81 inference(scs_inference,[],[38,39,340,386,245,55,45,46])).
% 1.69/1.81 cnf(437,plain,
% 1.69/1.81 (~P2(f3(x4371,f3(x4372,a2,a2,a1),x4373,x4373),a12,x4374,x4374)),
% 1.69/1.81 inference(scs_inference,[],[38,429,39,340,386,384,245,55,45,46,47])).
% 1.69/1.81 cnf(443,plain,
% 1.69/1.81 (~P2(a12,f3(x4431,f3(x4432,a2,a2,a1),x4433,x4433),a1,a2)),
% 1.69/1.81 inference(scs_inference,[],[38,429,39,57,405,340,95,386,384,245,55,45,46,47,3,35])).
% 1.69/1.81 cnf(444,plain,
% 1.69/1.81 (~P2(a12,f3(x4441,f3(x4442,a2,a2,a1),x4443,x4443),x4444,x4444)),
% 1.69/1.81 inference(rename_variables,[],[384])).
% 1.69/1.81 cnf(446,plain,
% 1.69/1.81 (~P2(a12,f3(x4461,f3(x4462,a2,a2,a1),x4463,x4463),x4464,x4464)),
% 1.69/1.81 inference(rename_variables,[],[384])).
% 1.69/1.81 cnf(448,plain,
% 1.69/1.81 (E(f3(x4481,x4482,x4483,x4483),x4482)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(449,plain,
% 1.69/1.81 (~P2(f3(x4491,a12,x4492,x4492),f3(x4493,f3(x4494,a2,a2,a1),x4495,x4495),x4496,x4496)),
% 1.69/1.81 inference(scs_inference,[],[38,429,41,39,57,405,340,95,386,384,444,446,233,448,245,55,45,46,47,3,35,34,29,32])).
% 1.69/1.81 cnf(450,plain,
% 1.69/1.81 (E(f3(x4501,x4502,x4503,x4503),x4502)),
% 1.69/1.81 inference(rename_variables,[],[233])).
% 1.69/1.81 cnf(453,plain,
% 1.69/1.81 (~P2(a12,f3(x4531,f3(x4532,a2,a2,a1),a2,a1),x4533,x4533)),
% 1.69/1.81 inference(scs_inference,[],[38,429,41,39,57,405,340,95,98,386,384,444,446,233,448,450,245,55,45,46,47,3,35,34,29,32,30,33])).
% 1.69/1.81 cnf(456,plain,
% 1.69/1.81 (~E(f3(x4561,x4562,a2,a12),x4561)),
% 1.69/1.81 inference(scs_inference,[],[38,429,41,39,57,405,340,95,98,386,384,444,446,233,448,450,245,55,45,46,47,3,35,34,29,32,30,33,2])).
% 1.69/1.81 cnf(471,plain,
% 1.69/1.81 (P2(x4711,a1,a2,x4711)),
% 1.69/1.81 inference(rename_variables,[],[60])).
% 1.69/1.81 cnf(472,plain,
% 1.69/1.81 (P1(x4721,x4722,f3(x4721,x4722,x4723,x4724))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(479,plain,
% 1.69/1.81 (P1(x4791,x4792,f3(x4791,x4792,x4793,x4794))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(484,plain,
% 1.69/1.81 (~P2(f3(x4841,x4842,a2,a12),x4841,x4843,x4843)),
% 1.69/1.81 inference(scs_inference,[],[39,472,60,58,456,426,213,245,70,55,56,45,46])).
% 1.69/1.81 cnf(486,plain,
% 1.69/1.81 (~P2(a2,a1,f3(x4861,a12,x4862,x4862),f3(x4863,f3(x4864,a2,a2,a1),x4865,x4865))),
% 1.69/1.81 inference(scs_inference,[],[39,472,60,471,58,449,456,426,213,245,70,55,56,45,46,47])).
% 1.69/1.81 cnf(488,plain,
% 1.69/1.81 (P2(x4881,a1,a2,x4881)),
% 1.69/1.81 inference(rename_variables,[],[60])).
% 1.69/1.81 cnf(492,plain,
% 1.69/1.81 (P1(a1,x4921,f3(a2,x4921,x4922,x4923))),
% 1.69/1.81 inference(scs_inference,[],[39,472,479,60,471,58,57,449,456,426,213,245,70,55,56,45,46,47,3,29])).
% 1.69/1.81 cnf(493,plain,
% 1.69/1.81 (P1(x4931,x4932,f3(x4931,x4932,x4933,x4934))),
% 1.69/1.81 inference(rename_variables,[],[39])).
% 1.69/1.81 cnf(494,plain,
% 1.69/1.81 (P2(f3(x4941,x4942,f6(x4943,x4944,x4945,a2,x4946,x4947),f6(x4943,x4944,x4945,a1,x4946,x4947)),a1,a2,x4942)),
% 1.69/1.81 inference(scs_inference,[],[39,472,479,60,471,488,58,57,434,449,456,426,213,245,70,55,56,45,46,47,3,29,32])).
% 1.69/1.81 cnf(495,plain,
% 1.69/1.81 (E(x4951,f3(x4952,x4951,f6(x4953,x4954,x4955,a2,x4956,x4957),f6(x4953,x4954,x4955,a1,x4956,x4957)))),
% 1.69/1.81 inference(rename_variables,[],[434])).
% 1.69/1.81 cnf(497,plain,
% 1.69/1.81 (E(x4971,f3(x4972,x4971,f6(x4973,x4974,x4975,a2,x4976,x4977),f6(x4973,x4974,x4975,a1,x4976,x4977)))),
% 1.69/1.81 inference(rename_variables,[],[434])).
% 1.69/1.81 cnf(498,plain,
% 1.69/1.81 (P2(x4981,a1,f3(x4982,a2,f6(x4983,x4984,x4985,a2,x4986,x4987),f6(x4983,x4984,x4985,a1,x4986,x4987)),x4981)),
% 1.69/1.81 inference(scs_inference,[],[39,472,479,60,471,488,58,57,434,495,497,449,456,426,213,245,70,55,56,45,46,47,3,29,32,35,34])).
% 1.69/1.81 cnf(499,plain,
% 1.69/1.81 (E(x4991,f3(x4992,x4991,f6(x4993,x4994,x4995,a2,x4996,x4997),f6(x4993,x4994,x4995,a1,x4996,x4997)))),
% 1.69/1.81 inference(rename_variables,[],[434])).
% 1.69/1.81 cnf(500,plain,
% 1.69/1.81 (P1(x5001,f3(x5002,x5003,f6(x5004,x5005,x5006,a2,x5007,x5008),f6(x5004,x5005,x5006,a1,x5007,x5008)),f3(x5001,x5003,x5009,x50010))),
% 1.69/1.81 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,434,495,497,499,449,456,426,213,245,70,55,56,45,46,47,3,29,32,35,34,30])).
% 1.69/1.81 cnf(501,plain,
% 1.69/1.82 (E(x5011,f3(x5012,x5011,f6(x5013,x5014,x5015,a2,x5016,x5017),f6(x5013,x5014,x5015,a1,x5016,x5017)))),
% 1.69/1.82 inference(rename_variables,[],[434])).
% 1.69/1.82 cnf(503,plain,
% 1.69/1.82 (P2(x5031,f3(x5032,a1,f6(x5033,x5034,x5035,a2,x5036,x5037),f6(x5033,x5034,x5035,a1,x5036,x5037)),a2,x5031)),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,449,456,426,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33])).
% 1.69/1.82 cnf(504,plain,
% 1.69/1.82 (E(x5041,f3(x5042,x5041,f6(x5043,x5044,x5045,a2,x5046,x5047),f6(x5043,x5044,x5045,a1,x5046,x5047)))),
% 1.69/1.82 inference(rename_variables,[],[434])).
% 1.69/1.82 cnf(505,plain,
% 1.69/1.82 (E(f3(x5051,x5052,f6(x5053,x5054,x5055,a2,x5056,x5057),f6(x5053,x5054,x5055,a1,x5056,x5057)),x5052)),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2])).
% 1.69/1.82 cnf(508,plain,
% 1.69/1.82 (E(f8(x5081,x5082,x5083,x5084,a1),f8(x5081,x5082,x5083,x5084,f3(x5085,a2,x5086,x5086)))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18])).
% 1.69/1.82 cnf(510,plain,
% 1.69/1.82 (E(f6(x5101,a1,x5102,x5103,x5104,x5105),f6(x5101,f3(x5106,a2,x5107,x5107),x5102,x5103,x5104,x5105))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9])).
% 1.69/1.82 cnf(519,plain,
% 1.69/1.82 (E(f6(x5191,x5192,x5193,a1,x5194,x5195),f6(x5191,x5192,x5193,f3(x5196,a2,x5197,x5197),x5194,x5195))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9,28,25,24,23,22,19,15,14,11])).
% 1.69/1.82 cnf(520,plain,
% 1.69/1.82 (E(f3(x5201,x5202,x5203,a1),f3(x5201,x5202,x5203,f3(x5204,a2,x5205,x5205)))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9,28,25,24,23,22,19,15,14,11,7])).
% 1.69/1.82 cnf(521,plain,
% 1.69/1.82 (E(f6(x5211,x5212,x5213,x5214,x5215,a1),f6(x5211,x5212,x5213,x5214,x5215,f3(x5216,a2,x5217,x5217)))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9,28,25,24,23,22,19,15,14,11,7,13])).
% 1.69/1.82 cnf(527,plain,
% 1.69/1.82 (E(f6(x5271,x5272,a1,x5273,x5274,x5275),f6(x5271,x5272,f3(x5276,a2,x5277,x5277),x5273,x5274,x5275))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9,28,25,24,23,22,19,15,14,11,7,13,4,5,21,20,17,10])).
% 1.69/1.82 cnf(529,plain,
% 1.69/1.82 (E(f3(x5291,x5292,a1,x5293),f3(x5291,x5292,f3(x5294,a2,x5295,x5295),x5293))),
% 1.69/1.82 inference(scs_inference,[],[39,472,479,493,60,471,488,58,57,124,434,495,497,499,501,504,449,456,426,147,213,245,70,55,56,45,46,47,3,29,32,35,34,30,31,33,2,27,26,18,16,9,28,25,24,23,22,19,15,14,11,7,13,4,5,21,20,17,10,8,6])).
% 1.69/1.82 cnf(540,plain,
% 1.69/1.82 (P2(x5401,f3(x5402,x5401,x5403,x5404),x5403,x5404)),
% 1.69/1.82 inference(rename_variables,[],[40])).
% 1.69/1.82 cnf(541,plain,
% 1.69/1.82 (P1(x5411,x5412,f3(x5411,x5412,x5413,x5414))),
% 1.69/1.82 inference(rename_variables,[],[39])).
% 1.69/1.82 cnf(544,plain,
% 1.69/1.82 (P1(a1,x5441,f3(a2,x5441,x5442,x5443))),
% 1.69/1.82 inference(rename_variables,[],[492])).
% 1.69/1.82 cnf(545,plain,
% 1.69/1.82 (P2(x5451,a2,a1,x5451)),
% 1.69/1.82 inference(rename_variables,[],[62])).
% 1.69/1.82 cnf(551,plain,
% 1.69/1.82 (E(f3(x5511,x5512,a2,a1),x5512)),
% 1.69/1.82 inference(scs_inference,[],[39,541,62,40,391,342,393,492,64,55,56,45,46])).
% 1.69/1.82 cnf(554,plain,
% 1.69/1.82 (P2(f3(x5541,a1,x5542,x5543),a2,x5542,x5543)),
% 1.69/1.82 inference(scs_inference,[],[39,541,62,58,40,540,391,342,393,492,64,55,56,45,46,47])).
% 1.69/1.82 cnf(562,plain,
% 1.69/1.82 (P2(x5621,a2,a1,x5621)),
% 1.69/1.82 inference(rename_variables,[],[62])).
% 1.69/1.82 cnf(563,plain,
% 1.69/1.82 (~P2(f3(x5631,x5632,a2,a12),x5631,x5633,x5633)),
% 1.69/1.82 inference(rename_variables,[],[484])).
% 1.69/1.82 cnf(565,plain,
% 1.69/1.82 (P2(x5651,a2,a1,x5651)),
% 1.69/1.82 inference(rename_variables,[],[62])).
% 1.69/1.82 cnf(566,plain,
% 1.69/1.82 (~P2(f3(x5661,x5662,a2,a12),x5661,x5663,x5663)),
% 1.69/1.82 inference(rename_variables,[],[484])).
% 1.69/1.82 cnf(575,plain,
% 1.69/1.82 (~E(f3(x5751,f3(x5752,a2,a2,a1),x5753,x5753),f3(x5754,a12,a2,a1))),
% 1.69/1.82 inference(scs_inference,[],[39,541,62,545,562,565,60,58,40,540,57,500,505,484,563,566,391,342,393,492,401,276,64,55,56,45,46,47,3,35,32,29,34,33,2])).
% 1.69/1.82 cnf(576,plain,
% 1.69/1.82 (~E(f3(a2,f3(a1,x5761,a2,a12),x5762,x5763),a1)),
% 1.69/1.82 inference(scs_inference,[],[39,541,62,545,562,565,60,58,40,540,57,500,505,484,563,566,432,391,342,393,492,544,401,276,64,55,56,45,46,47,3,35,32,29,34,33,2,31])).
% 1.69/1.82 cnf(590,plain,
% 1.69/1.82 (E(a1,f8(a1,a2,f3(a1,a2,x5901,x5902),a1,a1))),
% 1.69/1.82 inference(scs_inference,[],[355,45])).
% 1.69/1.82 cnf(596,plain,
% 1.69/1.82 (~P2(f3(x5961,f3(x5962,a2,a2,a1),x5963,x5963),f3(x5964,a12,a2,a1),x5965,x5965)),
% 1.69/1.82 inference(scs_inference,[],[64,575,355,486,45,47,46])).
% 1.69/1.82 cnf(598,plain,
% 1.69/1.82 (~P2(f3(x5981,f3(x5982,a2,a2,a1),f3(x5983,a2,x5984,x5984),a1),a12,x5985,x5985)),
% 1.69/1.82 inference(scs_inference,[],[64,520,575,437,355,486,45,47,46,32])).
% 1.69/1.82 cnf(599,plain,
% 1.69/1.82 (~P2(f3(x5991,f3(x5992,a2,a2,a1),x5993,x5993),a12,x5994,x5994)),
% 1.69/1.82 inference(rename_variables,[],[437])).
% 1.69/1.82 cnf(600,plain,
% 1.69/1.82 (E(f3(x6001,x6002,x6003,a1),f3(x6001,x6002,x6003,f3(x6004,a2,x6005,x6005)))),
% 1.69/1.82 inference(rename_variables,[],[520])).
% 1.69/1.82 cnf(602,plain,
% 1.69/1.82 (E(f3(x6021,x6022,a2,a1),x6022)),
% 1.69/1.82 inference(rename_variables,[],[551])).
% 1.69/1.82 cnf(605,plain,
% 1.69/1.82 (~P2(f3(x6051,f3(x6052,a2,a2,a1),x6053,x6053),a12,x6054,x6054)),
% 1.69/1.82 inference(rename_variables,[],[437])).
% 1.69/1.82 cnf(609,plain,
% 1.69/1.82 (E(f3(x6091,x6092,a2,a1),x6092)),
% 1.69/1.82 inference(rename_variables,[],[551])).
% 1.69/1.82 cnf(616,plain,
% 1.69/1.82 (P1(a11,f8(a2,a11,a2,a11,a2),a2)),
% 1.69/1.82 inference(scs_inference,[],[64,43,57,510,520,600,551,602,609,575,437,599,605,355,486,278,443,66,45,47,46,32,29,3,35,34,30,31,33,2,50])).
% 1.69/1.82 cnf(618,plain,
% 1.69/1.82 (P1(f8(a1,a11,a1,a11,a1),f8(a11,f8(a1,a11,a1,a11,a1),a1,f8(a1,a11,a1,a11,a1),a11),a11)),
% 1.69/1.82 inference(scs_inference,[],[64,43,57,510,520,600,551,602,609,575,437,599,605,355,486,278,443,66,371,45,47,46,32,29,3,35,34,30,31,33,2,50,51])).
% 1.69/1.82 cnf(627,plain,
% 1.69/1.82 (P1(f8(a2,a11,a2,a11,a2),f8(a11,f8(a2,a11,a2,a11,a2),a2,f8(a2,a11,a2,a11,a2),a11),a11)),
% 1.69/1.82 inference(scs_inference,[],[616,50])).
% 1.69/1.82 cnf(631,plain,
% 1.69/1.82 (~P2(x6311,f3(x6312,x6311,x6313,x6313),f3(x6314,f3(x6315,a2,a2,a1),x6316,x6316),f3(x6317,a12,a2,a1))),
% 1.69/1.82 inference(scs_inference,[],[40,596,616,247,50,45,47])).
% 1.69/1.82 cnf(633,plain,
% 1.69/1.82 (P2(x6331,f3(x6332,x6331,x6333,x6334),x6333,x6334)),
% 1.69/1.82 inference(rename_variables,[],[40])).
% 1.69/1.82 cnf(635,plain,
% 1.69/1.82 (E(f3(x6351,a1,x6352,x6352),a2)),
% 1.69/1.82 inference(scs_inference,[],[40,596,616,554,247,50,45,47,46])).
% 1.69/1.82 cnf(640,plain,
% 1.69/1.82 (P2(f6(x6401,a2,x6402,x6403,x6404,x6405),f3(x6406,f6(x6401,a1,x6402,x6403,x6404,x6405),x6407,x6408),x6407,x6408)),
% 1.69/1.82 inference(scs_inference,[],[40,633,57,344,96,596,616,554,247,50,45,47,46,29,32])).
% 1.69/1.82 cnf(641,plain,
% 1.69/1.82 (P2(x6411,f3(x6412,x6411,x6413,x6414),x6413,x6414)),
% 1.69/1.82 inference(rename_variables,[],[40])).
% 1.69/1.82 cnf(643,plain,
% 1.69/1.82 (P2(x6431,f3(x6432,x6431,x6433,a2),x6433,a1)),
% 1.69/1.82 inference(scs_inference,[],[40,633,641,57,344,96,596,616,554,576,247,50,45,47,46,29,32,3,35])).
% 1.69/1.82 cnf(644,plain,
% 1.69/1.82 (P2(x6441,f3(x6442,x6441,x6443,x6444),x6443,x6444)),
% 1.69/1.82 inference(rename_variables,[],[40])).
% 1.69/1.82 cnf(645,plain,
% 1.69/1.82 (P2(x6451,f3(x6452,x6451,a2,x6453),a1,x6453)),
% 1.69/1.82 inference(scs_inference,[],[40,633,641,644,57,344,96,596,616,554,576,247,50,45,47,46,29,32,3,35,34])).
% 1.69/1.82 cnf(649,plain,
% 1.69/1.82 (P1(a11,f8(a2,a11,a2,a11,a2),a1)),
% 1.69/1.82 inference(scs_inference,[],[40,633,641,644,57,344,96,596,616,554,576,247,153,50,45,47,46,29,32,3,35,34,30,31])).
% 1.69/1.82 cnf(652,plain,
% 1.69/1.82 (~E(a2,f3(x6521,a1,x6522,f3(x6523,x6522,a2,a12)))),
% 1.69/1.82 inference(scs_inference,[],[40,633,641,644,64,57,344,519,96,596,616,554,403,576,247,153,50,45,47,46,29,32,3,35,34,30,31,33,2])).
% 1.69/1.82 cnf(664,plain,
% 1.69/1.82 (P1(a2,f8(x6641,a2,f3(x6641,a2,x6642,x6643),a1,x6641),x6641)),
% 1.69/1.82 inference(rename_variables,[],[359])).
% 1.69/1.82 cnf(667,plain,
% 1.69/1.82 (P2(x6671,f6(x6672,x6673,x6674,x6675,x6676,a1),f6(x6672,x6673,x6674,x6675,x6676,a2),x6671)),
% 1.69/1.82 inference(rename_variables,[],[197])).
% 1.69/1.82 cnf(668,plain,
% 1.69/1.82 (P2(a2,x6681,x6681,a1)),
% 1.69/1.82 inference(rename_variables,[],[64])).
% 1.69/1.82 cnf(670,plain,
% 1.69/1.82 (~P2(a2,f3(x6701,a1,x6702,f3(x6703,x6702,a2,a12)),x6704,x6704)),
% 1.81/1.82 inference(scs_inference,[],[64,197,359,652,45,47,46])).
% 1.81/1.82 cnf(674,plain,
% 1.81/1.82 (P2(f6(x6741,a2,x6742,x6743,x6744,x6745),f3(x6746,f6(x6741,a1,x6742,x6743,x6744,x6745),x6747,a2),x6747,a1)),
% 1.81/1.82 inference(scs_inference,[],[64,57,640,197,627,302,359,652,45,47,46,29,35])).
% 1.81/1.82 cnf(676,plain,
% 1.81/1.82 (~E(f6(x6761,x6762,x6763,x6764,x6765,a2),f3(f6(x6761,x6762,x6763,x6764,x6765,a1),x6766,a2,a12))),
% 1.81/1.82 inference(scs_inference,[],[64,57,640,197,667,627,302,359,652,484,45,47,46,29,35,32])).
% 1.81/1.82 cnf(679,plain,
% 1.81/1.82 (~E(a12,f3(x6791,a2,x6792,x6792))),
% 1.81/1.82 inference(scs_inference,[],[64,668,57,640,197,667,627,302,359,652,287,484,45,47,46,29,35,32,34])).
% 1.81/1.82 cnf(680,plain,
% 1.81/1.82 (P2(a2,x6801,x6801,a1)),
% 1.81/1.82 inference(rename_variables,[],[64])).
% 1.81/1.82 cnf(681,plain,
% 1.81/1.82 (~E(a1,f3(x6811,a1,x6812,f3(x6813,x6812,a2,a12)))),
% 1.81/1.82 inference(scs_inference,[],[64,668,57,640,197,667,627,302,359,652,287,484,45,47,46,29,35,32,34,3])).
% 1.81/1.82 cnf(686,plain,
% 1.81/1.82 (~E(f3(x6861,a2,x6862,x6862),a12)),
% 1.81/1.82 inference(scs_inference,[],[66,64,668,680,57,640,197,667,521,627,302,359,664,652,287,141,484,45,47,46,29,35,32,34,3,30,2,31,33])).
% 1.81/1.82 cnf(697,plain,
% 1.81/1.82 (E(f3(x6971,x6972,x6973,f3(x6974,a2,x6975,x6975)),f3(x6971,x6972,x6973,a1))),
% 1.81/1.82 inference(scs_inference,[],[66,64,668,680,57,640,197,667,521,627,302,359,664,285,635,652,287,141,484,45,47,46,29,35,32,34,3,30,2,31,33,18,16,27,26,24,22,19,15,9,7])).
% 1.81/1.82 cnf(698,plain,
% 1.81/1.82 (E(f3(f3(x6981,a2,x6982,x6982),x6983,x6984,x6985),f3(a1,x6983,x6984,x6985))),
% 1.81/1.82 inference(scs_inference,[],[66,64,668,680,57,640,197,667,521,627,302,359,664,285,635,652,287,141,484,45,47,46,29,35,32,34,3,30,2,31,33,18,16,27,26,24,22,19,15,9,7,4])).
% 1.81/1.82 cnf(706,plain,
% 1.81/1.82 (E(f6(x7061,x7062,x7063,x7064,x7065,f3(x7066,a1,x7067,x7067)),f6(x7061,x7062,x7063,x7064,x7065,a2))),
% 1.81/1.82 inference(scs_inference,[],[66,64,668,680,57,640,197,667,521,627,302,359,664,285,635,652,287,141,484,45,47,46,29,35,32,34,3,30,2,31,33,18,16,27,26,24,22,19,15,9,7,4,28,25,23,17,14,11,8,13])).
% 1.81/1.82 cnf(712,plain,
% 1.81/1.82 (E(f3(x7121,x7122,f3(x7123,a2,x7124,x7124),x7125),f3(x7121,x7122,a1,x7125))),
% 1.81/1.82 inference(scs_inference,[],[66,64,668,680,57,640,197,667,521,627,302,359,664,285,635,652,287,141,484,45,47,46,29,35,32,34,3,30,2,31,33,18,16,27,26,24,22,19,15,9,7,4,28,25,23,17,14,11,8,13,12,5,21,20,10,6])).
% 1.81/1.82 cnf(726,plain,
% 1.81/1.82 (~P2(f3(x7261,a2,x7262,x7262),a1,f3(x7263,f3(x7264,a2,a2,a1),x7265,x7265),f3(x7266,a12,a2,a1))),
% 1.81/1.82 inference(scs_inference,[],[60,631,676,45,47])).
% 1.81/1.82 cnf(728,plain,
% 1.81/1.82 (~P2(x7281,f3(x7282,x7281,x7283,x7283),f3(x7284,f3(x7285,a2,a2,a1),x7286,x7286),f3(x7287,a12,a2,a1))),
% 1.81/1.82 inference(rename_variables,[],[631])).
% 1.81/1.82 cnf(734,plain,
% 1.81/1.82 (E(f3(x7341,x7342,f6(x7343,x7344,x7345,a2,x7346,x7347),f6(x7343,x7344,x7345,a1,x7346,x7347)),x7342)),
% 1.81/1.82 inference(rename_variables,[],[505])).
% 1.81/1.82 cnf(736,plain,
% 1.81/1.82 (~P2(a2,f3(x7361,a1,x7362,f3(x7363,x7362,a2,a12)),x7364,x7364)),
% 1.81/1.82 inference(rename_variables,[],[670])).
% 1.81/1.82 cnf(743,plain,
% 1.81/1.82 (E(f3(x7431,x7432,f6(x7433,x7434,x7435,a2,x7436,x7437),f6(x7433,x7434,x7435,a1,x7436,x7437)),x7432)),
% 1.81/1.82 inference(rename_variables,[],[505])).
% 1.81/1.82 cnf(744,plain,
% 1.81/1.82 (~E(f3(f6(x7441,x7442,x7443,x7444,x7445,a1),x7446,a2,a12),f6(x7441,x7442,x7443,x7444,x7445,a2))),
% 1.81/1.82 inference(scs_inference,[],[41,60,57,631,728,676,503,670,736,590,505,734,45,47,46,29,35,3,34,32,30,2])).
% 1.81/1.82 cnf(746,plain,
% 1.81/1.82 (E(f3(x7461,x7462,f6(x7463,x7464,x7465,a2,x7466,x7467),f6(x7463,x7464,x7465,a1,x7466,x7467)),x7462)),
% 1.81/1.82 inference(rename_variables,[],[505])).
% 1.81/1.82 cnf(749,plain,
% 1.81/1.82 (P1(a1,a1,a1)),
% 1.81/1.82 inference(scs_inference,[],[41,60,57,631,728,676,645,503,670,736,590,289,505,734,743,746,456,45,47,46,29,35,3,34,32,30,2,31,33,48])).
% 1.81/1.82 cnf(760,plain,
% 1.81/1.82 (P1(a2,f6(a1,a1,a2,a1,a1,a2),a2)),
% 1.81/1.82 inference(scs_inference,[],[58,749,55])).
% 1.81/1.82 cnf(763,plain,
% 1.81/1.82 (~P2(a1,a2,f3(x7631,f3(x7632,a2,a2,a1),f3(x7633,a2,x7634,x7634),a1),a12)),
% 1.81/1.82 inference(scs_inference,[],[62,58,749,598,55,47])).
% 1.81/1.82 cnf(765,plain,
% 1.81/1.82 (P2(x7651,a2,a1,x7651)),
% 1.81/1.82 inference(rename_variables,[],[62])).
% 1.81/1.82 cnf(767,plain,
% 1.81/1.82 (E(a1,f8(a2,a1,f3(a1,a1,x7671,x7672),a1,a1))),
% 1.81/1.82 inference(scs_inference,[],[62,58,749,598,373,55,47,45])).
% 1.81/1.82 cnf(768,plain,
% 1.81/1.82 (P1(x7681,f8(a2,x7681,f3(a1,x7681,x7682,x7683),x7681,a1),a1)),
% 1.81/1.82 inference(rename_variables,[],[373])).
% 1.81/1.82 cnf(770,plain,
% 1.81/1.82 (~P2(f3(f6(x7701,x7702,x7703,x7704,x7705,a1),x7706,a2,a12),f6(x7701,x7702,x7703,x7704,x7705,a2),x7707,x7707)),
% 1.81/1.82 inference(scs_inference,[],[62,58,749,744,598,373,55,47,45,46])).
% 1.81/1.82 cnf(772,plain,
% 1.81/1.82 (P1(a1,a2,f3(a2,a1,x7721,x7722))),
% 1.81/1.82 inference(scs_inference,[],[67,62,58,57,749,744,598,373,55,47,45,46,29])).
% 1.81/1.82 cnf(775,plain,
% 1.81/1.82 (P2(x7751,a2,a1,x7751)),
% 1.81/1.82 inference(rename_variables,[],[62])).
% 1.81/1.82 cnf(778,plain,
% 1.81/1.82 (P1(x7781,f8(a2,x7781,f3(a1,x7781,x7782,x7783),x7781,f3(x7784,a2,x7785,x7785)),a1)),
% 1.81/1.82 inference(scs_inference,[],[67,62,765,775,58,57,527,508,749,744,598,373,768,55,47,45,46,29,35,32,30])).
% 1.81/1.82 cnf(780,plain,
% 1.81/1.82 (~E(a12,f3(x7801,a2,a1,f3(x7802,a2,x7803,x7803)))),
% 1.81/1.82 inference(scs_inference,[],[67,62,765,775,58,57,527,508,529,749,744,598,373,768,679,55,47,45,46,29,35,32,30,3])).
% 1.81/1.82 cnf(809,plain,
% 1.81/1.82 (P1(a2,f8(x8091,a2,f3(x8091,a1,x8092,x8093),a2,x8091),x8091)),
% 1.81/1.82 inference(scs_inference,[],[67,51])).
% 1.81/1.82 cnf(816,plain,
% 1.81/1.82 (P2(f6(x8161,x8162,x8163,x8164,x8165,a2),x8166,x8166,f6(x8161,x8162,x8163,x8164,x8165,a1))),
% 1.81/1.82 inference(rename_variables,[],[199])).
% 1.81/1.82 cnf(819,plain,
% 1.81/1.82 (~P1(f3(x8191,a2,x8192,x8192),a12,f3(x8191,a2,x8192,x8192))),
% 1.81/1.82 inference(scs_inference,[],[67,62,60,199,686,649,70,37,51,56,47,45])).
% 1.81/1.82 cnf(826,plain,
% 1.81/1.82 (~E(f6(x8261,x8262,x8263,x8264,x8265,a1),f3(x8266,f6(x8261,x8262,x8263,x8264,x8265,a2),a2,a12))),
% 1.81/1.82 inference(scs_inference,[],[67,62,60,57,199,816,674,778,686,649,276,70,37,51,56,47,45,46,29,35])).
% 1.81/1.82 cnf(827,plain,
% 1.81/1.82 (P2(f6(x8271,x8272,x8273,x8274,x8275,a2),x8276,x8276,f6(x8271,x8272,x8273,x8274,x8275,a1))),
% 1.81/1.82 inference(rename_variables,[],[199])).
% 1.81/1.82 cnf(828,plain,
% 1.81/1.82 (~P2(x8281,f3(x8282,x8281,a2,a12),x8283,x8283)),
% 1.81/1.82 inference(rename_variables,[],[276])).
% 1.81/1.82 cnf(837,plain,
% 1.81/1.82 (~E(f3(x8371,f6(x8372,x8373,x8374,x8375,x8376,a2),a2,a12),f6(x8372,x8373,x8374,x8375,x8376,a1))),
% 1.81/1.82 inference(scs_inference,[],[67,62,60,66,57,199,816,827,697,498,674,778,686,649,432,276,828,484,70,37,51,56,47,45,46,29,35,30,3,32,34])).
% 1.81/1.82 cnf(839,plain,
% 1.81/1.82 (~P2(x8391,f3(x8392,x8391,a2,a12),x8393,x8393)),
% 1.81/1.82 inference(rename_variables,[],[276])).
% 1.81/1.82 cnf(844,plain,
% 1.81/1.82 (~E(f3(f3(x8441,a2,a2,a12),a1,x8442,x8443),f3(x8441,a2,a2,a12))),
% 1.81/1.82 inference(scs_inference,[],[67,62,60,66,57,199,816,827,206,697,498,674,778,686,681,649,432,333,276,828,839,484,70,37,51,56,47,45,46,29,35,30,3,32,34,33,2,31])).
% 1.81/1.82 cnf(865,plain,
% 1.81/1.82 (P1(a2,x8651,f3(a1,x8651,x8652,x8653))),
% 1.81/1.82 inference(rename_variables,[],[213])).
% 1.81/1.82 cnf(878,plain,
% 1.81/1.82 (~P2(f3(f3(x8781,a2,a2,a12),a1,x8782,x8783),f3(x8781,a2,a2,a12),x8784,x8784)),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,844,760,763,616,213,70,52,50,55,47,45,46])).
% 1.81/1.82 cnf(882,plain,
% 1.81/1.82 (~P1(f3(x8821,a2,x8822,x8822),a12,f3(x8821,a2,x8822,x8822))),
% 1.81/1.82 inference(rename_variables,[],[819])).
% 1.81/1.82 cnf(884,plain,
% 1.81/1.82 (E(f3(x8841,x8842,a2,a1),x8842)),
% 1.81/1.82 inference(rename_variables,[],[551])).
% 1.81/1.82 cnf(887,plain,
% 1.81/1.82 (~P2(f3(f6(x8871,x8872,x8873,x8874,x8875,a1),x8876,a2,a12),f6(x8871,x8872,x8873,x8874,x8875,a2),x8877,x8877)),
% 1.81/1.82 inference(rename_variables,[],[770])).
% 1.81/1.82 cnf(888,plain,
% 1.81/1.82 (~P2(f3(x8881,a12,a2,a1),f3(x8882,f3(x8883,a2,a2,a1),a2,a1),x8884,x8884)),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,712,770,844,760,453,819,882,767,763,551,884,616,213,70,52,50,55,47,45,46,29,30,3,35,32])).
% 1.81/1.82 cnf(897,plain,
% 1.81/1.82 (E(f8(x8971,x8972,x8973,x8974,x8975),f8(x8971,x8972,x8973,x8974,f3(x8976,x8975,x8977,x8977)))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,213,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18])).
% 1.81/1.82 cnf(898,plain,
% 1.81/1.82 (E(f8(x8981,x8982,x8983,x8984,x8985),f8(x8981,x8982,f3(x8986,x8983,x8987,x8987),x8984,x8985))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,213,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18,16])).
% 1.81/1.82 cnf(901,plain,
% 1.81/1.82 (E(f3(x9011,x9012,x9013,x9014),f3(x9011,x9012,x9013,f3(x9015,x9014,x9016,x9016)))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,213,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18,16,24,22,7])).
% 1.81/1.82 cnf(912,plain,
% 1.81/1.82 (E(f6(x9121,x9122,x9123,x9124,x9125,x9126),f6(x9121,x9122,x9123,f3(x9127,x9124,x9128,x9128),x9125,x9126))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,213,865,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18,16,24,22,7,53,28,27,26,25,23,19,15,11])).
% 1.81/1.82 cnf(913,plain,
% 1.81/1.82 (E(f6(x9131,x9132,x9133,x9134,x9135,x9136),f6(x9131,f3(x9137,x9132,x9138,x9138),x9133,x9134,x9135,x9136))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,213,865,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18,16,24,22,7,53,28,27,26,25,23,19,15,11,9])).
% 1.81/1.82 cnf(922,plain,
% 1.81/1.82 (E(f3(x9221,x9222,x9223,x9224),f3(x9221,x9222,f3(x9225,x9223,x9226,x9226),x9224))),
% 1.81/1.82 inference(scs_inference,[],[69,62,64,66,57,706,698,712,770,887,844,760,453,819,882,726,767,763,72,551,884,616,749,213,865,70,52,50,55,47,45,46,29,30,3,35,32,34,2,31,33,18,16,24,22,7,53,28,27,26,25,23,19,15,11,9,13,51,4,20,17,14,8,6])).
% 1.81/1.82 cnf(948,plain,
% 1.81/1.82 (P2(x9481,a1,a2,x9481)),
% 1.81/1.82 inference(rename_variables,[],[60])).
% 1.81/1.82 cnf(962,plain,
% 1.81/1.82 (P2(x9621,a1,a2,x9621)),
% 1.81/1.82 inference(rename_variables,[],[60])).
% 1.81/1.82 cnf(963,plain,
% 1.81/1.82 (P2(f6(x9631,x9632,x9633,f3(x9634,x9635,x9636,x9636),x9637,x9638),a1,a2,f6(x9631,x9632,x9633,x9635,x9637,x9638))),
% 1.81/1.82 inference(scs_inference,[],[43,60,948,962,62,67,912,897,901,137,878,826,494,780,643,772,233,55,47,45,46,3,30,29,35,32])).
% 1.81/1.82 cnf(999,plain,
% 1.81/1.82 (P2(x9991,x9992,x9991,x9992)),
% 1.81/1.82 inference(rename_variables,[],[70])).
% 1.81/1.82 cnf(1000,plain,
% 1.81/1.82 (~P2(f3(x10001,a12,a2,a1),f3(x10002,f3(x10003,a2,a2,a1),a2,a1),x10004,x10004)),
% 1.81/1.82 inference(rename_variables,[],[888])).
% 1.81/1.82 cnf(1004,plain,
% 1.81/1.82 (E(f6(x10041,x10042,x10043,x10044,x10045,x10046),f6(x10041,f3(x10047,x10042,x10048,x10048),x10043,x10044,x10045,x10046))),
% 1.81/1.82 inference(rename_variables,[],[913])).
% 1.81/1.82 cnf(1009,plain,
% 1.81/1.82 ($false),
% 1.81/1.82 inference(scs_inference,[],[57,67,64,70,999,66,913,1004,898,922,211,618,888,1000,837,809,963,170,505,47,45,46,3,30,35,29,32,34,2,31]),
% 1.81/1.82 ['proof']).
% 1.81/1.82 % SZS output end Proof
% 1.81/1.82 % Total time :1.170000s
%------------------------------------------------------------------------------