TSTP Solution File: LCL544+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n014.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 06:49:40 EDT 2023
% Result : Theorem 5.16s 5.23s
% Output : CNFRefutation 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 01:25:33 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 5.07/5.22 %-------------------------------------------
% 5.07/5.22 % File :CSE---1.6
% 5.07/5.22 % Problem :theBenchmark
% 5.07/5.22 % Transform :cnf
% 5.07/5.22 % Format :tptp:raw
% 5.07/5.22 % Command :java -jar mcs_scs.jar %d %s
% 5.07/5.22
% 5.07/5.22 % Result :Theorem 4.570000s
% 5.07/5.22 % Output :CNFRefutation 4.570000s
% 5.07/5.22 %-------------------------------------------
% 5.07/5.22 %------------------------------------------------------------------------------
% 5.07/5.22 % File : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% 5.07/5.22 % Domain : Logic Calculi (Propositional modal)
% 5.07/5.22 % Problem : Prove axiom m4 from KM4B axiomatization of S5
% 5.07/5.22 % Version : [HC96] axioms.
% 5.07/5.22 % English :
% 5.07/5.22
% 5.07/5.22 % Refs : [HC96] Hughes & Cresswell (1996), A New Introduction to Modal
% 5.07/5.22 % : [Hal] Halleck (URL), John Halleck's Logic Systems
% 5.07/5.22 % Source : [TPTP]
% 5.07/5.22 % Names :
% 5.07/5.22
% 5.07/5.22 % Status : Theorem
% 5.07/5.22 % Rating : 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.23 v7.3.0, 0.21 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.31 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.37 v6.0.0, 0.39 v5.5.0, 0.56 v5.4.0, 0.54 v5.3.0, 0.63 v5.2.0, 0.45 v5.1.0, 0.48 v5.0.0, 0.50 v4.1.0, 0.57 v4.0.1, 0.52 v4.0.0, 0.46 v3.7.0, 0.35 v3.5.0, 0.37 v3.4.0, 0.53 v3.3.0
% 5.07/5.22 % Syntax : Number of formulae : 89 ( 31 unt; 0 def)
% 5.07/5.22 % Number of atoms : 156 ( 11 equ)
% 5.07/5.22 % Maximal formula atoms : 4 ( 1 avg)
% 5.07/5.22 % Number of connectives : 67 ( 0 ~; 0 |; 3 &)
% 5.07/5.22 % ( 49 <=>; 15 =>; 0 <=; 0 <~>)
% 5.07/5.22 % Maximal formula depth : 6 ( 3 avg)
% 5.07/5.22 % Maximal term depth : 5 ( 2 avg)
% 5.07/5.22 % Number of predicates : 61 ( 60 usr; 59 prp; 0-2 aty)
% 5.07/5.22 % Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% 5.07/5.22 % Number of variables : 110 ( 110 !; 0 ?)
% 5.07/5.22 % SPC : FOF_THM_RFO_SEQ
% 5.07/5.22
% 5.07/5.22 % Comments :
% 5.07/5.22 %------------------------------------------------------------------------------
% 5.07/5.22 %----Include Hilbert's axiomatization of propositional logic
% 5.16/5.23 include('Axioms/LCL006+0.ax').
% 5.16/5.23 include('Axioms/LCL006+1.ax').
% 5.16/5.23 include('Axioms/LCL006+2.ax').
% 5.16/5.23 %----Include axioms of modal logic
% 5.16/5.23 include('Axioms/LCL007+0.ax').
% 5.16/5.23 include('Axioms/LCL007+1.ax').
% 5.16/5.23 %----Include axioms for KM4B
% 5.16/5.23 include('Axioms/LCL007+3.ax').
% 5.16/5.23 %------------------------------------------------------------------------------
% 5.16/5.23 %----Modal definitions
% 5.16/5.23 fof(s1_0_op_possibly,axiom,
% 5.16/5.23 op_possibly ).
% 5.16/5.23
% 5.16/5.23 fof(s1_0_op_or,axiom,
% 5.16/5.23 op_or ).
% 5.16/5.23
% 5.16/5.23 fof(s1_0_op_implies,axiom,
% 5.16/5.23 op_implies ).
% 5.16/5.23
% 5.16/5.23 fof(s1_0_op_strict_implies,axiom,
% 5.16/5.23 op_strict_implies ).
% 5.16/5.23
% 5.16/5.23 fof(s1_0_op_equiv,axiom,
% 5.16/5.23 op_equiv ).
% 5.16/5.23
% 5.16/5.23 fof(s1_0_op_strict_equiv,axiom,
% 5.16/5.23 op_strict_equiv ).
% 5.16/5.23
% 5.16/5.23 %----Conjecture
% 5.16/5.23 fof(s1_0_axiom_m4,conjecture,
% 5.16/5.23 axiom_m4 ).
% 5.16/5.23
% 5.16/5.23 %------------------------------------------------------------------------------
% 5.16/5.23 %-------------------------------------------
% 5.16/5.23 % Proof found
% 5.16/5.23 % SZS status Theorem for theBenchmark
% 5.16/5.23 % SZS output start Proof
% 5.16/5.23 %ClaNum:225(EqnAxiom:78)
% 5.16/5.23 %VarNum:219(SingletonVarNum:109)
% 5.16/5.23 %MaxLitNum:4
% 5.16/5.23 %MaxfuncDepth:4
% 5.16/5.23 %SharedTerms:428
% 5.16/5.23 %goalClause: 109
% 5.16/5.23 %singleGoalClaCount:1
% 5.16/5.23 [79]P1(a500)
% 5.16/5.23 [80]P38(a500)
% 5.16/5.23 [81]P39(a500)
% 5.16/5.23 [82]P2(a500)
% 5.16/5.23 [83]P32(a500)
% 5.16/5.23 [84]P33(a500)
% 5.16/5.23 [85]P3(a500)
% 5.16/5.23 [86]P5(a500)
% 5.16/5.23 [87]P6(a500)
% 5.16/5.23 [88]P41(a500)
% 5.16/5.23 [89]P53(a500)
% 5.16/5.23 [90]P54(a500)
% 5.16/5.23 [91]P7(a500)
% 5.16/5.23 [92]P30(a500)
% 5.16/5.23 [93]P31(a500)
% 5.16/5.23 [95]P42(a500)
% 5.16/5.23 [96]P43(a500)
% 5.16/5.23 [98]P44(a500)
% 5.16/5.23 [99]P45(a500)
% 5.16/5.23 [100]P8(a500)
% 5.16/5.23 [101]P12(a500)
% 5.16/5.23 [102]P9(a500)
% 5.16/5.23 [103]P10(a500)
% 5.16/5.23 [105]P50(a500)
% 5.16/5.23 [106]P51(a500)
% 5.16/5.23 [107]P52(a500)
% 5.16/5.23 [108]P47(a500)
% 5.16/5.23 [109]~P13(a500)
% 5.16/5.23 [111]P60(a500)+~E(a47,a48)
% 5.16/5.23 [114]P40(a500)+P34(a56)
% 5.16/5.23 [115]P4(a500)+P34(a57)
% 5.16/5.23 [116]P4(a500)+P34(a59)
% 5.16/5.23 [118]P40(a500)+~P34(a58)
% 5.16/5.23 [123]P40(a500)+P34(f99(a56,a58))
% 5.16/5.23 [124]P60(a500)+P34(f100(a48,a47))
% 5.16/5.23 [128]P4(a500)+~P34(f5(a57,a59))
% 5.16/5.23 [135]P18(a500)+~P34(f99(a63,f102(a63)))
% 5.16/5.23 [166]P21(a500)+~P34(f99(f102(f102(a92)),f102(a92)))
% 5.16/5.23 [170]P35(a500)+~P34(f62(a27,f5(a27,a27)))
% 5.16/5.23 [171]P55(a500)+~P34(f62(a37,f103(a38,a37)))
% 5.16/5.23 [172]P13(a500)+~P34(f99(a83,f5(a83,a83)))
% 5.16/5.23 [175]P36(a500)+~P34(f62(f5(a31,a32),a31))
% 5.16/5.23 [176]P56(a500)+~P34(f62(f103(a39,a39),a39))
% 5.16/5.23 [177]P16(a500)+~P34(f99(f5(a80,a84),a80))
% 5.16/5.23 [189]P57(a500)+~P34(f62(f103(a45,a46),f103(a46,a45)))
% 5.16/5.23 [190]P15(a500)+~P34(f99(f5(a81,a82),f5(a82,a81)))
% 5.16/5.23 [219]P19(a500)+~P34(f99(f5(f99(a88,a89),f99(a89,a90)),f99(a88,a90)))
% 5.16/5.23 [163]P11(a500)+~P34(f62(f102(a69),f61(f102(a69))))
% 5.16/5.23 [164]P20(a500)+~P34(f99(f61(a70),f61(f61(a70))))
% 5.16/5.23 [165]P14(a500)+~P34(f99(f102(a91),f61(f102(a91))))
% 5.16/5.23 [180]P27(a500)+~P34(f62(a40,f62(f101(a40),a43)))
% 5.16/5.23 [181]P29(a500)+~P34(f62(f62(f101(a44),a44),a44))
% 5.16/5.23 [194]P22(a500)+~P34(f99(f102(f5(a94,a95)),a94))
% 5.16/5.23 [195]P23(a500)+~P34(f99(f99(a96,a97),f99(f102(a96),f102(a97))))
% 5.16/5.23 [204]P24(a500)+~P34(f99(f102(f5(a73,a76)),f5(f102(a73),f102(a76))))
% 5.16/5.23 [215]P28(a500)+~P34(f62(f62(a33,a41),f62(f62(a41,a42),f62(a33,a42))))
% 5.16/5.23 [216]P58(a500)+~P34(f62(f62(a50,a55),f62(f103(a51,a50),f103(a51,a55))))
% 5.16/5.23 [217]P59(a500)+~P34(f62(f103(a52,f103(a53,a54)),f103(a53,f103(a52,a54))))
% 5.16/5.23 [218]P17(a500)+~P34(f99(f5(f5(a85,a86),a87),f5(a85,f5(a86,a87))))
% 5.16/5.23 [225]P25(a500)+~P34(f62(f5(f61(f62(a72,a74)),f61(f62(a74,a75))),f61(f62(a72,a75))))
% 5.16/5.23 [212]P26(a500)+~P34(f99(f99(a77,a78),f99(f101(f102(a78)),f101(f102(a77)))))
% 5.16/5.23 [224]P37(a500)+~P34(f62(f62(a34,a35),f62(f101(f5(a35,a36)),f101(f5(a36,a34)))))
% 5.16/5.23 [129]~P18(a500)+P34(f99(x1291,f102(x1291)))
% 5.16/5.23 [130]~P12(a500)+P34(f62(f61(x1301),x1301))
% 5.16/5.23 [147]~P21(a500)+P34(f99(f102(f102(x1471)),f102(x1471)))
% 5.16/5.23 [152]~P35(a500)+P34(f62(x1521,f5(x1521,x1521)))
% 5.16/5.23 [160]~P56(a500)+P34(f62(f103(x1601,x1601),x1601))
% 5.16/5.23 [125]~P48(a500)+E(f101(f102(f101(x1251))),f61(x1251))
% 5.16/5.23 [126]~P50(a500)+E(f101(f61(f101(x1261))),f102(x1261))
% 5.16/5.23 [140]~P10(a500)+P34(f62(x1401,f61(f102(x1401))))
% 5.16/5.23 [143]~P9(a500)+P34(f62(f61(x1431),f61(f61(x1431))))
% 5.16/5.23 [144]~P11(a500)+P34(f62(f102(x1441),f61(f102(x1441))))
% 5.16/5.23 [145]~P20(a500)+P34(f99(f61(x1451),f61(f61(x1451))))
% 5.16/5.23 [146]~P14(a500)+P34(f99(f102(x1461),f61(f102(x1461))))
% 5.16/5.23 [179]~P29(a500)+P34(f62(f62(f101(x1791),x1791),x1791))
% 5.16/5.23 [127]E(f103(f101(x1271),x1272),f62(x1271,x1272))+~P49(a500)
% 5.16/5.23 [131]E(f61(f62(x1311,x1312)),f99(x1311,x1312))+~P51(a500)
% 5.16/5.23 [148]E(f5(f62(x1481,x1482),f62(x1482,x1481)),f4(x1481,x1482))+~P44(a500)
% 5.16/5.23 [149]E(f5(f99(x1491,x1492),f99(x1492,x1491)),f100(x1491,x1492))+~P52(a500)
% 5.16/5.23 [151]~P2(a500)+P34(f62(x1511,f62(x1512,x1511)))
% 5.16/5.23 [153]~P53(a500)+P34(f62(x1531,f103(x1532,x1531)))
% 5.16/5.23 [154]~P55(a500)+P34(f62(x1541,f103(x1542,x1541)))
% 5.16/5.23 [155]~P41(a500)+P34(f62(x1551,f103(x1551,x1552)))
% 5.16/5.23 [157]~P5(a500)+P34(f62(f5(x1571,x1572),x1572))
% 5.16/5.23 [158]~P3(a500)+P34(f62(f5(x1581,x1582),x1581))
% 5.16/5.23 [159]~P36(a500)+P34(f62(f5(x1591,x1592),x1591))
% 5.16/5.23 [161]~P16(a500)+P34(f99(f5(x1611,x1612),x1611))
% 5.16/5.23 [182]~P30(a500)+P34(f62(f4(x1821,x1822),f62(x1822,x1821)))
% 5.16/5.23 [183]~P7(a500)+P34(f62(f4(x1831,x1832),f62(x1831,x1832)))
% 5.16/5.23 [184]~P57(a500)+P34(f62(f103(x1841,x1842),f103(x1842,x1841)))
% 5.16/5.23 [185]~P15(a500)+P34(f99(f5(x1851,x1852),f5(x1852,x1851)))
% 5.16/5.23 [192]~P39(a500)+P34(f62(f62(f101(x1921),f101(x1922)),f62(x1922,x1921)))
% 5.16/5.23 [197]~P32(a500)+P34(f62(f62(x1971,f62(x1971,x1972)),f62(x1971,x1972)))
% 5.16/5.23 [137]~P43(a500)+E(f101(f5(x1371,f101(x1372))),f62(x1371,x1372))
% 5.16/5.23 [141]~P46(a500)+E(f101(f103(f101(x1411),f101(x1412))),f5(x1411,x1412))
% 5.16/5.23 [142]~P42(a500)+E(f101(f5(f101(x1421),f101(x1422))),f103(x1421,x1422))
% 5.16/5.23 [178]~P27(a500)+P34(f62(x1781,f62(f101(x1781),x1782)))
% 5.16/5.23 [186]~P22(a500)+P34(f99(f102(f5(x1861,x1862)),x1861))
% 5.16/5.23 [191]~P23(a500)+P34(f99(f99(x1911,x1912),f99(f102(x1911),f102(x1912))))
% 5.16/5.23 [193]~P6(a500)+P34(f62(x1931,f62(x1932,f5(x1931,x1932))))
% 5.16/5.23 [199]~P8(a500)+P34(f62(f61(f62(x1991,x1992)),f62(f61(x1991),f61(x1992))))
% 5.16/5.23 [200]~P24(a500)+P34(f99(f102(f5(x2001,x2002)),f5(f102(x2001),f102(x2002))))
% 5.16/5.23 [207]~P31(a500)+P34(f62(f62(x2071,x2072),f62(f62(x2072,x2071),f4(x2071,x2072))))
% 5.16/5.23 [201]~P26(a500)+P34(f99(f99(x2011,x2012),f99(f101(f102(x2012)),f101(f102(x2011)))))
% 5.16/5.23 [211]~P19(a500)+P34(f99(f5(f99(x2111,x2112),f99(x2112,x2113)),f99(x2111,x2113)))
% 5.16/5.23 [205]~P33(a500)+P34(f62(f62(x2051,x2052),f62(f62(x2052,x2053),f62(x2051,x2053))))
% 5.16/5.23 [206]~P28(a500)+P34(f62(f62(x2061,x2062),f62(f62(x2062,x2063),f62(x2061,x2063))))
% 5.16/5.23 [208]~P58(a500)+P34(f62(f62(x2081,x2082),f62(f103(x2083,x2081),f103(x2083,x2082))))
% 5.16/5.23 [209]~P59(a500)+P34(f62(f103(x2091,f103(x2092,x2093)),f103(x2092,f103(x2091,x2093))))
% 5.16/5.23 [210]~P17(a500)+P34(f99(f5(f5(x2101,x2102),x2103),f5(x2101,f5(x2102,x2103))))
% 5.16/5.23 [222]~P25(a500)+P34(f62(f5(f61(f62(x2221,x2222)),f61(f62(x2222,x2223))),f61(f62(x2221,x2223))))
% 5.16/5.23 [220]~P54(a500)+P34(f62(f62(x2201,x2202),f62(f62(x2203,x2202),f62(f103(x2201,x2203),x2202))))
% 5.16/5.23 [221]~P37(a500)+P34(f62(f62(x2211,x2212),f62(f101(f5(x2212,x2213)),f101(f5(x2213,x2211)))))
% 5.16/5.23 [120]~P34(x1201)+P34(f61(x1201))+~P45(a500)
% 5.16/5.23 [133]E(x1331,x1332)+~P38(a500)+~P34(f4(x1331,x1332))
% 5.16/5.23 [134]E(x1341,x1342)+~P60(a500)+~P34(f100(x1341,x1342))
% 5.16/5.23 [132]~P34(x1322)+~P34(x1321)+P34(f5(x1321,x1322))+~P4(a500)
% 5.16/5.23 [138]P34(x1381)+~P34(x1382)+~P1(a500)+~P34(f62(x1382,x1381))
% 5.16/5.23 [139]P34(x1391)+~P34(x1392)+~P40(a500)+~P34(f99(x1392,x1391))
% 5.16/5.23 %EqnAxiom
% 5.16/5.23 [1]E(x11,x11)
% 5.16/5.23 [2]E(x22,x21)+~E(x21,x22)
% 5.16/5.23 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 5.16/5.23 [4]~E(x41,x42)+E(f61(x41),f61(x42))
% 5.16/5.23 [5]~E(x51,x52)+E(f62(x51,x53),f62(x52,x53))
% 5.16/5.23 [6]~E(x61,x62)+E(f62(x63,x61),f62(x63,x62))
% 5.16/5.23 [7]~E(x71,x72)+E(f103(x71,x73),f103(x72,x73))
% 5.16/5.23 [8]~E(x81,x82)+E(f103(x83,x81),f103(x83,x82))
% 5.16/5.23 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 5.16/5.23 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 5.16/5.23 [11]~E(x111,x112)+E(f99(x111,x113),f99(x112,x113))
% 5.16/5.23 [12]~E(x121,x122)+E(f99(x123,x121),f99(x123,x122))
% 5.16/5.23 [13]~E(x131,x132)+E(f100(x131,x133),f100(x132,x133))
% 5.16/5.23 [14]~E(x141,x142)+E(f100(x143,x141),f100(x143,x142))
% 5.16/5.23 [15]~E(x151,x152)+E(f101(x151),f101(x152))
% 5.16/5.23 [16]~E(x161,x162)+E(f102(x161),f102(x162))
% 5.16/5.23 [17]~E(x171,x172)+E(f5(x171,x173),f5(x172,x173))
% 5.16/5.23 [18]~E(x181,x182)+E(f5(x183,x181),f5(x183,x182))
% 5.16/5.23 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 5.16/5.23 [20]~P38(x201)+P38(x202)+~E(x201,x202)
% 5.16/5.23 [21]~P39(x211)+P39(x212)+~E(x211,x212)
% 5.16/5.23 [22]~P2(x221)+P2(x222)+~E(x221,x222)
% 5.16/5.23 [23]~P32(x231)+P32(x232)+~E(x231,x232)
% 5.16/5.23 [24]~P33(x241)+P33(x242)+~E(x241,x242)
% 5.16/5.23 [25]~P3(x251)+P3(x252)+~E(x251,x252)
% 5.16/5.23 [26]~P5(x261)+P5(x262)+~E(x261,x262)
% 5.16/5.23 [27]~P6(x271)+P6(x272)+~E(x271,x272)
% 5.16/5.23 [28]~P41(x281)+P41(x282)+~E(x281,x282)
% 5.16/5.23 [29]~P53(x291)+P53(x292)+~E(x291,x292)
% 5.16/5.23 [30]~P54(x301)+P54(x302)+~E(x301,x302)
% 5.16/5.23 [31]~P7(x311)+P7(x312)+~E(x311,x312)
% 5.16/5.23 [32]~P30(x321)+P30(x322)+~E(x321,x322)
% 5.16/5.23 [33]~P31(x331)+P31(x332)+~E(x331,x332)
% 5.16/5.23 [34]~P42(x341)+P42(x342)+~E(x341,x342)
% 5.16/5.23 [35]~P34(x351)+P34(x352)+~E(x351,x352)
% 5.16/5.23 [36]~P43(x361)+P43(x362)+~E(x361,x362)
% 5.16/5.23 [37]~P44(x371)+P44(x372)+~E(x371,x372)
% 5.16/5.23 [38]~P55(x381)+P55(x382)+~E(x381,x382)
% 5.16/5.23 [39]~P45(x391)+P45(x392)+~E(x391,x392)
% 5.16/5.23 [40]~P8(x401)+P8(x402)+~E(x401,x402)
% 5.16/5.23 [41]~P12(x411)+P12(x412)+~E(x411,x412)
% 5.16/5.23 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 5.16/5.23 [43]~P10(x431)+P10(x432)+~E(x431,x432)
% 5.16/5.23 [44]~P50(x441)+P50(x442)+~E(x441,x442)
% 5.16/5.23 [45]~P16(x451)+P16(x452)+~E(x451,x452)
% 5.16/5.23 [46]~P51(x461)+P51(x462)+~E(x461,x462)
% 5.16/5.23 [47]~P52(x471)+P52(x472)+~E(x471,x472)
% 5.16/5.23 [48]~P47(x481)+P47(x482)+~E(x481,x482)
% 5.16/5.23 [49]~P13(x491)+P13(x492)+~E(x491,x492)
% 5.16/5.23 [50]~P59(x501)+P59(x502)+~E(x501,x502)
% 5.16/5.23 [51]~P60(x511)+P60(x512)+~E(x511,x512)
% 5.16/5.23 [52]~P28(x521)+P28(x522)+~E(x521,x522)
% 5.16/5.23 [53]~P19(x531)+P19(x532)+~E(x531,x532)
% 5.16/5.23 [54]~P20(x541)+P20(x542)+~E(x541,x542)
% 5.16/5.23 [55]~P24(x551)+P24(x552)+~E(x551,x552)
% 5.16/5.24 [56]~P40(x561)+P40(x562)+~E(x561,x562)
% 5.16/5.24 [57]~P21(x571)+P21(x572)+~E(x571,x572)
% 5.16/5.24 [58]~P4(x581)+P4(x582)+~E(x581,x582)
% 5.16/5.24 [59]~P26(x591)+P26(x592)+~E(x591,x592)
% 5.16/5.24 [60]~P56(x601)+P56(x602)+~E(x601,x602)
% 5.16/5.24 [61]~P37(x611)+P37(x612)+~E(x611,x612)
% 5.16/5.24 [62]~P25(x621)+P25(x622)+~E(x621,x622)
% 5.16/5.24 [63]~P14(x631)+P14(x632)+~E(x631,x632)
% 5.16/5.24 [64]~P11(x641)+P11(x642)+~E(x641,x642)
% 5.16/5.24 [65]~P29(x651)+P29(x652)+~E(x651,x652)
% 5.16/5.24 [66]~P27(x661)+P27(x662)+~E(x661,x662)
% 5.16/5.24 [67]~P23(x671)+P23(x672)+~E(x671,x672)
% 5.16/5.24 [68]~P22(x681)+P22(x682)+~E(x681,x682)
% 5.16/5.24 [69]~P46(x691)+P46(x692)+~E(x691,x692)
% 5.16/5.24 [70]~P58(x701)+P58(x702)+~E(x701,x702)
% 5.16/5.24 [71]~P17(x711)+P17(x712)+~E(x711,x712)
% 5.16/5.24 [72]~P15(x721)+P15(x722)+~E(x721,x722)
% 5.16/5.24 [73]~P57(x731)+P57(x732)+~E(x731,x732)
% 5.16/5.24 [74]~P18(x741)+P18(x742)+~E(x741,x742)
% 5.16/5.24 [75]~P35(x751)+P35(x752)+~E(x751,x752)
% 5.16/5.24 [76]~P36(x761)+P36(x762)+~E(x761,x762)
% 5.16/5.24 [77]~P49(x771)+P49(x772)+~E(x771,x772)
% 5.16/5.24 [78]~P48(x781)+P48(x782)+~E(x781,x782)
% 5.16/5.24
% 5.16/5.24 %-------------------------------------------
% 5.16/5.24 cnf(226,plain,
% 5.16/5.24 (~P34(f99(a83,f5(a83,a83)))),
% 5.16/5.24 inference(scs_inference,[],[109,172])).
% 5.16/5.24 cnf(227,plain,
% 5.16/5.24 (P34(f62(f5(x2271,x2272),x2271))),
% 5.16/5.24 inference(scs_inference,[],[109,85,172,158])).
% 5.16/5.24 cnf(232,plain,
% 5.16/5.24 (P34(f62(f61(x2321),x2321))),
% 5.16/5.24 inference(scs_inference,[],[109,82,85,86,88,89,101,172,158,157,155,153,151,130])).
% 5.16/5.24 cnf(233,plain,
% 5.16/5.24 (P34(f62(x2331,f62(x2332,f5(x2331,x2332))))),
% 5.16/5.24 inference(scs_inference,[],[109,82,85,86,87,88,89,101,172,158,157,155,153,151,130,193])).
% 5.16/5.24 cnf(237,plain,
% 5.16/5.24 (E(f61(f62(x2371,x2372)),f99(x2371,x2372))),
% 5.16/5.24 inference(scs_inference,[],[109,82,85,86,87,88,89,91,92,101,103,106,172,158,157,155,153,151,130,193,183,182,140,131])).
% 5.16/5.24 cnf(238,plain,
% 5.16/5.24 (P34(f62(f62(x2381,f62(x2381,x2382)),f62(x2381,x2382)))),
% 5.16/5.24 inference(scs_inference,[],[109,82,83,85,86,87,88,89,91,92,101,103,106,172,158,157,155,153,151,130,193,183,182,140,131,197])).
% 5.16/5.24 cnf(240,plain,
% 5.16/5.24 (E(f5(f62(x2401,x2402),f62(x2402,x2401)),f4(x2401,x2402))),
% 5.16/5.24 inference(scs_inference,[],[109,82,83,85,86,87,88,89,91,92,98,101,103,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148])).
% 5.16/5.24 cnf(242,plain,
% 5.16/5.24 (E(f101(f5(x2421,f101(x2422))),f62(x2421,x2422))),
% 5.16/5.24 inference(scs_inference,[],[109,82,83,85,86,87,88,89,91,92,96,98,101,102,103,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137])).
% 5.16/5.24 cnf(244,plain,
% 5.16/5.24 (P34(f62(f62(x2441,x2442),f62(f62(x2442,x2441),f4(x2441,x2442))))),
% 5.16/5.24 inference(scs_inference,[],[109,82,83,85,86,87,88,89,91,92,93,96,98,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207])).
% 5.16/5.24 cnf(247,plain,
% 5.16/5.24 (E(f101(f5(f101(x2471),f101(x2472))),f103(x2471,x2472))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,91,92,93,95,96,98,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142])).
% 5.16/5.24 cnf(250,plain,
% 5.16/5.24 (E(f5(x2501,f61(f62(x2502,x2503))),f5(x2501,f99(x2502,x2503)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18])).
% 5.16/5.24 cnf(256,plain,
% 5.16/5.24 (E(f99(x2561,f61(f62(x2562,x2563))),f99(x2561,f99(x2562,x2563)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12])).
% 5.16/5.24 cnf(258,plain,
% 5.16/5.24 (E(f4(x2581,f61(f62(x2582,x2583))),f4(x2581,f99(x2582,x2583)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10])).
% 5.16/5.24 cnf(262,plain,
% 5.16/5.24 (E(f62(x2621,f61(f62(x2622,x2623))),f62(x2621,f99(x2622,x2623)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10,9,8,7,6])).
% 5.16/5.24 cnf(266,plain,
% 5.16/5.24 (~E(f62(f5(x2661,x2662),x2661),f99(a83,f5(a83,a83)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,108,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,48,35])).
% 5.16/5.24 cnf(267,plain,
% 5.16/5.24 (~E(f62(f5(f61(f62(x2671,x2672)),x2673),f99(x2671,x2672)),f99(a83,f5(a83,a83)))),
% 5.16/5.24 inference(scs_inference,[],[109,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,108,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,48,35,3])).
% 5.16/5.24 cnf(268,plain,
% 5.16/5.24 (~P34(f5(x2681,f99(a83,f5(a83,a83))))),
% 5.16/5.24 inference(scs_inference,[],[109,79,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,108,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,48,35,3,138])).
% 5.16/5.24 cnf(270,plain,
% 5.16/5.24 (E(f99(x2701,x2702),f61(f62(x2701,x2702)))),
% 5.16/5.24 inference(scs_inference,[],[109,79,81,82,83,84,85,86,87,88,89,90,91,92,93,95,96,98,100,101,102,103,105,106,107,108,172,158,157,155,153,151,130,193,183,182,140,131,197,149,148,143,137,126,207,205,192,142,220,199,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,48,35,3,138,2])).
% 5.16/5.24 cnf(284,plain,
% 5.16/5.24 (~P34(x2841)+P34(f61(x2841))),
% 5.16/5.24 inference(scs_inference,[],[99,120])).
% 5.16/5.24 cnf(285,plain,
% 5.16/5.24 (E(x2851,x2852)+~P34(f4(x2851,x2852))),
% 5.16/5.24 inference(scs_inference,[],[80,133])).
% 5.16/5.24 cnf(286,plain,
% 5.16/5.24 (P34(x2861)+~P34(x2862)+~P34(f62(x2862,x2861))),
% 5.16/5.24 inference(scs_inference,[],[79,138])).
% 5.16/5.24 cnf(288,plain,
% 5.16/5.24 (P34(f62(f62(f62(x2881,x2882),f62(x2881,f62(x2881,x2882))),f4(f62(x2881,f62(x2881,x2882)),f62(x2881,x2882))))),
% 5.16/5.24 inference(scs_inference,[],[244,238,286])).
% 5.16/5.24 cnf(291,plain,
% 5.16/5.24 (~E(f99(a83,f5(a83,a83)),f62(f5(f61(f62(x2911,x2912)),x2913),f99(x2911,x2912)))),
% 5.16/5.24 inference(scs_inference,[],[244,238,267,286,2])).
% 5.16/5.24 cnf(295,plain,
% 5.16/5.24 (E(f61(f62(x2951,f61(f62(x2952,x2953)))),f99(x2951,f99(x2952,x2953)))),
% 5.16/5.24 inference(scs_inference,[],[244,238,237,250,256,268,267,286,2,35,3])).
% 5.16/5.24 cnf(297,plain,
% 5.16/5.24 (~P34(f4(f62(f5(x2971,x2972),x2971),f99(a83,f5(a83,a83))))),
% 5.16/5.24 inference(scs_inference,[],[244,238,237,250,256,268,267,266,286,2,35,3,285])).
% 5.16/5.24 cnf(307,plain,
% 5.16/5.24 (P34(f62(f61(f61(f62(x3071,x3072))),f99(x3071,x3072)))),
% 5.16/5.24 inference(scs_inference,[],[240,232,262,2,35])).
% 5.16/5.24 cnf(324,plain,
% 5.16/5.24 (~E(f99(a83,f5(a83,a83)),f62(f5(x3241,x3242),x3241))),
% 5.16/5.24 inference(scs_inference,[],[226,288,307,266,286,35,2])).
% 5.16/5.24 cnf(325,plain,
% 5.16/5.24 (~E(f61(f62(a83,f5(a83,a83))),f62(f5(f61(f62(x3251,x3252)),x3253),f99(x3251,x3252)))),
% 5.16/5.24 inference(scs_inference,[],[226,288,270,307,291,266,286,35,2,3])).
% 5.16/5.24 cnf(328,plain,
% 5.16/5.24 (~P34(f61(f62(a83,f5(a83,a83))))),
% 5.16/5.24 inference(scs_inference,[],[107,226,288,270,307,291,266,286,35,2,3,47,284])).
% 5.16/5.24 cnf(334,plain,
% 5.16/5.24 (P34(f61(f62(f5(x3341,x3342),x3341)))),
% 5.16/5.24 inference(scs_inference,[],[227,284])).
% 5.16/5.24 cnf(341,plain,
% 5.16/5.24 (E(f62(x3411,x3412),f101(f5(x3411,f101(x3412))))),
% 5.16/5.24 inference(scs_inference,[],[227,226,242,258,297,284,286,35,2])).
% 5.16/5.24 cnf(380,plain,
% 5.16/5.24 (~P34(f62(a27,f5(a27,a27)))),
% 5.16/5.24 inference(scs_inference,[],[105,227,226,247,295,341,334,325,324,328,284,286,35,2,3,152,44,285,170])).
% 5.16/5.24 cnf(868,plain,
% 5.16/5.24 ($false),
% 5.16/5.24 inference(scs_inference,[],[238,233,380,286]),
% 5.16/5.24 ['proof']).
% 5.16/5.24 % SZS output end Proof
% 5.16/5.24 % Total time :4.570000s
%------------------------------------------------------------------------------