%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:19:18 AM UTC 2026
% Result : Theorem 0.50s 0.76s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n028.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 16:05:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 0.50/0.75 %-------------------------------------------
% 0.50/0.75 % File :CSE---1.7
% 0.50/0.75 % Problem :theBenchmark
% 0.50/0.75 % Transform :cnf
% 0.50/0.75 % Format :tptp:raw
% 0.50/0.75 % Command :java -jar mcs_scs.jar %d %s
% 0.50/0.75
% 0.50/0.75 % Result :Theorem 0.206411s
% 0.50/0.75 % Output :CNFRefutation 0.206411s
% 0.50/0.75 %-------------------------------------------
% 0.50/0.75 %------------------------------------------------------------------------------
% 0.50/0.75 % File : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.50/0.75 % Domain : Logic calculi
% 0.50/0.75 % Problem : Prove adjunction from KM4B axiomatization of S5
% 0.50/0.75 % Version : [HC96] axioms.
% 0.50/0.75 % English :
% 0.50/0.75
% 0.50/0.75 % Refs : [HC96] Hughes & Cresswell (1996), A New Introduction to Modal
% 0.50/0.75 % : [Hal] Halleck (URL), John Halleck's Logic Systems
% 0.50/0.75 % Source : [TPTP]
% 0.50/0.75 % Names :
% 0.50/0.75
% 0.50/0.75 % Status : Theorem
% 0.50/0.75 % Rating : 1.00 v9.3.0
% 0.50/0.75 % Syntax : Number of formulae : 89 ( 31 unt; 0 def)
% 0.50/0.75 % Number of atoms : 156 ( 11 equ)
% 0.50/0.75 % Maximal formula atoms : 4 ( 1 avg)
% 0.50/0.75 % Number of connectives : 67 ( 0 ~; 0 |; 3 &)
% 0.50/0.75 % ( 49 <=>; 15 =>; 0 <=; 0 <~>)
% 0.50/0.75 % Maximal formula depth : 6 ( 3 avg)
% 0.50/0.75 % Maximal term depth : 5 ( 2 avg)
% 0.50/0.75 % Number of predicates : 61 ( 60 usr; 59 prp; 0-2 aty)
% 0.50/0.76 % Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% 0.50/0.76 % Number of variables : 110 ( 110 !; 0 ?)
% 0.50/0.76 % SPC : FOF_THM_RFO_SEQ
% 0.50/0.76
% 0.50/0.76 % Comments :
% 0.50/0.76 % Bugfixes : v9.2.0 - Bugfix in LCL006+2.ax
% 0.50/0.76 %------------------------------------------------------------------------------
% 0.50/0.76 %----Include Hilbert's axiomatization of propositional logic
% 0.50/0.76 include('Axioms/LCL006+0.ax').
% 0.50/0.76 include('Axioms/LCL006+1.ax').
% 0.50/0.76 include('Axioms/LCL006+2.ax').
% 0.50/0.76 %----Include axioms of modal logic
% 0.50/0.76 include('Axioms/LCL007+0.ax').
% 0.50/0.76 include('Axioms/LCL007+1.ax').
% 0.50/0.76 %----Include axioms for KM4B
% 0.50/0.76 include('Axioms/LCL007+3.ax').
% 0.50/0.76 %------------------------------------------------------------------------------
% 0.50/0.76 %----Modal definitions
% 0.50/0.76 fof(s1_0_op_possibly,axiom,
% 0.50/0.76 op_possibly ).
% 0.50/0.76
% 0.50/0.76 fof(s1_0_op_or,axiom,
% 0.50/0.76 op_or ).
% 0.50/0.76
% 0.50/0.76 fof(s1_0_op_implies,axiom,
% 0.50/0.76 op_implies ).
% 0.50/0.76
% 0.50/0.76 fof(s1_0_op_strict_implies,axiom,
% 0.50/0.76 op_strict_implies ).
% 0.50/0.76
% 0.50/0.76 fof(s1_0_op_equiv,axiom,
% 0.50/0.76 op_equiv ).
% 0.50/0.76
% 0.50/0.76 fof(s1_0_op_strict_equiv,axiom,
% 0.50/0.76 op_strict_equiv ).
% 0.50/0.76
% 0.50/0.76 %----Conjecture
% 0.50/0.76 fof(s1_0_adjunction,conjecture,
% 0.50/0.76 adjunction ).
% 0.50/0.76
% 0.50/0.76 %------------------------------------------------------------------------------
% 0.50/0.76 %-------------------------------------------
% 0.50/0.76 % Proof found
% 0.50/0.76 % SZS status Theorem for theBenchmark
% 0.50/0.76 % SZS output start Proof
% 0.50/0.76 %ClaNum:225(EqnAxiom:78)
% 0.50/0.76 %VarNum:218(SingletonVarNum:108)
% 0.50/0.76 %MaxLitNum:4
% 0.50/0.76 %MaxfuncDepth:4
% 0.50/0.76 %SharedTerms:428
% 0.50/0.76 %goalClause: 109
% 0.50/0.76 %singleGoalClaCount:1
% 0.50/0.76 [79]P1(a5000)
% 0.50/0.76 [80]P38(a5000)
% 0.50/0.76 [81]P39(a5000)
% 0.50/0.76 [82]P2(a5000)
% 0.50/0.76 [83]P32(a5000)
% 0.50/0.76 [84]P33(a5000)
% 0.50/0.76 [85]P3(a5000)
% 0.50/0.76 [86]P5(a5000)
% 0.50/0.76 [87]P6(a5000)
% 0.50/0.76 [88]P41(a5000)
% 0.50/0.76 [89]P53(a5000)
% 0.50/0.76 [90]P54(a5000)
% 0.50/0.76 [91]P7(a5000)
% 0.50/0.76 [92]P30(a5000)
% 0.50/0.76 [93]P31(a5000)
% 0.50/0.76 [95]P42(a5000)
% 0.50/0.76 [96]P43(a5000)
% 0.50/0.76 [98]P44(a5000)
% 0.50/0.76 [99]P45(a5000)
% 0.50/0.76 [100]P8(a5000)
% 0.50/0.76 [101]P12(a5000)
% 0.50/0.76 [102]P9(a5000)
% 0.50/0.76 [103]P10(a5000)
% 0.50/0.76 [105]P50(a5000)
% 0.50/0.76 [106]P51(a5000)
% 0.50/0.76 [107]P52(a5000)
% 0.50/0.76 [108]P47(a5000)
% 0.50/0.76 [109]~P4(a5000)
% 0.50/0.76 [111]P60(a5000)+~E(a47,a48)
% 0.50/0.76 [114]P40(a5000)+P34(a56)
% 0.50/0.76 [115]P4(a5000)+P34(a57)
% 0.50/0.76 [116]P4(a5000)+P34(a59)
% 0.50/0.76 [118]P40(a5000)+~P34(a58)
% 0.50/0.76 [123]P40(a5000)+P34(f99(a56,a58))
% 0.50/0.76 [124]P60(a5000)+P34(f100(a48,a47))
% 0.50/0.76 [128]P4(a5000)+~P34(f5(a57,a59))
% 0.50/0.76 [135]P13(a5000)+~P34(f99(a63,f102(a63)))
% 0.50/0.76 [166]P21(a5000)+~P34(f99(f102(f102(a92)),f102(a92)))
% 0.50/0.76 [170]P35(a5000)+~P34(f62(a27,f5(a27,a27)))
% 0.50/0.76 [171]P55(a5000)+~P34(f62(a37,f103(a38,a37)))
% 0.50/0.76 [172]P16(a5000)+~P34(f99(a83,f5(a83,a83)))
% 0.50/0.76 [175]P36(a5000)+~P34(f62(f5(a31,a32),a31))
% 0.50/0.76 [176]P56(a5000)+~P34(f62(f103(a39,a39),a39))
% 0.50/0.76 [177]P17(a5000)+~P34(f99(f5(a80,a84),a80))
% 0.50/0.76 [189]P57(a5000)+~P34(f62(f103(a45,a46),f103(a46,a45)))
% 0.50/0.76 [190]P15(a5000)+~P34(f99(f5(a81,a82),f5(a82,a81)))
% 0.50/0.76 [219]P19(a5000)+~P34(f99(f5(f99(a88,a89),f99(a89,a90)),f99(a88,a90)))
% 0.50/0.76 [163]P11(a5000)+~P34(f62(f102(a69),f61(f102(a69))))
% 0.50/0.76 [164]P20(a5000)+~P34(f99(f61(a70),f61(f61(a70))))
% 0.50/0.76 [165]P14(a5000)+~P34(f99(f102(a91),f61(f102(a91))))
% 0.50/0.76 [180]P27(a5000)+~P34(f62(a40,f62(f101(a40),a43)))
% 0.50/0.76 [181]P29(a5000)+~P34(f62(f62(f101(a44),a44),a44))
% 0.50/0.76 [194]P22(a5000)+~P34(f99(f102(f5(a94,a95)),a94))
% 0.50/0.76 [195]P23(a5000)+~P34(f99(f99(a96,a97),f99(f102(a96),f102(a97))))
% 0.50/0.76 [204]P24(a5000)+~P34(f99(f102(f5(a73,a76)),f5(f102(a73),f102(a76))))
% 0.50/0.76 [215]P28(a5000)+~P34(f62(f62(a33,a41),f62(f62(a41,a42),f62(a33,a42))))
% 0.50/0.76 [216]P58(a5000)+~P34(f62(f62(a50,a55),f62(f103(a51,a50),f103(a51,a55))))
% 0.50/0.76 [217]P59(a5000)+~P34(f62(f103(a52,f103(a53,a54)),f103(a53,f103(a52,a54))))
% 0.50/0.76 [218]P18(a5000)+~P34(f99(f5(f5(a85,a86),a87),f5(a85,f5(a86,a87))))
% 0.50/0.76 [225]P25(a5000)+~P34(f62(f5(f61(f62(a72,a74)),f61(f62(a74,a75))),f61(f62(a72,a75))))
% 0.50/0.76 [212]P26(a5000)+~P34(f99(f99(a77,a78),f99(f101(f102(a78)),f101(f102(a77)))))
% 0.50/0.76 [224]P37(a5000)+~P34(f62(f62(a34,a35),f62(f101(f5(a35,a36)),f101(f5(a36,a34)))))
% 0.50/0.76 [129]~P13(a5000)+P34(f99(x1291,f102(x1291)))
% 0.50/0.76 [130]~P12(a5000)+P34(f62(f61(x1301),x1301))
% 0.50/0.76 [147]~P21(a5000)+P34(f99(f102(f102(x1471)),f102(x1471)))
% 0.50/0.76 [152]~P35(a5000)+P34(f62(x1521,f5(x1521,x1521)))
% 0.50/0.76 [156]~P16(a5000)+P34(f99(x1561,f5(x1561,x1561)))
% 0.50/0.76 [160]~P56(a5000)+P34(f62(f103(x1601,x1601),x1601))
% 0.50/0.76 [125]~P48(a5000)+E(f101(f102(f101(x1251))),f61(x1251))
% 0.50/0.76 [126]~P50(a5000)+E(f101(f61(f101(x1261))),f102(x1261))
% 0.50/0.76 [140]~P10(a5000)+P34(f62(x1401,f61(f102(x1401))))
% 0.50/0.76 [143]~P9(a5000)+P34(f62(f61(x1431),f61(f61(x1431))))
% 0.50/0.76 [144]~P11(a5000)+P34(f62(f102(x1441),f61(f102(x1441))))
% 0.50/0.76 [145]~P20(a5000)+P34(f99(f61(x1451),f61(f61(x1451))))
% 0.50/0.76 [146]~P14(a5000)+P34(f99(f102(x1461),f61(f102(x1461))))
% 0.50/0.76 [179]~P29(a5000)+P34(f62(f62(f101(x1791),x1791),x1791))
% 0.50/0.76 [127]E(f103(f101(x1271),x1272),f62(x1271,x1272))+~P49(a5000)
% 0.50/0.76 [131]E(f61(f62(x1311,x1312)),f99(x1311,x1312))+~P51(a5000)
% 0.50/0.76 [148]E(f5(f62(x1481,x1482),f62(x1482,x1481)),f4(x1481,x1482))+~P44(a5000)
% 0.50/0.76 [149]E(f5(f99(x1491,x1492),f99(x1492,x1491)),f100(x1491,x1492))+~P52(a5000)
% 0.50/0.76 [151]~P2(a5000)+P34(f62(x1511,f62(x1512,x1511)))
% 0.50/0.76 [153]~P53(a5000)+P34(f62(x1531,f103(x1532,x1531)))
% 0.50/0.76 [154]~P55(a5000)+P34(f62(x1541,f103(x1542,x1541)))
% 0.50/0.76 [155]~P41(a5000)+P34(f62(x1551,f103(x1551,x1552)))
% 0.50/0.76 [157]~P5(a5000)+P34(f62(f5(x1571,x1572),x1572))
% 0.50/0.76 [158]~P3(a5000)+P34(f62(f5(x1581,x1582),x1581))
% 0.50/0.76 [159]~P36(a5000)+P34(f62(f5(x1591,x1592),x1591))
% 0.50/0.76 [161]~P17(a5000)+P34(f99(f5(x1611,x1612),x1611))
% 0.50/0.76 [182]~P30(a5000)+P34(f62(f4(x1821,x1822),f62(x1822,x1821)))
% 0.50/0.76 [183]~P7(a5000)+P34(f62(f4(x1831,x1832),f62(x1831,x1832)))
% 0.50/0.76 [184]~P57(a5000)+P34(f62(f103(x1841,x1842),f103(x1842,x1841)))
% 0.50/0.76 [185]~P15(a5000)+P34(f99(f5(x1851,x1852),f5(x1852,x1851)))
% 0.50/0.76 [192]~P39(a5000)+P34(f62(f62(f101(x1921),f101(x1922)),f62(x1922,x1921)))
% 0.50/0.76 [197]~P32(a5000)+P34(f62(f62(x1971,f62(x1971,x1972)),f62(x1971,x1972)))
% 0.50/0.76 [137]~P43(a5000)+E(f101(f5(x1371,f101(x1372))),f62(x1371,x1372))
% 0.50/0.76 [141]~P46(a5000)+E(f101(f103(f101(x1411),f101(x1412))),f5(x1411,x1412))
% 0.50/0.76 [142]~P42(a5000)+E(f101(f5(f101(x1421),f101(x1422))),f103(x1421,x1422))
% 0.50/0.76 [178]~P27(a5000)+P34(f62(x1781,f62(f101(x1781),x1782)))
% 0.50/0.76 [186]~P22(a5000)+P34(f99(f102(f5(x1861,x1862)),x1861))
% 0.50/0.76 [191]~P23(a5000)+P34(f99(f99(x1911,x1912),f99(f102(x1911),f102(x1912))))
% 0.50/0.76 [193]~P6(a5000)+P34(f62(x1931,f62(x1932,f5(x1931,x1932))))
% 0.50/0.76 [199]~P8(a5000)+P34(f62(f61(f62(x1991,x1992)),f62(f61(x1991),f61(x1992))))
% 0.50/0.76 [200]~P24(a5000)+P34(f99(f102(f5(x2001,x2002)),f5(f102(x2001),f102(x2002))))
% 0.50/0.76 [207]~P31(a5000)+P34(f62(f62(x2071,x2072),f62(f62(x2072,x2071),f4(x2071,x2072))))
% 0.50/0.76 [201]~P26(a5000)+P34(f99(f99(x2011,x2012),f99(f101(f102(x2012)),f101(f102(x2011)))))
% 0.50/0.76 [211]~P19(a5000)+P34(f99(f5(f99(x2111,x2112),f99(x2112,x2113)),f99(x2111,x2113)))
% 0.50/0.76 [205]~P33(a5000)+P34(f62(f62(x2051,x2052),f62(f62(x2052,x2053),f62(x2051,x2053))))
% 0.50/0.76 [206]~P28(a5000)+P34(f62(f62(x2061,x2062),f62(f62(x2062,x2063),f62(x2061,x2063))))
% 0.50/0.76 [208]~P58(a5000)+P34(f62(f62(x2081,x2082),f62(f103(x2083,x2081),f103(x2083,x2082))))
% 0.50/0.76 [209]~P59(a5000)+P34(f62(f103(x2091,f103(x2092,x2093)),f103(x2092,f103(x2091,x2093))))
% 0.50/0.76 [210]~P18(a5000)+P34(f99(f5(f5(x2101,x2102),x2103),f5(x2101,f5(x2102,x2103))))
% 0.50/0.76 [222]~P25(a5000)+P34(f62(f5(f61(f62(x2221,x2222)),f61(f62(x2222,x2223))),f61(f62(x2221,x2223))))
% 0.50/0.76 [220]~P54(a5000)+P34(f62(f62(x2201,x2202),f62(f62(x2203,x2202),f62(f103(x2201,x2203),x2202))))
% 0.50/0.76 [221]~P37(a5000)+P34(f62(f62(x2211,x2212),f62(f101(f5(x2212,x2213)),f101(f5(x2213,x2211)))))
% 0.50/0.76 [120]~P34(x1201)+P34(f61(x1201))+~P45(a5000)
% 0.50/0.76 [133]E(x1331,x1332)+~P38(a5000)+~P34(f4(x1331,x1332))
% 0.50/0.76 [134]E(x1341,x1342)+~P60(a5000)+~P34(f100(x1341,x1342))
% 0.50/0.76 [138]P34(x1381)+~P34(x1382)+~P1(a5000)+~P34(f62(x1382,x1381))
% 0.50/0.76 [139]P34(x1391)+~P34(x1392)+~P40(a5000)+~P34(f99(x1392,x1391))
% 0.50/0.76 %EqnAxiom
% 0.50/0.76 [1]E(x11,x11)
% 0.50/0.76 [2]E(x22,x21)+~E(x21,x22)
% 0.50/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.50/0.76 [4]~E(x41,x42)+E(f61(x41),f61(x42))
% 0.50/0.76 [5]~E(x51,x52)+E(f62(x51,x53),f62(x52,x53))
% 0.50/0.76 [6]~E(x61,x62)+E(f62(x63,x61),f62(x63,x62))
% 0.50/0.76 [7]~E(x71,x72)+E(f103(x71,x73),f103(x72,x73))
% 0.50/0.76 [8]~E(x81,x82)+E(f103(x83,x81),f103(x83,x82))
% 0.50/0.76 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.50/0.76 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.50/0.76 [11]~E(x111,x112)+E(f99(x111,x113),f99(x112,x113))
% 0.50/0.76 [12]~E(x121,x122)+E(f99(x123,x121),f99(x123,x122))
% 0.50/0.76 [13]~E(x131,x132)+E(f100(x131,x133),f100(x132,x133))
% 0.50/0.76 [14]~E(x141,x142)+E(f100(x143,x141),f100(x143,x142))
% 0.50/0.77 [15]~E(x151,x152)+E(f101(x151),f101(x152))
% 0.50/0.77 [16]~E(x161,x162)+E(f102(x161),f102(x162))
% 0.50/0.77 [17]~E(x171,x172)+E(f5(x171,x173),f5(x172,x173))
% 0.50/0.77 [18]~E(x181,x182)+E(f5(x183,x181),f5(x183,x182))
% 0.50/0.77 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 0.50/0.77 [20]~P38(x201)+P38(x202)+~E(x201,x202)
% 0.50/0.77 [21]~P39(x211)+P39(x212)+~E(x211,x212)
% 0.50/0.77 [22]~P2(x221)+P2(x222)+~E(x221,x222)
% 0.50/0.77 [23]~P32(x231)+P32(x232)+~E(x231,x232)
% 0.50/0.77 [24]~P33(x241)+P33(x242)+~E(x241,x242)
% 0.50/0.77 [25]~P3(x251)+P3(x252)+~E(x251,x252)
% 0.50/0.77 [26]~P5(x261)+P5(x262)+~E(x261,x262)
% 0.50/0.77 [27]~P6(x271)+P6(x272)+~E(x271,x272)
% 0.50/0.77 [28]~P41(x281)+P41(x282)+~E(x281,x282)
% 0.50/0.77 [29]~P53(x291)+P53(x292)+~E(x291,x292)
% 0.50/0.77 [30]~P54(x301)+P54(x302)+~E(x301,x302)
% 0.50/0.77 [31]~P7(x311)+P7(x312)+~E(x311,x312)
% 0.50/0.77 [32]~P30(x321)+P30(x322)+~E(x321,x322)
% 0.50/0.77 [33]~P31(x331)+P31(x332)+~E(x331,x332)
% 0.50/0.77 [34]~P42(x341)+P42(x342)+~E(x341,x342)
% 0.50/0.77 [35]~P34(x351)+P34(x352)+~E(x351,x352)
% 0.50/0.77 [36]~P43(x361)+P43(x362)+~E(x361,x362)
% 0.50/0.77 [37]~P44(x371)+P44(x372)+~E(x371,x372)
% 0.50/0.77 [38]~P55(x381)+P55(x382)+~E(x381,x382)
% 0.50/0.77 [39]~P45(x391)+P45(x392)+~E(x391,x392)
% 0.50/0.77 [40]~P8(x401)+P8(x402)+~E(x401,x402)
% 0.50/0.77 [41]~P12(x411)+P12(x412)+~E(x411,x412)
% 0.50/0.77 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 0.50/0.77 [43]~P10(x431)+P10(x432)+~E(x431,x432)
% 0.50/0.77 [44]~P50(x441)+P50(x442)+~E(x441,x442)
% 0.50/0.77 [45]~P17(x451)+P17(x452)+~E(x451,x452)
% 0.50/0.77 [46]~P51(x461)+P51(x462)+~E(x461,x462)
% 0.50/0.77 [47]~P52(x471)+P52(x472)+~E(x471,x472)
% 0.50/0.77 [48]~P47(x481)+P47(x482)+~E(x481,x482)
% 0.50/0.77 [49]~P4(x491)+P4(x492)+~E(x491,x492)
% 0.50/0.77 [50]~P59(x501)+P59(x502)+~E(x501,x502)
% 0.50/0.77 [51]~P60(x511)+P60(x512)+~E(x511,x512)
% 0.50/0.77 [52]~P28(x521)+P28(x522)+~E(x521,x522)
% 0.50/0.77 [53]~P19(x531)+P19(x532)+~E(x531,x532)
% 0.50/0.77 [54]~P40(x541)+P40(x542)+~E(x541,x542)
% 0.50/0.77 [55]~P24(x551)+P24(x552)+~E(x551,x552)
% 0.50/0.77 [56]~P16(x561)+P16(x562)+~E(x561,x562)
% 0.50/0.77 [57]~P56(x571)+P56(x572)+~E(x571,x572)
% 0.50/0.77 [58]~P11(x581)+P11(x582)+~E(x581,x582)
% 0.50/0.77 [59]~P26(x591)+P26(x592)+~E(x591,x592)
% 0.50/0.77 [60]~P36(x601)+P36(x602)+~E(x601,x602)
% 0.50/0.77 [61]~P14(x611)+P14(x612)+~E(x611,x612)
% 0.50/0.77 [62]~P25(x621)+P25(x622)+~E(x621,x622)
% 0.50/0.77 [63]~P21(x631)+P21(x632)+~E(x631,x632)
% 0.50/0.77 [64]~P35(x641)+P35(x642)+~E(x641,x642)
% 0.50/0.77 [65]~P37(x651)+P37(x652)+~E(x651,x652)
% 0.50/0.77 [66]~P13(x661)+P13(x662)+~E(x661,x662)
% 0.50/0.77 [67]~P23(x671)+P23(x672)+~E(x671,x672)
% 0.50/0.77 [68]~P22(x681)+P22(x682)+~E(x681,x682)
% 0.50/0.77 [69]~P46(x691)+P46(x692)+~E(x691,x692)
% 0.50/0.77 [70]~P58(x701)+P58(x702)+~E(x701,x702)
% 0.50/0.77 [71]~P18(x711)+P18(x712)+~E(x711,x712)
% 0.50/0.77 [72]~P15(x721)+P15(x722)+~E(x721,x722)
% 0.50/0.77 [73]~P57(x731)+P57(x732)+~E(x731,x732)
% 0.50/0.77 [74]~P20(x741)+P20(x742)+~E(x741,x742)
% 0.50/0.77 [75]~P27(x751)+P27(x752)+~E(x751,x752)
% 0.50/0.77 [76]~P29(x761)+P29(x762)+~E(x761,x762)
% 0.50/0.77 [77]~P49(x771)+P49(x772)+~E(x771,x772)
% 0.50/0.77 [78]~P48(x781)+P48(x782)+~E(x781,x782)
% 0.50/0.77
% 0.50/0.77 %-------------------------------------------
% 0.50/0.77 cnf(226,plain,
% 0.50/0.77 (P34(a57)),
% 0.50/0.77 inference(scs_inference,[],[109,115])).
% 0.50/0.77 cnf(227,plain,
% 0.50/0.77 (P34(a59)),
% 0.50/0.77 inference(scs_inference,[],[109,115,116])).
% 0.50/0.77 cnf(233,plain,
% 0.50/0.77 (~P34(f5(a57,a59))),
% 0.50/0.77 inference(scs_inference,[],[109,128])).
% 0.50/0.77 cnf(237,plain,
% 0.50/0.77 (P34(x2371)+~P34(x2372)+~P34(f62(x2372,x2371))),
% 0.50/0.77 inference(scs_inference,[],[79,138])).
% 0.50/0.77 cnf(251,plain,
% 0.50/0.77 (P34(f62(x2511,f62(x2512,f5(x2511,x2512))))),
% 0.50/0.77 inference(scs_inference,[],[87,193])).
% 0.50/0.77 cnf(412,plain,
% 0.50/0.77 (P34(f62(x4121,f5(a57,x4121)))),
% 0.50/0.77 inference(scs_inference,[],[226,251,237])).
% 0.50/0.77 cnf(419,plain,
% 0.50/0.77 ($false),
% 0.50/0.77 inference(scs_inference,[],[227,233,412,237]),
% 0.50/0.77 ['proof']).
% 0.50/0.77 % SZS output end Proof
% 0.50/0.77 % Total time :0.206411s
%------------------------------------------------------------------------------