%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 11:19:12 AM UTC 2026
% Result : Theorem 0.26s 0.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n026.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 20:43:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.26/0.53 start to proof:theBenchmark
% 0.26/0.53 %-------------------------------------------
% 0.26/0.53 % File :CSE---1.7
% 0.26/0.53 % Problem :theBenchmark
% 0.26/0.53 % Transform :cnf
% 0.26/0.53 % Format :tptp:raw
% 0.26/0.53 % Command :java -jar mcs_scs.jar %d %s
% 0.26/0.53
% 0.26/0.53 % Result :Theorem 0.012430s
% 0.26/0.53 % Output :CNFRefutation 0.012430s
% 0.26/0.53 %-------------------------------------------
% 0.26/0.53 %------------------------------------------------------------------------------
% 0.26/0.53 % File : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.26/0.53 % Domain : Logic Calculi (Propositional)
% 0.26/0.53 % Problem : Prove Lukasiewicz's cn1 axiom from Hilbert's axiomatization
% 0.26/0.53 % Version : [HB34] axioms.
% 0.26/0.53 % English :
% 0.26/0.53
% 0.26/0.53 % Refs : [HB34] Hilbert & Bernays (1934), Grundlagen der Mathematick
% 0.26/0.53 % : [Hal] Halleck (URL), John Halleck's Logic Systems
% 0.26/0.53 % Source : [TPTP]
% 0.26/0.53 % Names :
% 0.26/0.53
% 0.26/0.53 % Status : Theorem
% 0.26/0.53 % Rating : 0.00 v9.3.0
% 0.26/0.53 % Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% 0.26/0.53 % Number of atoms : 87 ( 6 equ)
% 0.26/0.53 % Maximal formula atoms : 4 ( 1 avg)
% 0.26/0.53 % Number of connectives : 34 ( 0 ~; 0 |; 1 &)
% 0.26/0.53 % ( 26 <=>; 7 =>; 0 <=; 0 <~>)
% 0.26/0.53 % Maximal formula depth : 6 ( 3 avg)
% 0.26/0.53 % Maximal term depth : 5 ( 2 avg)
% 0.26/0.53 % Number of predicates : 34 ( 33 usr; 32 prp; 0-2 aty)
% 0.26/0.53 % Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% 0.26/0.53 % Number of variables : 65 ( 65 !; 0 ?)
% 0.26/0.53 % SPC : FOF_THM_RFO_SEQ
% 0.26/0.53
% 0.26/0.53 % Comments :
% 0.26/0.53 % Bugfixes : v9.2.0 - Bugfix in LCL006+2.ax
% 0.26/0.53 %------------------------------------------------------------------------------
% 0.26/0.53 %----Include axioms of propositional logic
% 0.26/0.53 include('Axioms/LCL006+0.ax').
% 0.26/0.53 include('Axioms/LCL006+1.ax').
% 0.26/0.53 %----Include Hilbert's axiomatization of propositional logic
% 0.26/0.53 include('Axioms/LCL006+2.ax').
% 0.26/0.53 %------------------------------------------------------------------------------
% 0.26/0.53 %----Operator definitions to reduce everything to and & not
% 0.26/0.53 fof(luka_op_or,axiom,
% 0.26/0.53 op_or ).
% 0.26/0.53
% 0.26/0.53 fof(luka_op_implies,axiom,
% 0.26/0.53 op_implies ).
% 0.26/0.53
% 0.26/0.53 fof(luka_op_equiv,axiom,
% 0.26/0.53 op_equiv ).
% 0.26/0.53
% 0.26/0.53 fof(luka_cn1,conjecture,
% 0.26/0.53 cn1 ).
% 0.26/0.53
% 0.26/0.53 %------------------------------------------------------------------------------
% 0.26/0.54 %-------------------------------------------
% 0.26/0.54 % Proof found
% 0.26/0.54 % SZS status Theorem for theBenchmark
% 0.26/0.54 % SZS output start Proof
% 0.26/0.54 %ClaNum:127(EqnAxiom:45)
% 0.26/0.54 %VarNum:125(SingletonVarNum:62)
% 0.26/0.54 %MaxLitNum:4
% 0.26/0.54 %MaxfuncDepth:4
% 0.26/0.54 %SharedTerms:229
% 0.26/0.54 %goalClause: 67
% 0.26/0.54 %singleGoalClaCount:1
% 0.26/0.54 [46]P1(a5000)
% 0.26/0.54 [47]P18(a5000)
% 0.26/0.54 [48]P19(a5000)
% 0.26/0.54 [49]P2(a5000)
% 0.26/0.54 [50]P12(a5000)
% 0.26/0.54 [51]P13(a5000)
% 0.26/0.54 [52]P3(a5000)
% 0.26/0.54 [53]P4(a5000)
% 0.26/0.54 [54]P5(a5000)
% 0.26/0.54 [55]P20(a5000)
% 0.26/0.54 [56]P27(a5000)
% 0.26/0.54 [57]P28(a5000)
% 0.26/0.54 [58]P6(a5000)
% 0.26/0.54 [59]P10(a5000)
% 0.26/0.54 [60]P11(a5000)
% 0.26/0.54 [62]P21(a5000)
% 0.26/0.54 [63]P22(a5000)
% 0.26/0.54 [65]P23(a5000)
% 0.26/0.54 [66]P25(a5000)
% 0.26/0.54 [67]~P7(a5000)
% 0.26/0.54 [92]P15(a5000)+~P14(f47(a27,f5(a27,a27)))
% 0.26/0.54 [93]P29(a5000)+~P14(f47(a37,f60(a38,a37)))
% 0.26/0.54 [96]P16(a5000)+~P14(f47(f5(a31,a32),a31))
% 0.26/0.54 [97]P30(a5000)+~P14(f47(f60(a39,a39),a39))
% 0.26/0.54 [107]P31(a5000)+~P14(f47(f60(a45,a46),f60(a46,a45)))
% 0.26/0.54 [100]P8(a5000)+~P14(f47(a40,f47(f59(a40),a43)))
% 0.26/0.54 [101]P9(a5000)+~P14(f47(f47(f59(a44),a44),a44))
% 0.26/0.54 [121]P7(a5000)+~P14(f47(f47(a33,a41),f47(f47(a41,a42),f47(a33,a42))))
% 0.26/0.54 [122]P32(a5000)+~P14(f47(f47(a51,a56),f47(f60(a52,a51),f60(a52,a56))))
% 0.26/0.54 [123]P33(a5000)+~P14(f47(f60(a53,f60(a54,a55)),f60(a54,f60(a53,a55))))
% 0.26/0.54 [127]P17(a5000)+~P14(f47(f47(a34,a35),f47(f59(f5(a35,a36)),f59(f5(a36,a34)))))
% 0.26/0.54 [81]~P15(a5000)+P14(f47(x811,f5(x811,x811)))
% 0.26/0.54 [88]~P30(a5000)+P14(f47(f60(x881,x881),x881))
% 0.26/0.54 [99]~P9(a5000)+P14(f47(f47(f59(x991),x991),x991))
% 0.26/0.54 [73]E(f60(f59(x731),x732),f47(x731,x732))+~P26(a5000)
% 0.26/0.54 [79]E(f5(f47(x791,x792),f47(x792,x791)),f4(x791,x792))+~P23(a5000)
% 0.26/0.54 [80]~P2(a5000)+P14(f47(x801,f47(x802,x801)))
% 0.26/0.54 [82]~P27(a5000)+P14(f47(x821,f60(x822,x821)))
% 0.26/0.54 [83]~P29(a5000)+P14(f47(x831,f60(x832,x831)))
% 0.26/0.54 [84]~P20(a5000)+P14(f47(x841,f60(x841,x842)))
% 0.26/0.54 [85]~P4(a5000)+P14(f47(f5(x851,x852),x852))
% 0.26/0.54 [86]~P3(a5000)+P14(f47(f5(x861,x862),x861))
% 0.26/0.54 [87]~P16(a5000)+P14(f47(f5(x871,x872),x871))
% 0.26/0.54 [102]~P10(a5000)+P14(f47(f4(x1021,x1022),f47(x1022,x1021)))
% 0.26/0.54 [103]~P6(a5000)+P14(f47(f4(x1031,x1032),f47(x1031,x1032)))
% 0.26/0.54 [104]~P31(a5000)+P14(f47(f60(x1041,x1042),f60(x1042,x1041)))
% 0.26/0.54 [108]~P19(a5000)+P14(f47(f47(f59(x1081),f59(x1082)),f47(x1082,x1081)))
% 0.26/0.54 [111]~P12(a5000)+P14(f47(f47(x1111,f47(x1111,x1112)),f47(x1111,x1112)))
% 0.26/0.54 [75]~P22(a5000)+E(f59(f5(x751,f59(x752))),f47(x751,x752))
% 0.26/0.54 [77]~P24(a5000)+E(f59(f60(f59(x771),f59(x772))),f5(x771,x772))
% 0.26/0.54 [78]~P21(a5000)+E(f59(f5(f59(x781),f59(x782))),f60(x781,x782))
% 0.26/0.54 [98]~P8(a5000)+P14(f47(x981,f47(f59(x981),x982)))
% 0.26/0.54 [109]~P5(a5000)+P14(f47(x1091,f47(x1092,f5(x1091,x1092))))
% 0.26/0.54 [116]~P11(a5000)+P14(f47(f47(x1161,x1162),f47(f47(x1162,x1161),f4(x1161,x1162))))
% 0.26/0.54 [114]~P13(a5000)+P14(f47(f47(x1141,x1142),f47(f47(x1142,x1143),f47(x1141,x1143))))
% 0.26/0.54 [117]~P32(a5000)+P14(f47(f47(x1171,x1172),f47(f60(x1173,x1171),f60(x1173,x1172))))
% 0.26/0.54 [118]~P33(a5000)+P14(f47(f60(x1181,f60(x1182,x1183)),f60(x1182,f60(x1181,x1183))))
% 0.26/0.54 [124]~P28(a5000)+P14(f47(f47(x1241,x1242),f47(f47(x1243,x1242),f47(f60(x1241,x1243),x1242))))
% 0.26/0.54 [125]~P17(a5000)+P14(f47(f47(x1251,x1252),f47(f59(f5(x1252,x1253)),f59(f5(x1253,x1251)))))
% 0.26/0.54 [74]E(x741,x742)+~P18(a5000)+~P14(f4(x741,x742))
% 0.26/0.54 [76]P14(x761)+~P14(x762)+~P1(a5000)+~P14(f47(x762,x761))
% 0.26/0.54 %EqnAxiom
% 0.26/0.54 [1]E(x11,x11)
% 0.26/0.54 [2]E(x22,x21)+~E(x21,x22)
% 0.26/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.26/0.54 [4]~E(x41,x42)+E(f47(x41,x43),f47(x42,x43))
% 0.26/0.54 [5]~E(x51,x52)+E(f47(x53,x51),f47(x53,x52))
% 0.26/0.54 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.26/0.54 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.26/0.54 [8]~E(x81,x82)+E(f59(x81),f59(x82))
% 0.26/0.54 [9]~E(x91,x92)+E(f60(x91,x93),f60(x92,x93))
% 0.26/0.54 [10]~E(x101,x102)+E(f60(x103,x101),f60(x103,x102))
% 0.26/0.54 [11]~E(x111,x112)+E(f5(x111,x113),f5(x112,x113))
% 0.26/0.54 [12]~E(x121,x122)+E(f5(x123,x121),f5(x123,x122))
% 0.26/0.54 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.26/0.54 [14]~P18(x141)+P18(x142)+~E(x141,x142)
% 0.26/0.54 [15]~P19(x151)+P19(x152)+~E(x151,x152)
% 0.26/0.54 [16]~P2(x161)+P2(x162)+~E(x161,x162)
% 0.26/0.54 [17]~P12(x171)+P12(x172)+~E(x171,x172)
% 0.26/0.54 [18]~P13(x181)+P13(x182)+~E(x181,x182)
% 0.26/0.54 [19]~P3(x191)+P3(x192)+~E(x191,x192)
% 0.26/0.54 [20]~P4(x201)+P4(x202)+~E(x201,x202)
% 0.26/0.54 [21]~P5(x211)+P5(x212)+~E(x211,x212)
% 0.26/0.54 [22]~P20(x221)+P20(x222)+~E(x221,x222)
% 0.26/0.54 [23]~P27(x231)+P27(x232)+~E(x231,x232)
% 0.26/0.54 [24]~P28(x241)+P28(x242)+~E(x241,x242)
% 0.26/0.54 [25]~P6(x251)+P6(x252)+~E(x251,x252)
% 0.26/0.54 [26]~P10(x261)+P10(x262)+~E(x261,x262)
% 0.26/0.54 [27]~P11(x271)+P11(x272)+~E(x271,x272)
% 0.26/0.54 [28]~P21(x281)+P21(x282)+~E(x281,x282)
% 0.26/0.54 [29]~P14(x291)+P14(x292)+~E(x291,x292)
% 0.26/0.54 [30]~P22(x301)+P22(x302)+~E(x301,x302)
% 0.26/0.54 [31]~P23(x311)+P23(x312)+~E(x311,x312)
% 0.26/0.54 [32]~P32(x321)+P32(x322)+~E(x321,x322)
% 0.26/0.54 [33]~P25(x331)+P25(x332)+~E(x331,x332)
% 0.26/0.54 [34]~P7(x341)+P7(x342)+~E(x341,x342)
% 0.26/0.54 [35]~P17(x351)+P17(x352)+~E(x351,x352)
% 0.26/0.54 [36]~P31(x361)+P31(x362)+~E(x361,x362)
% 0.26/0.54 [37]~P16(x371)+P16(x372)+~E(x371,x372)
% 0.26/0.54 [38]~P15(x381)+P15(x382)+~E(x381,x382)
% 0.26/0.54 [39]~P9(x391)+P9(x392)+~E(x391,x392)
% 0.26/0.54 [40]~P8(x401)+P8(x402)+~E(x401,x402)
% 0.26/0.54 [41]~P30(x411)+P30(x412)+~E(x411,x412)
% 0.26/0.54 [42]~P33(x421)+P33(x422)+~E(x421,x422)
% 0.26/0.54 [43]~P29(x431)+P29(x432)+~E(x431,x432)
% 0.26/0.54 [44]~P26(x441)+P26(x442)+~E(x441,x442)
% 0.26/0.54 [45]~P24(x451)+P24(x452)+~E(x451,x452)
% 0.26/0.54
% 0.26/0.54 %-------------------------------------------
% 0.26/0.54 cnf(145,plain,
% 0.26/0.54 (P14(f47(f47(x1451,x1452),f47(f47(x1452,x1453),f47(x1451,x1453))))),
% 0.26/0.54 inference(scs_inference,[],[51,114])).
% 0.26/0.54 cnf(147,plain,
% 0.26/0.54 (~P14(f47(f47(a33,a41),f47(f47(a41,a42),f47(a33,a42))))),
% 0.26/0.54 inference(scs_inference,[],[67,121])).
% 0.26/0.54 cnf(149,plain,
% 0.26/0.54 ($false),
% 0.26/0.54 inference(scs_inference,[],[147,145]),
% 0.26/0.54 ['proof']).
% 0.26/0.54 % SZS output end Proof
% 0.26/0.54 % Total time :0.012430s
%------------------------------------------------------------------------------