TSTP Solution File: LCL456+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n017.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 06:49:26 EDT 2023
% Result : Theorem 4.33s 4.40s
% Output : CNFRefutation 4.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 00:51:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.59 start to proof:theBenchmark
% 4.33/4.39 %-------------------------------------------
% 4.33/4.39 % File :CSE---1.6
% 4.33/4.39 % Problem :theBenchmark
% 4.33/4.39 % Transform :cnf
% 4.33/4.39 % Format :tptp:raw
% 4.33/4.39 % Command :java -jar mcs_scs.jar %d %s
% 4.33/4.39
% 4.33/4.39 % Result :Theorem 3.730000s
% 4.33/4.39 % Output :CNFRefutation 3.730000s
% 4.33/4.39 %-------------------------------------------
% 4.33/4.40 %------------------------------------------------------------------------------
% 4.33/4.40 % File : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 4.33/4.40 % Domain : Logic Calculi (Propositional)
% 4.33/4.40 % Problem : Prove Principia's r3 axiom from Hilbert's axiomatization
% 4.33/4.40 % Version : [HB34] axioms.
% 4.33/4.40 % English :
% 4.33/4.40
% 4.33/4.40 % Refs : [HB34] Hilbert & Bernays (1934), Grundlagen der Mathematick
% 4.33/4.40 % : [Hal] Halleck (URL), John Halleck's Logic Systems
% 4.33/4.40 % Source : [TPTP]
% 4.33/4.40 % Names :
% 4.33/4.40
% 4.33/4.40 % Status : Theorem
% 4.33/4.40 % Rating : 0.25 v7.4.0, 0.20 v7.3.0, 0.24 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.31 v6.3.0, 0.25 v6.2.0, 0.24 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.48 v5.2.0, 0.35 v5.1.0, 0.38 v5.0.0, 0.46 v4.1.0, 0.48 v4.0.0, 0.46 v3.7.0, 0.40 v3.5.0, 0.42 v3.3.0
% 4.33/4.40 % Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% 4.33/4.40 % Number of atoms : 87 ( 6 equ)
% 4.33/4.40 % Maximal formula atoms : 4 ( 1 avg)
% 4.33/4.40 % Number of connectives : 34 ( 0 ~; 0 |; 1 &)
% 4.33/4.40 % ( 26 <=>; 7 =>; 0 <=; 0 <~>)
% 4.33/4.40 % Maximal formula depth : 6 ( 3 avg)
% 4.33/4.40 % Maximal term depth : 5 ( 2 avg)
% 4.33/4.40 % Number of predicates : 33 ( 32 usr; 31 prp; 0-2 aty)
% 4.33/4.40 % Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% 4.33/4.40 % Number of variables : 65 ( 65 !; 0 ?)
% 4.33/4.40 % SPC : FOF_THM_RFO_SEQ
% 4.33/4.40
% 4.33/4.40 % Comments :
% 4.33/4.40 %------------------------------------------------------------------------------
% 4.33/4.40 %----Include axioms of propositional logic
% 4.33/4.40 include('Axioms/LCL006+0.ax').
% 4.33/4.40 include('Axioms/LCL006+1.ax').
% 4.33/4.40 %----Include Hilbert's axiomatization of propositional logic
% 4.33/4.40 include('Axioms/LCL006+2.ax').
% 4.33/4.40 %------------------------------------------------------------------------------
% 4.33/4.40 %----Operator definitions to reduce everything to and & not
% 4.33/4.40 fof(principia_op_implies_or,axiom,
% 4.33/4.40 op_implies_or ).
% 4.33/4.40
% 4.33/4.40 fof(principia_op_and,axiom,
% 4.33/4.40 op_and ).
% 4.33/4.40
% 4.33/4.40 fof(principia_op_equiv,axiom,
% 4.33/4.40 op_equiv ).
% 4.33/4.40
% 4.33/4.40 fof(principia_r3,conjecture,
% 4.33/4.40 r3 ).
% 4.33/4.40
% 4.33/4.40 %------------------------------------------------------------------------------
% 4.33/4.40 %-------------------------------------------
% 4.33/4.40 % Proof found
% 4.33/4.40 % SZS status Theorem for theBenchmark
% 4.33/4.40 % SZS output start Proof
% 4.33/4.40 %ClaNum:126(EqnAxiom:44)
% 4.33/4.40 %VarNum:127(SingletonVarNum:63)
% 4.33/4.40 %MaxLitNum:4
% 4.33/4.40 %MaxfuncDepth:4
% 4.33/4.40 %SharedTerms:230
% 4.33/4.40 %goalClause: 66
% 4.33/4.40 %singleGoalClaCount:1
% 4.33/4.40 [45]P1(a500)
% 4.33/4.40 [46]P18(a500)
% 4.33/4.40 [47]P19(a500)
% 4.33/4.40 [48]P2(a500)
% 4.33/4.40 [49]P12(a500)
% 4.33/4.40 [50]P13(a500)
% 4.33/4.40 [51]P3(a500)
% 4.33/4.40 [52]P4(a500)
% 4.33/4.40 [53]P5(a500)
% 4.33/4.40 [54]P20(a500)
% 4.33/4.40 [55]P26(a500)
% 4.33/4.40 [56]P27(a500)
% 4.33/4.40 [57]P6(a500)
% 4.33/4.40 [58]P10(a500)
% 4.33/4.40 [59]P11(a500)
% 4.33/4.40 [60]P21(a500)
% 4.33/4.40 [61]P22(a500)
% 4.33/4.40 [62]P23(a500)
% 4.33/4.40 [63]P25(a500)
% 4.33/4.40 [65]P24(a500)
% 4.33/4.40 [66]~P28(a500)
% 4.33/4.40 [91]P15(a500)+~P14(f47(a27,f5(a27,a27)))
% 4.33/4.40 [92]P29(a500)+~P14(f47(a37,f60(a38,a37)))
% 4.33/4.40 [95]P16(a500)+~P14(f47(f5(a31,a32),a31))
% 4.33/4.40 [96]P30(a500)+~P14(f47(f60(a39,a39),a39))
% 4.33/4.40 [106]P28(a500)+~P14(f47(f60(a45,a46),f60(a46,a45)))
% 4.33/4.40 [99]P7(a500)+~P14(f47(a40,f47(f59(a40),a43)))
% 4.33/4.40 [100]P9(a500)+~P14(f47(f47(f59(a44),a44),a44))
% 4.33/4.40 [120]P8(a500)+~P14(f47(f47(a33,a41),f47(f47(a41,a42),f47(a33,a42))))
% 4.33/4.40 [121]P31(a500)+~P14(f47(f47(a51,a56),f47(f60(a52,a51),f60(a52,a56))))
% 4.33/4.40 [122]P32(a500)+~P14(f47(f60(a53,f60(a54,a55)),f60(a54,f60(a53,a55))))
% 4.33/4.40 [126]P17(a500)+~P14(f47(f47(a34,a35),f47(f59(f5(a35,a36)),f59(f5(a36,a34)))))
% 4.33/4.40 [80]~P15(a500)+P14(f47(x801,f5(x801,x801)))
% 4.33/4.40 [87]~P30(a500)+P14(f47(f60(x871,x871),x871))
% 4.33/4.40 [98]~P9(a500)+P14(f47(f47(f59(x981),x981),x981))
% 4.33/4.40 [72]E(f60(f59(x721),x722),f47(x721,x722))+~P25(a500)
% 4.33/4.40 [78]E(f5(f47(x781,x782),f47(x782,x781)),f4(x781,x782))+~P24(a500)
% 4.33/4.41 [79]~P2(a500)+P14(f47(x791,f47(x792,x791)))
% 4.33/4.41 [81]~P26(a500)+P14(f47(x811,f60(x812,x811)))
% 4.33/4.41 [82]~P29(a500)+P14(f47(x821,f60(x822,x821)))
% 4.33/4.41 [83]~P20(a500)+P14(f47(x831,f60(x831,x832)))
% 4.33/4.41 [84]~P4(a500)+P14(f47(f5(x841,x842),x842))
% 4.33/4.41 [85]~P3(a500)+P14(f47(f5(x851,x852),x851))
% 4.33/4.41 [86]~P16(a500)+P14(f47(f5(x861,x862),x861))
% 4.33/4.41 [101]~P10(a500)+P14(f47(f4(x1011,x1012),f47(x1012,x1011)))
% 4.33/4.41 [102]~P6(a500)+P14(f47(f4(x1021,x1022),f47(x1021,x1022)))
% 4.33/4.41 [107]~P19(a500)+P14(f47(f47(f59(x1071),f59(x1072)),f47(x1072,x1071)))
% 4.33/4.41 [110]~P12(a500)+P14(f47(f47(x1101,f47(x1101,x1102)),f47(x1101,x1102)))
% 4.33/4.41 [74]~P23(a500)+E(f59(f5(x741,f59(x742))),f47(x741,x742))
% 4.33/4.41 [76]~P22(a500)+E(f59(f60(f59(x761),f59(x762))),f5(x761,x762))
% 4.33/4.41 [77]~P21(a500)+E(f59(f5(f59(x771),f59(x772))),f60(x771,x772))
% 4.33/4.41 [97]~P7(a500)+P14(f47(x971,f47(f59(x971),x972)))
% 4.33/4.41 [108]~P5(a500)+P14(f47(x1081,f47(x1082,f5(x1081,x1082))))
% 4.33/4.41 [115]~P11(a500)+P14(f47(f47(x1151,x1152),f47(f47(x1152,x1151),f4(x1151,x1152))))
% 4.33/4.41 [113]~P13(a500)+P14(f47(f47(x1131,x1132),f47(f47(x1132,x1133),f47(x1131,x1133))))
% 4.33/4.41 [114]~P8(a500)+P14(f47(f47(x1141,x1142),f47(f47(x1142,x1143),f47(x1141,x1143))))
% 4.33/4.41 [116]~P31(a500)+P14(f47(f47(x1161,x1162),f47(f60(x1163,x1161),f60(x1163,x1162))))
% 4.33/4.41 [117]~P32(a500)+P14(f47(f60(x1171,f60(x1172,x1173)),f60(x1172,f60(x1171,x1173))))
% 4.33/4.41 [123]~P27(a500)+P14(f47(f47(x1231,x1232),f47(f47(x1233,x1232),f47(f60(x1231,x1233),x1232))))
% 4.33/4.41 [124]~P17(a500)+P14(f47(f47(x1241,x1242),f47(f59(f5(x1242,x1243)),f59(f5(x1243,x1241)))))
% 4.33/4.41 [73]E(x731,x732)+~P18(a500)+~P14(f4(x731,x732))
% 4.33/4.41 [75]P14(x751)+~P14(x752)+~P1(a500)+~P14(f47(x752,x751))
% 4.33/4.41 %EqnAxiom
% 4.33/4.41 [1]E(x11,x11)
% 4.33/4.41 [2]E(x22,x21)+~E(x21,x22)
% 4.33/4.41 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 4.33/4.41 [4]~E(x41,x42)+E(f47(x41,x43),f47(x42,x43))
% 4.33/4.41 [5]~E(x51,x52)+E(f47(x53,x51),f47(x53,x52))
% 4.33/4.41 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 4.33/4.41 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 4.33/4.41 [8]~E(x81,x82)+E(f59(x81),f59(x82))
% 4.33/4.41 [9]~E(x91,x92)+E(f60(x91,x93),f60(x92,x93))
% 4.33/4.41 [10]~E(x101,x102)+E(f60(x103,x101),f60(x103,x102))
% 4.33/4.41 [11]~E(x111,x112)+E(f5(x111,x113),f5(x112,x113))
% 4.33/4.41 [12]~E(x121,x122)+E(f5(x123,x121),f5(x123,x122))
% 4.33/4.41 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 4.33/4.41 [14]~P18(x141)+P18(x142)+~E(x141,x142)
% 4.33/4.41 [15]~P19(x151)+P19(x152)+~E(x151,x152)
% 4.33/4.41 [16]~P2(x161)+P2(x162)+~E(x161,x162)
% 4.33/4.41 [17]~P12(x171)+P12(x172)+~E(x171,x172)
% 4.33/4.41 [18]~P13(x181)+P13(x182)+~E(x181,x182)
% 4.33/4.41 [19]~P3(x191)+P3(x192)+~E(x191,x192)
% 4.33/4.41 [20]~P4(x201)+P4(x202)+~E(x201,x202)
% 4.33/4.41 [21]~P5(x211)+P5(x212)+~E(x211,x212)
% 4.33/4.41 [22]~P20(x221)+P20(x222)+~E(x221,x222)
% 4.33/4.41 [23]~P26(x231)+P26(x232)+~E(x231,x232)
% 4.33/4.41 [24]~P27(x241)+P27(x242)+~E(x241,x242)
% 4.33/4.41 [25]~P6(x251)+P6(x252)+~E(x251,x252)
% 4.33/4.41 [26]~P10(x261)+P10(x262)+~E(x261,x262)
% 4.33/4.41 [27]~P11(x271)+P11(x272)+~E(x271,x272)
% 4.33/4.41 [28]~P21(x281)+P21(x282)+~E(x281,x282)
% 4.33/4.41 [29]~P22(x291)+P22(x292)+~E(x291,x292)
% 4.33/4.41 [30]~P23(x301)+P23(x302)+~E(x301,x302)
% 4.33/4.41 [31]~P25(x311)+P25(x312)+~E(x311,x312)
% 4.33/4.41 [32]~P24(x321)+P24(x322)+~E(x321,x322)
% 4.33/4.41 [33]~P14(x331)+P14(x332)+~E(x331,x332)
% 4.33/4.41 [34]~P28(x341)+P28(x342)+~E(x341,x342)
% 4.33/4.41 [35]~P17(x351)+P17(x352)+~E(x351,x352)
% 4.33/4.41 [36]~P32(x361)+P32(x362)+~E(x361,x362)
% 4.33/4.41 [37]~P15(x371)+P15(x372)+~E(x371,x372)
% 4.33/4.41 [38]~P29(x381)+P29(x382)+~E(x381,x382)
% 4.33/4.41 [39]~P9(x391)+P9(x392)+~E(x391,x392)
% 4.33/4.41 [40]~P7(x401)+P7(x402)+~E(x401,x402)
% 4.33/4.41 [41]~P31(x411)+P31(x412)+~E(x411,x412)
% 4.33/4.41 [42]~P8(x421)+P8(x422)+~E(x421,x422)
% 4.33/4.41 [43]~P30(x431)+P30(x432)+~E(x431,x432)
% 4.33/4.41 [44]~P16(x441)+P16(x442)+~E(x441,x442)
% 4.33/4.41
% 4.33/4.41 %-------------------------------------------
% 4.33/4.41 cnf(127,plain,
% 4.33/4.41 (~P14(f47(f60(a45,a46),f60(a46,a45)))),
% 4.33/4.41 inference(scs_inference,[],[66,106])).
% 4.33/4.41 cnf(130,plain,
% 4.33/4.41 (P14(f47(x1301,f60(x1301,x1302)))),
% 4.33/4.41 inference(scs_inference,[],[66,51,52,54,106,85,84,83])).
% 4.33/4.41 cnf(131,plain,
% 4.33/4.41 (P14(f47(x1311,f60(x1312,x1311)))),
% 4.33/4.41 inference(scs_inference,[],[66,51,52,54,55,106,85,84,83,81])).
% 4.33/4.41 cnf(145,plain,
% 4.33/4.41 (P14(f47(f47(x1451,x1452),f47(f47(x1453,x1452),f47(f60(x1451,x1453),x1452))))),
% 4.33/4.41 inference(scs_inference,[],[66,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,65,106,85,84,83,81,79,108,102,101,72,110,78,74,115,113,107,77,76,123])).
% 4.33/4.41 cnf(169,plain,
% 4.33/4.41 (P14(x1691)+~P14(x1692)+~P14(f47(x1692,x1691))),
% 4.33/4.41 inference(scs_inference,[],[45,75])).
% 4.33/4.41 cnf(266,plain,
% 4.33/4.41 (~P14(f47(f47(x2661,f60(x2661,x2662)),f47(f60(a45,a46),f60(a46,a45))))),
% 4.33/4.41 inference(scs_inference,[],[130,127,169])).
% 4.33/4.41 cnf(867,plain,
% 4.33/4.41 ($false),
% 4.33/4.41 inference(scs_inference,[],[145,266,131,169]),
% 4.33/4.41 ['proof']).
% 4.33/4.41 % SZS output end Proof
% 4.33/4.41 % Total time :3.730000s
%------------------------------------------------------------------------------