TSTP Solution File: LAT382+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LAT382+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n027.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 05:58:58 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT382+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 04:43:32 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % File :CSE---1.6
% 0.20/0.64 % Problem :theBenchmark
% 0.20/0.64 % Transform :cnf
% 0.20/0.64 % Format :tptp:raw
% 0.20/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.64
% 0.20/0.64 % Result :Theorem 0.010000s
% 0.20/0.64 % Output :CNFRefutation 0.010000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 % File : LAT382+1 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.64 % Domain : Lattice Theory
% 0.20/0.64 % Problem : Tarski-Knaster fixed point theorem 02, 00 expansion
% 0.20/0.64 % Version : Especial.
% 0.20/0.64 % English :
% 0.20/0.64
% 0.20/0.64 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.64 % : [VL+08] Verchinine et al. (2008), On Correctness of Mathematic
% 0.20/0.64 % Source : [Pas08]
% 0.20/0.64 % Names : tarski_02.00 [Pas08]
% 0.20/0.64
% 0.20/0.64 % Status : Theorem
% 0.20/0.64 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.10 v7.3.0, 0.07 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.1, 0.70 v4.0.0
% 0.20/0.64 % Syntax : Number of formulae : 18 ( 3 unt; 6 def)
% 0.20/0.64 % Number of atoms : 68 ( 3 equ)
% 0.20/0.64 % Maximal formula atoms : 7 ( 3 avg)
% 0.20/0.64 % Number of connectives : 51 ( 1 ~; 0 |; 15 &)
% 0.20/0.64 % ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% 0.20/0.64 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.64 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.64 % Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% 0.20/0.64 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.20/0.64 % Number of variables : 37 ( 36 !; 1 ?)
% 0.20/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.64
% 0.20/0.64 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 fof(mSetSort,axiom,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aSet0(W0)
% 0.20/0.64 => $true ) ).
% 0.20/0.64
% 0.20/0.64 fof(mElmSort,axiom,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aElement0(W0)
% 0.20/0.64 => $true ) ).
% 0.20/0.64
% 0.20/0.64 fof(mEOfElem,axiom,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aSet0(W0)
% 0.20/0.64 => ! [W1] :
% 0.20/0.64 ( aElementOf0(W1,W0)
% 0.20/0.64 => aElement0(W1) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mDefEmpty,definition,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aSet0(W0)
% 0.20/0.64 => ( isEmpty0(W0)
% 0.20/0.64 <=> ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mDefSub,definition,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aSet0(W0)
% 0.20/0.64 => ! [W1] :
% 0.20/0.64 ( aSubsetOf0(W1,W0)
% 0.20/0.64 <=> ( aSet0(W1)
% 0.20/0.64 & ! [W2] :
% 0.20/0.64 ( aElementOf0(W2,W1)
% 0.20/0.64 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mLessRel,axiom,
% 0.20/0.64 ! [W0,W1] :
% 0.20/0.64 ( ( aElement0(W0)
% 0.20/0.64 & aElement0(W1) )
% 0.20/0.64 => ( sdtlseqdt0(W0,W1)
% 0.20/0.64 => $true ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mARefl,axiom,
% 0.20/0.64 ! [W0] :
% 0.20/0.64 ( aElement0(W0)
% 0.20/0.64 => sdtlseqdt0(W0,W0) ) ).
% 0.20/0.64
% 0.20/0.64 fof(mASymm,axiom,
% 0.20/0.64 ! [W0,W1] :
% 0.20/0.64 ( ( aElement0(W0)
% 0.20/0.64 & aElement0(W1) )
% 0.20/0.65 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.65 & sdtlseqdt0(W1,W0) )
% 0.20/0.65 => W0 = W1 ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mTrans,axiom,
% 0.20/0.65 ! [W0,W1,W2] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aElement0(W1)
% 0.20/0.65 & aElement0(W2) )
% 0.20/0.65 => ( ( sdtlseqdt0(W0,W1)
% 0.20/0.65 & sdtlseqdt0(W1,W2) )
% 0.20/0.65 => sdtlseqdt0(W0,W2) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefLB,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( aLowerBoundOfIn0(W2,W1,W0)
% 0.20/0.65 <=> ( aElementOf0(W2,W0)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aElementOf0(W3,W1)
% 0.20/0.65 => sdtlseqdt0(W2,W3) ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefUB,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( aUpperBoundOfIn0(W2,W1,W0)
% 0.20/0.65 <=> ( aElementOf0(W2,W0)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aElementOf0(W3,W1)
% 0.20/0.65 => sdtlseqdt0(W3,W2) ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefInf,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( aInfimumOfIn0(W2,W1,W0)
% 0.20/0.65 <=> ( aElementOf0(W2,W0)
% 0.20/0.65 & aLowerBoundOfIn0(W2,W1,W0)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aLowerBoundOfIn0(W3,W1,W0)
% 0.20/0.65 => sdtlseqdt0(W3,W2) ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mDefSup,definition,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( aSupremumOfIn0(W2,W1,W0)
% 0.20/0.65 <=> ( aElementOf0(W2,W0)
% 0.20/0.65 & aUpperBoundOfIn0(W2,W1,W0)
% 0.20/0.65 & ! [W3] :
% 0.20/0.65 ( aUpperBoundOfIn0(W3,W1,W0)
% 0.20/0.65 => sdtlseqdt0(W2,W3) ) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mSupUn,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aSet0(W0)
% 0.20/0.65 => ! [W1] :
% 0.20/0.65 ( aSubsetOf0(W1,W0)
% 0.20/0.65 => ! [W2,W3] :
% 0.20/0.65 ( ( aSupremumOfIn0(W2,W1,W0)
% 0.20/0.65 & aSupremumOfIn0(W3,W1,W0) )
% 0.20/0.65 => W2 = W3 ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(m__773,hypothesis,
% 0.20/0.65 aSet0(xT) ).
% 0.20/0.65
% 0.20/0.65 fof(m__773_01,hypothesis,
% 0.20/0.65 aSubsetOf0(xS,xT) ).
% 0.20/0.65
% 0.20/0.65 fof(m__792,hypothesis,
% 0.20/0.65 ( aInfimumOfIn0(xu,xS,xT)
% 0.20/0.65 & aInfimumOfIn0(xv,xS,xT) ) ).
% 0.20/0.65
% 0.20/0.65 fof(m__,conjecture,
% 0.20/0.65 xu = xv ).
% 0.20/0.65
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark
% 0.20/0.65 % SZS output start Proof
% 0.20/0.65 %ClaNum:73(EqnAxiom:39)
% 0.20/0.65 %VarNum:270(SingletonVarNum:82)
% 0.20/0.65 %MaxLitNum:6
% 0.20/0.65 %MaxfuncDepth:1
% 0.20/0.65 %SharedTerms:9
% 0.20/0.65 %goalClause: 44
% 0.20/0.65 %singleGoalClaCount:1
% 0.20/0.65 [40]P1(a1)
% 0.20/0.65 [41]P6(a2,a1)
% 0.20/0.65 [42]P2(a9,a2,a1)
% 0.20/0.65 [43]P2(a10,a2,a1)
% 0.20/0.65 [44]~E(a10,a9)
% 0.20/0.65 [45]~P3(x451)+P7(x451,x451)
% 0.20/0.65 [46]~P1(x461)+P8(x461)+P4(f3(x461),x461)
% 0.20/0.65 [47]~P6(x471,x472)+P1(x471)+~P1(x472)
% 0.20/0.65 [48]~P4(x481,x482)+P3(x481)+~P1(x482)
% 0.20/0.65 [49]~P8(x491)+~P1(x491)+~P4(x492,x491)
% 0.20/0.65 [52]~P1(x521)+~P1(x522)+P6(x521,x522)+P4(f4(x522,x521),x521)
% 0.20/0.65 [54]~P1(x541)+~P1(x542)+P6(x541,x542)+~P4(f4(x542,x541),x542)
% 0.20/0.65 [51]~P1(x512)+~P6(x513,x512)+P4(x511,x512)+~P4(x511,x513)
% 0.20/0.65 [55]~P1(x552)+~P5(x551,x553,x552)+P4(x551,x552)+~P6(x553,x552)
% 0.20/0.65 [56]~P1(x562)+~P9(x561,x563,x562)+P4(x561,x562)+~P6(x563,x562)
% 0.20/0.65 [57]~P1(x572)+~P2(x571,x573,x572)+P4(x571,x572)+~P6(x573,x572)
% 0.20/0.65 [58]~P1(x582)+~P10(x581,x583,x582)+P4(x581,x582)+~P6(x583,x582)
% 0.20/0.65 [61]~P1(x613)+~P6(x612,x613)+~P2(x611,x612,x613)+P5(x611,x612,x613)
% 0.20/0.65 [62]~P1(x623)+~P6(x622,x623)+~P10(x621,x622,x623)+P9(x621,x622,x623)
% 0.20/0.65 [50]~P3(x502)+~P3(x501)+~P7(x502,x501)+~P7(x501,x502)+E(x501,x502)
% 0.20/0.65 [66]~P1(x663)+~P4(x661,x663)+~P6(x662,x663)+P5(x661,x662,x663)+P4(f5(x663,x662,x661),x662)
% 0.20/0.65 [67]~P1(x673)+~P4(x671,x673)+~P6(x672,x673)+P9(x671,x672,x673)+P4(f6(x673,x672,x671),x672)
% 0.20/0.65 [68]~P1(x683)+~P4(x681,x683)+~P6(x682,x683)+P5(x681,x682,x683)+~P7(x681,f5(x683,x682,x681))
% 0.20/0.65 [69]~P1(x693)+~P4(x691,x693)+~P6(x692,x693)+P9(x691,x692,x693)+~P7(f6(x693,x692,x691),x691)
% 0.20/0.65 [59]~P6(x594,x593)+~P5(x591,x594,x593)+P7(x591,x592)+~P4(x592,x594)+~P1(x593)
% 0.20/0.65 [60]~P6(x604,x603)+~P9(x602,x604,x603)+P7(x601,x602)+~P4(x601,x604)+~P1(x603)
% 0.20/0.65 [63]~P10(x632,x634,x633)+~P10(x631,x634,x633)+E(x631,x632)+~P6(x634,x633)+~P1(x633)
% 0.20/0.65 [64]~P9(x642,x644,x643)+~P10(x641,x644,x643)+P7(x641,x642)+~P6(x644,x643)+~P1(x643)
% 0.20/0.65 [65]~P5(x651,x654,x653)+~P2(x652,x654,x653)+P7(x651,x652)+~P6(x654,x653)+~P1(x653)
% 0.20/0.65 [53]~P3(x532)+~P3(x531)+~P7(x533,x532)+~P7(x531,x533)+P7(x531,x532)+~P3(x533)
% 0.20/0.65 [70]~P1(x703)+~P4(x701,x703)+~P6(x702,x703)+~P5(x701,x702,x703)+P2(x701,x702,x703)+P5(f7(x703,x702,x701),x702,x703)
% 0.20/0.65 [71]~P1(x713)+~P4(x711,x713)+~P6(x712,x713)+~P9(x711,x712,x713)+P10(x711,x712,x713)+P9(f8(x713,x712,x711),x712,x713)
% 0.20/0.65 [72]~P1(x723)+~P4(x721,x723)+~P6(x722,x723)+~P9(x721,x722,x723)+P10(x721,x722,x723)+~P7(x721,f8(x723,x722,x721))
% 0.20/0.65 [73]~P1(x733)+~P4(x731,x733)+~P6(x732,x733)+~P5(x731,x732,x733)+P2(x731,x732,x733)+~P7(f7(x733,x732,x731),x731)
% 0.20/0.65 %EqnAxiom
% 0.20/0.65 [1]E(x11,x11)
% 0.20/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.65 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.20/0.65 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 0.20/0.65 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 0.20/0.65 [7]~E(x71,x72)+E(f7(x71,x73,x74),f7(x72,x73,x74))
% 0.20/0.65 [8]~E(x81,x82)+E(f7(x83,x81,x84),f7(x83,x82,x84))
% 0.20/0.65 [9]~E(x91,x92)+E(f7(x93,x94,x91),f7(x93,x94,x92))
% 0.20/0.65 [10]~E(x101,x102)+E(f5(x101,x103,x104),f5(x102,x103,x104))
% 0.20/0.65 [11]~E(x111,x112)+E(f5(x113,x111,x114),f5(x113,x112,x114))
% 0.20/0.65 [12]~E(x121,x122)+E(f5(x123,x124,x121),f5(x123,x124,x122))
% 0.20/0.65 [13]~E(x131,x132)+E(f6(x131,x133,x134),f6(x132,x133,x134))
% 0.20/0.65 [14]~E(x141,x142)+E(f6(x143,x141,x144),f6(x143,x142,x144))
% 0.20/0.65 [15]~E(x151,x152)+E(f6(x153,x154,x151),f6(x153,x154,x152))
% 0.20/0.65 [16]~E(x161,x162)+E(f8(x161,x163,x164),f8(x162,x163,x164))
% 0.20/0.65 [17]~E(x171,x172)+E(f8(x173,x171,x174),f8(x173,x172,x174))
% 0.20/0.65 [18]~E(x181,x182)+E(f8(x183,x184,x181),f8(x183,x184,x182))
% 0.20/0.65 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 0.20/0.65 [20]P6(x202,x203)+~E(x201,x202)+~P6(x201,x203)
% 0.20/0.65 [21]P6(x213,x212)+~E(x211,x212)+~P6(x213,x211)
% 0.20/0.65 [22]P2(x222,x223,x224)+~E(x221,x222)+~P2(x221,x223,x224)
% 0.20/0.65 [23]P2(x233,x232,x234)+~E(x231,x232)+~P2(x233,x231,x234)
% 0.20/0.65 [24]P2(x243,x244,x242)+~E(x241,x242)+~P2(x243,x244,x241)
% 0.20/0.65 [25]P7(x252,x253)+~E(x251,x252)+~P7(x251,x253)
% 0.20/0.65 [26]P7(x263,x262)+~E(x261,x262)+~P7(x263,x261)
% 0.20/0.65 [27]P10(x272,x273,x274)+~E(x271,x272)+~P10(x271,x273,x274)
% 0.20/0.65 [28]P10(x283,x282,x284)+~E(x281,x282)+~P10(x283,x281,x284)
% 0.20/0.65 [29]P10(x293,x294,x292)+~E(x291,x292)+~P10(x293,x294,x291)
% 0.20/0.65 [30]~P3(x301)+P3(x302)+~E(x301,x302)
% 0.20/0.65 [31]~P8(x311)+P8(x312)+~E(x311,x312)
% 0.20/0.65 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.20/0.65 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.20/0.65 [34]P5(x342,x343,x344)+~E(x341,x342)+~P5(x341,x343,x344)
% 0.20/0.65 [35]P5(x353,x352,x354)+~E(x351,x352)+~P5(x353,x351,x354)
% 0.20/0.65 [36]P5(x363,x364,x362)+~E(x361,x362)+~P5(x363,x364,x361)
% 0.20/0.65 [37]P9(x372,x373,x374)+~E(x371,x372)+~P9(x371,x373,x374)
% 0.20/0.65 [38]P9(x383,x382,x384)+~E(x381,x382)+~P9(x383,x381,x384)
% 0.20/0.65 [39]P9(x393,x394,x392)+~E(x391,x392)+~P9(x393,x394,x391)
% 0.20/0.65
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 cnf(74,plain,
% 0.20/0.65 (~E(a9,a10)),
% 0.20/0.65 inference(scs_inference,[],[44,2])).
% 0.20/0.65 cnf(78,plain,
% 0.20/0.65 (P5(a9,a2,a1)),
% 0.20/0.65 inference(scs_inference,[],[44,40,41,42,2,19,47,61])).
% 0.20/0.65 cnf(86,plain,
% 0.20/0.65 (P3(a9)),
% 0.20/0.65 inference(scs_inference,[],[44,40,41,42,2,19,47,61,57,65,49,48])).
% 0.20/0.65 cnf(110,plain,
% 0.20/0.65 (P7(a9,a10)),
% 0.20/0.65 inference(scs_inference,[],[43,41,40,78,65])).
% 0.20/0.65 cnf(112,plain,
% 0.20/0.65 (P5(a10,a2,a1)),
% 0.20/0.65 inference(scs_inference,[],[43,41,40,78,65,61])).
% 0.20/0.65 cnf(114,plain,
% 0.20/0.65 (P4(a10,a1)),
% 0.20/0.65 inference(scs_inference,[],[43,41,40,78,65,61,57])).
% 0.20/0.65 cnf(140,plain,
% 0.20/0.65 (~P3(a10)),
% 0.20/0.65 inference(scs_inference,[],[40,74,42,41,110,112,86,65,3,50])).
% 0.20/0.65 cnf(161,plain,
% 0.20/0.65 ($false),
% 0.20/0.65 inference(scs_inference,[],[40,140,114,48]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------