TSTP Solution File: NUM427+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM427+3 : 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 : 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 10:22:02 EDT 2023
% Result : Theorem 0.18s 0.71s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM427+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 15:26:40 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.55 start to proof:theBenchmark
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 % File :CSE---1.6
% 0.18/0.70 % Problem :theBenchmark
% 0.18/0.70 % Transform :cnf
% 0.18/0.70 % Format :tptp:raw
% 0.18/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.70
% 0.18/0.70 % Result :Theorem 0.090000s
% 0.18/0.70 % Output :CNFRefutation 0.090000s
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 % File : NUM427+3 : TPTP v8.1.2. Released v4.0.0.
% 0.18/0.70 % Domain : Number Theory
% 0.18/0.70 % Problem : Fuerstenberg's infinitude of primes 04_03, 02 expansion
% 0.18/0.70 % Version : Especial.
% 0.18/0.70 % English :
% 0.18/0.70
% 0.18/0.70 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.18/0.70 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.18/0.70 % Source : [Pas08]
% 0.18/0.70 % Names : fuerst_04_03.02 [Pas08]
% 0.18/0.70
% 0.18/0.70 % Status : Theorem
% 0.18/0.70 % Rating : 0.06 v8.1.0, 0.03 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.04 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.26 v5.2.0, 0.05 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.30 v4.0.1, 0.65 v4.0.0
% 0.18/0.70 % Syntax : Number of formulae : 25 ( 3 unt; 2 def)
% 0.18/0.70 % Number of atoms : 82 ( 28 equ)
% 0.18/0.70 % Maximal formula atoms : 6 ( 3 avg)
% 0.18/0.70 % Number of connectives : 61 ( 4 ~; 3 |; 33 &)
% 0.18/0.70 % ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% 0.18/0.70 % Maximal formula depth : 9 ( 5 avg)
% 0.18/0.70 % Maximal term depth : 3 ( 1 avg)
% 0.18/0.70 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% 0.18/0.70 % Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% 0.18/0.70 % Number of variables : 36 ( 33 !; 3 ?)
% 0.18/0.70 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.70
% 0.18/0.70 % Comments : Problem generated by the SAD system [VLP07]
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 fof(mIntegers,axiom,
% 0.18/0.70 ! [W0] :
% 0.18/0.70 ( aInteger0(W0)
% 0.18/0.70 => $true ) ).
% 0.18/0.70
% 0.18/0.70 fof(mIntZero,axiom,
% 0.18/0.70 aInteger0(sz00) ).
% 0.18/0.70
% 0.18/0.70 fof(mIntOne,axiom,
% 0.18/0.70 aInteger0(sz10) ).
% 0.18/0.70
% 0.18/0.70 fof(mIntNeg,axiom,
% 0.18/0.70 ! [W0] :
% 0.18/0.70 ( aInteger0(W0)
% 0.18/0.70 => aInteger0(smndt0(W0)) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mIntPlus,axiom,
% 0.18/0.70 ! [W0,W1] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1) )
% 0.18/0.70 => aInteger0(sdtpldt0(W0,W1)) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mIntMult,axiom,
% 0.18/0.70 ! [W0,W1] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1) )
% 0.18/0.70 => aInteger0(sdtasdt0(W0,W1)) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mAddAsso,axiom,
% 0.18/0.70 ! [W0,W1,W2] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1)
% 0.18/0.70 & aInteger0(W2) )
% 0.18/0.70 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mAddComm,axiom,
% 0.18/0.70 ! [W0,W1] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1) )
% 0.18/0.70 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mAddZero,axiom,
% 0.18/0.70 ! [W0] :
% 0.18/0.70 ( aInteger0(W0)
% 0.18/0.70 => ( sdtpldt0(W0,sz00) = W0
% 0.18/0.70 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mAddNeg,axiom,
% 0.18/0.70 ! [W0] :
% 0.18/0.70 ( aInteger0(W0)
% 0.18/0.70 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.18/0.70 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mMulAsso,axiom,
% 0.18/0.70 ! [W0,W1,W2] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1)
% 0.18/0.70 & aInteger0(W2) )
% 0.18/0.70 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mMulComm,axiom,
% 0.18/0.70 ! [W0,W1] :
% 0.18/0.70 ( ( aInteger0(W0)
% 0.18/0.70 & aInteger0(W1) )
% 0.18/0.70 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.18/0.70
% 0.18/0.70 fof(mMulOne,axiom,
% 0.18/0.70 ! [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 => ( sdtasdt0(W0,sz10) = W0
% 0.18/0.71 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mDistrib,axiom,
% 0.18/0.71 ! [W0,W1,W2] :
% 0.18/0.71 ( ( aInteger0(W0)
% 0.18/0.71 & aInteger0(W1)
% 0.18/0.71 & aInteger0(W2) )
% 0.18/0.71 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.18/0.71 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mMulZero,axiom,
% 0.18/0.71 ! [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 => ( sdtasdt0(W0,sz00) = sz00
% 0.18/0.71 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mMulMinOne,axiom,
% 0.18/0.71 ! [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.18/0.71 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mZeroDiv,axiom,
% 0.18/0.71 ! [W0,W1] :
% 0.18/0.71 ( ( aInteger0(W0)
% 0.18/0.71 & aInteger0(W1) )
% 0.18/0.71 => ( sdtasdt0(W0,W1) = sz00
% 0.18/0.71 => ( W0 = sz00
% 0.18/0.71 | W1 = sz00 ) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mDivisor,definition,
% 0.18/0.71 ! [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 => ! [W1] :
% 0.18/0.71 ( aDivisorOf0(W1,W0)
% 0.18/0.71 <=> ( aInteger0(W1)
% 0.18/0.71 & W1 != sz00
% 0.18/0.71 & ? [W2] :
% 0.18/0.71 ( aInteger0(W2)
% 0.18/0.71 & sdtasdt0(W1,W2) = W0 ) ) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mEquMod,definition,
% 0.18/0.71 ! [W0,W1,W2] :
% 0.18/0.71 ( ( aInteger0(W0)
% 0.18/0.71 & aInteger0(W1)
% 0.18/0.71 & aInteger0(W2)
% 0.18/0.71 & W2 != sz00 )
% 0.18/0.71 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.18/0.71 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ).
% 0.18/0.71
% 0.18/0.71 fof(mEquModRef,axiom,
% 0.18/0.71 ! [W0,W1] :
% 0.18/0.71 ( ( aInteger0(W0)
% 0.18/0.71 & aInteger0(W1)
% 0.18/0.71 & W1 != sz00 )
% 0.18/0.71 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ).
% 0.18/0.71
% 0.18/0.71 fof(m__704,hypothesis,
% 0.18/0.71 ( aInteger0(xa)
% 0.18/0.71 & aInteger0(xb)
% 0.18/0.71 & aInteger0(xq)
% 0.18/0.71 & xq != sz00 ) ).
% 0.18/0.71
% 0.18/0.71 fof(m__724,hypothesis,
% 0.18/0.71 ( ? [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
% 0.18/0.71 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
% 0.18/0.71 & sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ).
% 0.18/0.71
% 0.18/0.71 fof(m__747,hypothesis,
% 0.18/0.71 ( aInteger0(xn)
% 0.18/0.71 & sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ).
% 0.18/0.71
% 0.18/0.71 fof(m__767,hypothesis,
% 0.18/0.71 sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) ).
% 0.18/0.71
% 0.18/0.71 fof(m__,conjecture,
% 0.18/0.71 ( ? [W0] :
% 0.18/0.71 ( aInteger0(W0)
% 0.18/0.71 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) )
% 0.18/0.71 | aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
% 0.18/0.71 | sdteqdtlpzmzozddtrp0(xb,xa,xq) ) ).
% 0.18/0.71
% 0.18/0.71 %------------------------------------------------------------------------------
% 0.18/0.71 %-------------------------------------------
% 0.18/0.71 % Proof found
% 0.18/0.71 % SZS status Theorem for theBenchmark
% 0.18/0.71 % SZS output start Proof
% 0.18/0.71 %ClaNum:60(EqnAxiom:16)
% 0.18/0.71 %VarNum:151(SingletonVarNum:53)
% 0.18/0.71 %MaxLitNum:6
% 0.18/0.71 %MaxfuncDepth:2
% 0.18/0.71 %SharedTerms:31
% 0.18/0.71 %goalClause: 30 31 50
% 0.18/0.71 %singleGoalClaCount:2
% 0.18/0.71 [17]P1(a1)
% 0.18/0.71 [18]P1(a7)
% 0.18/0.71 [19]P1(a8)
% 0.18/0.71 [20]P1(a9)
% 0.18/0.71 [21]P1(a10)
% 0.18/0.71 [22]P1(a11)
% 0.18/0.71 [23]P1(a2)
% 0.18/0.71 [28]P3(a8,a9,a10)
% 0.18/0.71 [29]~E(a1,a10)
% 0.18/0.71 [31]~P3(a9,a8,a10)
% 0.18/0.71 [24]E(f5(a8,f4(a9)),f6(a10,a11))
% 0.18/0.71 [25]E(f5(a8,f4(a9)),f6(a10,a2))
% 0.18/0.71 [26]E(f5(a9,f4(a8)),f6(a10,f4(a11)))
% 0.18/0.71 [27]P2(a10,f5(a8,f4(a9)))
% 0.18/0.71 [30]~P2(a10,f5(a9,f4(a8)))
% 0.18/0.71 [32]~P1(x321)+P1(f4(x321))
% 0.18/0.71 [33]~P1(x331)+E(f6(a1,x331),a1)
% 0.18/0.71 [34]~P1(x341)+E(f6(x341,a1),a1)
% 0.18/0.71 [35]~P1(x351)+E(f5(a1,x351),x351)
% 0.18/0.71 [36]~P1(x361)+E(f6(a7,x361),x361)
% 0.18/0.71 [37]~P1(x371)+E(f5(x371,a1),x371)
% 0.18/0.71 [38]~P1(x381)+E(f6(x381,a7),x381)
% 0.18/0.71 [39]~P1(x391)+E(f5(f4(x391),x391),a1)
% 0.18/0.71 [40]~P1(x401)+E(f5(x401,f4(x401)),a1)
% 0.18/0.71 [41]~P1(x411)+E(f6(x411,f4(a7)),f4(x411))
% 0.18/0.71 [42]~P1(x421)+E(f6(f4(a7),x421),f4(x421))
% 0.18/0.71 [50]~P1(x501)+~E(f6(a10,x501),f5(a9,f4(a8)))
% 0.18/0.71 [43]~P2(x431,x432)+~P1(x432)+~E(x431,a1)
% 0.18/0.71 [44]~P2(x441,x442)+P1(x441)+~P1(x442)
% 0.18/0.71 [46]~P1(x462)+~P1(x461)+E(f5(x461,x462),f5(x462,x461))
% 0.18/0.71 [47]~P1(x472)+~P1(x471)+E(f6(x471,x472),f6(x472,x471))
% 0.18/0.71 [48]~P1(x482)+~P1(x481)+P1(f5(x481,x482))
% 0.18/0.71 [49]~P1(x492)+~P1(x491)+P1(f6(x491,x492))
% 0.18/0.71 [51]~P1(x511)+~P2(x512,x511)+P1(f3(x511,x512))
% 0.18/0.71 [54]~P1(x542)+~P2(x541,x542)+E(f6(x541,f3(x542,x541)),x542)
% 0.18/0.71 [53]~P1(x531)+~P1(x532)+P3(x532,x532,x531)+E(x531,a1)
% 0.18/0.71 [55]~P1(x553)+~P1(x552)+~P1(x551)+E(f5(f5(x551,x552),x553),f5(x551,f5(x552,x553)))
% 0.18/0.71 [56]~P1(x563)+~P1(x562)+~P1(x561)+E(f6(f6(x561,x562),x563),f6(x561,f6(x562,x563)))
% 0.18/0.71 [57]~P1(x573)+~P1(x572)+~P1(x571)+E(f5(f6(x571,x572),f6(x571,x573)),f6(x571,f5(x572,x573)))
% 0.18/0.71 [58]~P1(x582)+~P1(x583)+~P1(x581)+E(f5(f6(x581,x582),f6(x583,x582)),f6(f5(x581,x583),x582))
% 0.18/0.71 [45]~P1(x451)+~P1(x452)+E(x451,a1)+E(x452,a1)+~E(f6(x452,x451),a1)
% 0.18/0.71 [52]~P1(x522)+~P1(x523)+~P1(x521)+P2(x521,x522)+E(x521,a1)+~E(f6(x521,x523),x522)
% 0.18/0.71 [59]~P1(x593)+~P1(x592)+~P1(x591)+P3(x592,x593,x591)+E(x591,a1)+~P2(x591,f5(x592,f4(x593)))
% 0.18/0.71 [60]~P1(x601)+~P1(x603)+~P1(x602)+~P3(x602,x603,x601)+E(x601,a1)+P2(x601,f5(x602,f4(x603)))
% 0.18/0.71 %EqnAxiom
% 0.18/0.71 [1]E(x11,x11)
% 0.18/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.71 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.18/0.71 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53))
% 0.18/0.71 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62))
% 0.18/0.71 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.18/0.71 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.18/0.71 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93))
% 0.18/0.71 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102))
% 0.18/0.71 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.18/0.71 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124)
% 0.18/0.71 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134)
% 0.18/0.71 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141)
% 0.18/0.71 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.18/0.71 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.18/0.71
% 0.18/0.71 %-------------------------------------------
% 0.18/0.71 cnf(62,plain,
% 0.18/0.71 (~E(f5(a8,f4(a9)),f5(a9,f4(a8)))),
% 0.18/0.71 inference(scs_inference,[],[30,27,25,2,16])).
% 0.18/0.71 cnf(80,plain,
% 0.18/0.71 (E(f3(x801,f6(a10,a2)),f3(x801,f6(a10,a11)))),
% 0.18/0.71 inference(scs_inference,[],[30,17,18,19,27,25,24,2,16,3,50,38,37,36,35,34,33,32,10])).
% 0.18/0.71 cnf(81,plain,
% 0.18/0.71 (E(f3(f6(a10,a2),x811),f3(f6(a10,a11),x811))),
% 0.18/0.71 inference(scs_inference,[],[30,17,18,19,27,25,24,2,16,3,50,38,37,36,35,34,33,32,10,9])).
% 0.18/0.71 cnf(91,plain,
% 0.18/0.71 (E(f5(a1,f4(a1)),a1)),
% 0.18/0.71 inference(scs_inference,[],[30,17,18,19,27,25,24,2,16,3,50,38,37,36,35,34,33,32,10,9,8,7,6,5,4,42,41,40])).
% 0.18/0.71 cnf(122,plain,
% 0.18/0.71 (~E(a10,a1)),
% 0.18/0.71 inference(scs_inference,[],[20,29,57,2])).
% 0.18/0.71 cnf(128,plain,
% 0.18/0.71 (P3(a9,a9,a10)),
% 0.18/0.71 inference(scs_inference,[],[20,29,21,24,62,57,2,3,49,48,53])).
% 0.18/0.71 cnf(174,plain,
% 0.18/0.71 (E(f6(a10,f4(a11)),f5(a9,f4(a8)))),
% 0.18/0.71 inference(scs_inference,[],[31,22,26,21,80,81,122,128,57,53,58,13,3,56,55,2])).
% 0.18/0.71 cnf(230,plain,
% 0.18/0.71 ($false),
% 0.18/0.71 inference(scs_inference,[],[22,174,91,50,6,32]),
% 0.18/0.71 ['proof']).
% 0.18/0.71 % SZS output end Proof
% 0.18/0.71 % Total time :0.090000s
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