%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM434+3 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n021.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 : Mon Jun 24 12:24:14 EDT 2024 % Result : Theorem 0.50s 0.62s % Output : CNFRefutation 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM434+3 : TPTP v8.2.0. Released v4.0.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Jun 22 21:20:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.58 start to proof:theBenchmark % 0.50/0.61 %------------------------------------------- % 0.50/0.61 % File :CSE---1.7 % 0.50/0.61 % Problem :theBenchmark % 0.50/0.61 % Transform :cnf % 0.50/0.61 % Format :tptp:raw % 0.50/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.50/0.61 % 0.50/0.61 % Result :Theorem 0.000000s % 0.50/0.61 % Output :CNFRefutation 0.000000s % 0.50/0.61 %------------------------------------------- % 0.50/0.61 %------------------------------------------------------------------------------ % 0.50/0.61 % File : NUM434+3 : TPTP v8.2.0. Released v4.0.0. % 0.50/0.61 % Domain : Number Theory % 0.50/0.61 % Problem : Fuerstenberg's infinitude of primes 06_01, 02 expansion % 0.50/0.61 % Version : Especial. % 0.50/0.61 % English : % 0.50/0.61 % 0.50/0.61 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.50/0.61 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.50/0.61 % Source : [Pas08] % 0.50/0.61 % Names : fuerst_06_01.02 [Pas08] % 0.50/0.61 % 0.50/0.61 % Status : Theorem % 0.50/0.61 % Rating : 0.03 v8.1.0, 0.00 v7.3.0, 0.03 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.20 v5.1.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.65 v4.0.0 % 0.50/0.61 % Syntax : Number of formulae : 25 ( 2 unt; 2 def) % 0.50/0.61 % Number of atoms : 94 ( 30 equ) % 0.50/0.61 % Maximal formula atoms : 8 ( 3 avg) % 0.50/0.61 % Number of connectives : 77 ( 8 ~; 1 |; 43 &) % 0.50/0.61 % ( 2 <=>; 23 =>; 0 <=; 0 <~>) % 0.50/0.61 % Maximal formula depth : 11 ( 5 avg) % 0.50/0.61 % Maximal term depth : 3 ( 1 avg) % 0.50/0.62 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty) % 0.50/0.62 % Number of functors : 9 ( 9 usr; 6 con; 0-2 aty) % 0.50/0.62 % Number of variables : 43 ( 40 !; 3 ?) % 0.50/0.62 % SPC : FOF_THM_RFO_SEQ % 0.50/0.62 % 0.50/0.62 % Comments : Problem generated by the SAD system [VLP07] % 0.50/0.62 %------------------------------------------------------------------------------ % 0.50/0.62 fof(mIntegers,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => $true ) ). % 0.50/0.62 % 0.50/0.62 fof(mIntZero,axiom, % 0.50/0.62 aInteger0(sz00) ). % 0.50/0.62 % 0.50/0.62 fof(mIntOne,axiom, % 0.50/0.62 aInteger0(sz10) ). % 0.50/0.62 % 0.50/0.62 fof(mIntNeg,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => aInteger0(smndt0(W0)) ) ). % 0.50/0.62 % 0.50/0.62 fof(mIntPlus,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) ) % 0.50/0.62 => aInteger0(sdtpldt0(W0,W1)) ) ). % 0.50/0.62 % 0.50/0.62 fof(mIntMult,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) ) % 0.50/0.62 => aInteger0(sdtasdt0(W0,W1)) ) ). % 0.50/0.62 % 0.50/0.62 fof(mAddAsso,axiom, % 0.50/0.62 ! [W0,W1,W2] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) ) % 0.50/0.62 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ). % 0.50/0.62 % 0.50/0.62 fof(mAddComm,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) ) % 0.50/0.62 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.50/0.62 % 0.50/0.62 fof(mAddZero,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ( sdtpldt0(W0,sz00) = W0 % 0.50/0.62 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mAddNeg,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ( sdtpldt0(W0,smndt0(W0)) = sz00 % 0.50/0.62 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mMulAsso,axiom, % 0.50/0.62 ! [W0,W1,W2] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) ) % 0.50/0.62 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ). % 0.50/0.62 % 0.50/0.62 fof(mMulComm,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) ) % 0.50/0.62 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.50/0.62 % 0.50/0.62 fof(mMulOne,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ( sdtasdt0(W0,sz10) = W0 % 0.50/0.62 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mDistrib,axiom, % 0.50/0.62 ! [W0,W1,W2] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) ) % 0.50/0.62 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.50/0.62 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mMulZero,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ( sdtasdt0(W0,sz00) = sz00 % 0.50/0.62 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mMulMinOne,axiom, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) % 0.50/0.62 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mZeroDiv,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) ) % 0.50/0.62 => ( sdtasdt0(W0,W1) = sz00 % 0.50/0.62 => ( W0 = sz00 % 0.50/0.62 | W1 = sz00 ) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mDivisor,definition, % 0.50/0.62 ! [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 => ! [W1] : % 0.50/0.62 ( aDivisorOf0(W1,W0) % 0.50/0.62 <=> ( aInteger0(W1) % 0.50/0.62 & W1 != sz00 % 0.50/0.62 & ? [W2] : % 0.50/0.62 ( aInteger0(W2) % 0.50/0.62 & sdtasdt0(W1,W2) = W0 ) ) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mEquMod,definition, % 0.50/0.62 ! [W0,W1,W2] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) % 0.50/0.62 & W2 != sz00 ) % 0.50/0.62 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.50/0.62 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mEquModRef,axiom, % 0.50/0.62 ! [W0,W1] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & W1 != sz00 ) % 0.50/0.62 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ). % 0.50/0.62 % 0.50/0.62 fof(mEquModSym,axiom, % 0.50/0.62 ! [W0,W1,W2] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) % 0.50/0.62 & W2 != sz00 ) % 0.50/0.62 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.50/0.62 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(mEquModTrn,axiom, % 0.50/0.62 ! [W0,W1,W2,W3] : % 0.50/0.62 ( ( aInteger0(W0) % 0.50/0.62 & aInteger0(W1) % 0.50/0.62 & aInteger0(W2) % 0.50/0.62 & W2 != sz00 % 0.50/0.62 & aInteger0(W3) ) % 0.50/0.62 => ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.50/0.62 & sdteqdtlpzmzozddtrp0(W1,W3,W2) ) % 0.50/0.62 => sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ) ). % 0.50/0.62 % 0.50/0.62 fof(m__979,hypothesis, % 0.50/0.62 ( aInteger0(xa) % 0.50/0.62 & aInteger0(xb) % 0.50/0.62 & aInteger0(xp) % 0.50/0.62 & xp != sz00 % 0.50/0.62 & aInteger0(xq) % 0.50/0.62 & xq != sz00 ) ). % 0.50/0.62 % 0.50/0.62 fof(m__1003,hypothesis, % 0.50/0.62 ( sdtasdt0(xp,xq) != sz00 % 0.50/0.62 & ? [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 & sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) % 0.50/0.62 & aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) % 0.50/0.62 & sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ) ). % 0.50/0.62 % 0.50/0.62 fof(m__,conjecture, % 0.50/0.62 ? [W0] : % 0.50/0.62 ( aInteger0(W0) % 0.50/0.62 & sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ). % 0.50/0.62 % 0.50/0.62 %------------------------------------------------------------------------------ % 0.50/0.62 %------------------------------------------- % 0.50/0.62 % Proof found % 0.50/0.62 % SZS status Theorem for theBenchmark % 0.50/0.62 % SZS output start Proof % 0.50/0.62 %ClaNum:60(EqnAxiom:16) % 0.50/0.62 %VarNum:175(SingletonVarNum:60) % 0.50/0.62 %MaxLitNum:8 % 0.50/0.62 %MaxfuncDepth:2 % 0.50/0.62 %SharedTerms:25 % 0.50/0.62 %goalClause: 52 % 0.50/0.62 [17]P1(a1) % 0.50/0.62 [18]P1(a7) % 0.50/0.62 [19]P1(a8) % 0.50/0.62 [20]P1(a9) % 0.50/0.62 [21]P1(a10) % 0.50/0.62 [22]P1(a11) % 0.50/0.62 [23]P1(a2) % 0.50/0.62 [27]~E(a1,a10) % 0.50/0.62 [28]~E(a1,a11) % 0.50/0.62 [26]P3(a8,a9,f4(a10,a11)) % 0.50/0.62 [29]~E(f4(a10,a11),a1) % 0.50/0.62 [24]E(f4(f4(a10,a11),a2),f6(a8,f5(a9))) % 0.50/0.62 [25]P2(f4(a10,a11),f6(a8,f5(a9))) % 0.50/0.62 [30]~P1(x301)+P1(f5(x301)) % 0.50/0.62 [31]~P1(x311)+E(f4(a1,x311),a1) % 0.50/0.62 [32]~P1(x321)+E(f4(x321,a1),a1) % 0.50/0.62 [33]~P1(x331)+E(f6(a1,x331),x331) % 0.50/0.62 [34]~P1(x341)+E(f4(a7,x341),x341) % 0.50/0.62 [35]~P1(x351)+E(f6(x351,a1),x351) % 0.50/0.62 [36]~P1(x361)+E(f4(x361,a7),x361) % 0.50/0.62 [37]~P1(x371)+E(f6(f5(x371),x371),a1) % 0.50/0.62 [38]~P1(x381)+E(f6(x381,f5(x381)),a1) % 0.50/0.62 [39]~P1(x391)+E(f4(x391,f5(a7)),f5(x391)) % 0.50/0.62 [40]~P1(x401)+E(f4(f5(a7),x401),f5(x401)) % 0.50/0.62 [52]~P1(x521)+~E(f4(f4(a10,a11),x521),f6(a8,f5(a9))) % 0.50/0.62 [41]~P2(x411,x412)+~P1(x412)+~E(x411,a1) % 0.50/0.62 [42]~P2(x421,x422)+P1(x421)+~P1(x422) % 0.50/0.62 [44]~P1(x442)+~P1(x441)+E(f6(x441,x442),f6(x442,x441)) % 0.50/0.62 [45]~P1(x452)+~P1(x451)+E(f4(x451,x452),f4(x452,x451)) % 0.50/0.62 [46]~P1(x462)+~P1(x461)+P1(f6(x461,x462)) % 0.50/0.62 [47]~P1(x472)+~P1(x471)+P1(f4(x471,x472)) % 0.50/0.62 [48]~P1(x481)+~P2(x482,x481)+P1(f3(x481,x482)) % 0.50/0.62 [51]~P1(x512)+~P2(x511,x512)+E(f4(x511,f3(x512,x511)),x512) % 0.50/0.62 [50]~P1(x501)+~P1(x502)+P3(x502,x502,x501)+E(x501,a1) % 0.50/0.62 [53]~P1(x533)+~P1(x532)+~P1(x531)+E(f6(f6(x531,x532),x533),f6(x531,f6(x532,x533))) % 0.50/0.62 [54]~P1(x543)+~P1(x542)+~P1(x541)+E(f4(f4(x541,x542),x543),f4(x541,f4(x542,x543))) % 0.50/0.62 [55]~P1(x553)+~P1(x552)+~P1(x551)+E(f6(f4(x551,x552),f4(x551,x553)),f4(x551,f6(x552,x553))) % 0.50/0.62 [56]~P1(x562)+~P1(x563)+~P1(x561)+E(f6(f4(x561,x562),f4(x563,x562)),f4(f6(x561,x563),x562)) % 0.50/0.62 [43]~P1(x431)+~P1(x432)+E(x431,a1)+E(x432,a1)+~E(f4(x432,x431),a1) % 0.50/0.62 [59]~P1(x591)+~P1(x592)+~P1(x593)+~P3(x593,x592,x591)+P3(x592,x593,x591)+E(x591,a1) % 0.50/0.62 [49]~P1(x492)+~P1(x493)+~P1(x491)+P2(x491,x492)+E(x491,a1)+~E(f4(x491,x493),x492) % 0.50/0.62 [57]~P1(x573)+~P1(x572)+~P1(x571)+P3(x572,x573,x571)+E(x571,a1)+~P2(x571,f6(x572,f5(x573))) % 0.50/0.62 [58]~P1(x581)+~P1(x583)+~P1(x582)+~P3(x582,x583,x581)+E(x581,a1)+P2(x581,f6(x582,f5(x583))) % 0.50/0.62 [60]~P1(x603)+~P1(x601)+~P1(x602)+~P3(x604,x603,x601)+~P3(x602,x604,x601)+P3(x602,x603,x601)+~P1(x604)+E(x601,a1) % 0.50/0.62 %EqnAxiom % 0.50/0.63 [1]E(x11,x11) % 0.50/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.50/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.50/0.63 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43)) % 0.50/0.63 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52)) % 0.50/0.63 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 0.50/0.63 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 0.50/0.63 [8]~E(x81,x82)+E(f5(x81),f5(x82)) % 0.50/0.63 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93)) % 0.50/0.63 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102)) % 0.50/0.63 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.50/0.63 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.50/0.63 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.50/0.63 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.50/0.63 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 0.50/0.63 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 0.50/0.63 % 0.50/0.63 %------------------------------------------- % 0.50/0.63 cnf(63,plain, % 0.50/0.63 ($false), % 0.50/0.63 inference(scs_inference,[],[23,24,52]), % 0.50/0.63 ['proof']). % 0.50/0.63 % SZS output end Proof % 0.50/0.63 % Total time :0.000000s %------------------------------------------------------------------------------