%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM429+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 : n019.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 12:24:13 EDT 2024 % Result : Theorem 0.56s 0.71s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM429+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 % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Jun 22 19:26:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.21/0.57 start to proof:theBenchmark % 0.56/0.70 %------------------------------------------- % 0.56/0.70 % File :CSE---1.7 % 0.56/0.70 % Problem :theBenchmark % 0.56/0.70 % Transform :cnf % 0.56/0.70 % Format :tptp:raw % 0.56/0.70 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.70 % 0.56/0.70 % Result :Theorem 0.000000s % 0.56/0.70 % Output :CNFRefutation 0.000000s % 0.56/0.70 %------------------------------------------- % 0.56/0.71 %------------------------------------------------------------------------------ % 0.56/0.71 % File : NUM429+3 : TPTP v8.2.0. Released v4.0.0. % 0.56/0.71 % Domain : Number Theory % 0.56/0.71 % Problem : Fuerstenberg's infinitude of primes 05_01, 02 expansion % 0.56/0.71 % Version : Especial. % 0.56/0.71 % English : % 0.56/0.71 % 0.56/0.71 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.56/0.71 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.56/0.71 % Source : [Pas08] % 0.56/0.71 % Names : fuerst_05_01.02 [Pas08] % 0.56/0.71 % 0.56/0.71 % Status : Theorem % 0.56/0.71 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.04 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.65 v4.0.0 % 0.56/0.71 % Syntax : Number of formulae : 24 ( 2 unt; 2 def) % 0.56/0.71 % Number of atoms : 88 ( 28 equ) % 0.56/0.71 % Maximal formula atoms : 8 ( 3 avg) % 0.56/0.71 % Number of connectives : 69 ( 5 ~; 1 |; 40 &) % 0.56/0.71 % ( 2 <=>; 21 =>; 0 <=; 0 <~>) % 0.56/0.71 % Maximal formula depth : 9 ( 5 avg) % 0.56/0.71 % Maximal term depth : 3 ( 1 avg) % 0.56/0.71 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty) % 0.56/0.71 % Number of functors : 9 ( 9 usr; 6 con; 0-2 aty) % 0.56/0.71 % Number of variables : 40 ( 36 !; 4 ?) % 0.56/0.71 % SPC : FOF_THM_RFO_SEQ % 0.56/0.71 % 0.56/0.71 % Comments : Problem generated by the SAD system [VLP07] % 0.56/0.71 %------------------------------------------------------------------------------ % 0.56/0.71 fof(mIntegers,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => $true ) ). % 0.56/0.71 % 0.56/0.71 fof(mIntZero,axiom, % 0.56/0.71 aInteger0(sz00) ). % 0.56/0.71 % 0.56/0.71 fof(mIntOne,axiom, % 0.56/0.71 aInteger0(sz10) ). % 0.56/0.71 % 0.56/0.71 fof(mIntNeg,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => aInteger0(smndt0(W0)) ) ). % 0.56/0.71 % 0.56/0.71 fof(mIntPlus,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) ) % 0.56/0.71 => aInteger0(sdtpldt0(W0,W1)) ) ). % 0.56/0.71 % 0.56/0.71 fof(mIntMult,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) ) % 0.56/0.71 => aInteger0(sdtasdt0(W0,W1)) ) ). % 0.56/0.71 % 0.56/0.71 fof(mAddAsso,axiom, % 0.56/0.71 ! [W0,W1,W2] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & aInteger0(W2) ) % 0.56/0.71 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ). % 0.56/0.71 % 0.56/0.71 fof(mAddComm,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) ) % 0.56/0.71 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.56/0.71 % 0.56/0.71 fof(mAddZero,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ( sdtpldt0(W0,sz00) = W0 % 0.56/0.71 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mAddNeg,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ( sdtpldt0(W0,smndt0(W0)) = sz00 % 0.56/0.71 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mMulAsso,axiom, % 0.56/0.71 ! [W0,W1,W2] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & aInteger0(W2) ) % 0.56/0.71 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ). % 0.56/0.71 % 0.56/0.71 fof(mMulComm,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) ) % 0.56/0.71 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.56/0.71 % 0.56/0.71 fof(mMulOne,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ( sdtasdt0(W0,sz10) = W0 % 0.56/0.71 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mDistrib,axiom, % 0.56/0.71 ! [W0,W1,W2] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & aInteger0(W2) ) % 0.56/0.71 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.56/0.71 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mMulZero,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ( sdtasdt0(W0,sz00) = sz00 % 0.56/0.71 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mMulMinOne,axiom, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) % 0.56/0.71 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mZeroDiv,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) ) % 0.56/0.71 => ( sdtasdt0(W0,W1) = sz00 % 0.56/0.71 => ( W0 = sz00 % 0.56/0.71 | W1 = sz00 ) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mDivisor,definition, % 0.56/0.71 ! [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 => ! [W1] : % 0.56/0.71 ( aDivisorOf0(W1,W0) % 0.56/0.71 <=> ( aInteger0(W1) % 0.56/0.71 & W1 != sz00 % 0.56/0.71 & ? [W2] : % 0.56/0.71 ( aInteger0(W2) % 0.56/0.71 & sdtasdt0(W1,W2) = W0 ) ) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mEquMod,definition, % 0.56/0.71 ! [W0,W1,W2] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & aInteger0(W2) % 0.56/0.71 & W2 != sz00 ) % 0.56/0.71 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.56/0.71 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(mEquModRef,axiom, % 0.56/0.71 ! [W0,W1] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & W1 != sz00 ) % 0.56/0.71 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ). % 0.56/0.71 % 0.56/0.71 fof(mEquModSym,axiom, % 0.56/0.71 ! [W0,W1,W2] : % 0.56/0.71 ( ( aInteger0(W0) % 0.56/0.71 & aInteger0(W1) % 0.56/0.71 & aInteger0(W2) % 0.56/0.71 & W2 != sz00 ) % 0.56/0.71 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.56/0.71 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ). % 0.56/0.71 % 0.56/0.71 fof(m__818,hypothesis, % 0.56/0.71 ( aInteger0(xa) % 0.56/0.71 & aInteger0(xb) % 0.56/0.71 & aInteger0(xq) % 0.56/0.71 & xq != sz00 % 0.56/0.71 & aInteger0(xc) ) ). % 0.56/0.71 % 0.56/0.71 fof(m__853,hypothesis, % 0.56/0.71 ( ? [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) % 0.56/0.71 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) % 0.56/0.71 & sdteqdtlpzmzozddtrp0(xa,xb,xq) % 0.56/0.71 & ? [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) % 0.56/0.71 & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))) % 0.56/0.71 & sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ). % 0.56/0.71 % 0.56/0.71 fof(m__,conjecture, % 0.56/0.71 ? [W0] : % 0.56/0.71 ( aInteger0(W0) % 0.56/0.71 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) ). % 0.56/0.71 % 0.56/0.71 %------------------------------------------------------------------------------ % 0.56/0.71 %------------------------------------------- % 0.56/0.71 % Proof found % 0.56/0.71 % SZS status Theorem for theBenchmark % 0.56/0.71 % SZS output start Proof % 0.56/0.71 %ClaNum:61(EqnAxiom:16) % 0.56/0.71 %VarNum:161(SingletonVarNum:56) % 0.56/0.71 %MaxLitNum:6 % 0.56/0.71 %MaxfuncDepth:2 % 0.56/0.71 %SharedTerms:30 % 0.56/0.71 %goalClause: 50 % 0.56/0.71 [17]P1(a1) % 0.56/0.71 [18]P1(a8) % 0.56/0.71 [19]P1(a9) % 0.56/0.71 [20]P1(a10) % 0.56/0.71 [21]P1(a11) % 0.56/0.71 [22]P1(a12) % 0.56/0.71 [23]P1(a2) % 0.56/0.71 [24]P1(a4) % 0.56/0.71 [29]P3(a9,a10,a11) % 0.56/0.71 [30]P3(a10,a12,a11) % 0.56/0.71 [31]~E(a1,a11) % 0.56/0.71 [25]E(f6(a9,f5(a10)),f7(a11,a2)) % 0.56/0.71 [26]E(f6(a10,f5(a12)),f7(a11,a4)) % 0.56/0.71 [27]P2(a11,f6(a9,f5(a10))) % 0.56/0.71 [28]P2(a11,f6(a10,f5(a12))) % 0.56/0.72 [32]~P1(x321)+P1(f5(x321)) % 0.56/0.72 [33]~P1(x331)+E(f7(a1,x331),a1) % 0.56/0.72 [34]~P1(x341)+E(f7(x341,a1),a1) % 0.56/0.72 [35]~P1(x351)+E(f6(a1,x351),x351) % 0.56/0.72 [36]~P1(x361)+E(f7(a8,x361),x361) % 0.56/0.72 [37]~P1(x371)+E(f6(x371,a1),x371) % 0.56/0.72 [38]~P1(x381)+E(f7(x381,a8),x381) % 0.56/0.72 [39]~P1(x391)+E(f6(f5(x391),x391),a1) % 0.56/0.72 [40]~P1(x401)+E(f6(x401,f5(x401)),a1) % 0.56/0.72 [41]~P1(x411)+E(f7(x411,f5(a8)),f5(x411)) % 0.56/0.72 [42]~P1(x421)+E(f7(f5(a8),x421),f5(x421)) % 0.56/0.72 [50]~P1(x501)+~E(f7(a11,x501),f6(a9,f5(a10))) % 0.56/0.72 [43]~P2(x431,x432)+~P1(x432)+~E(x431,a1) % 0.56/0.72 [44]~P2(x441,x442)+P1(x441)+~P1(x442) % 0.56/0.72 [46]~P1(x462)+~P1(x461)+E(f6(x461,x462),f6(x462,x461)) % 0.56/0.72 [47]~P1(x472)+~P1(x471)+E(f7(x471,x472),f7(x472,x471)) % 0.56/0.72 [48]~P1(x482)+~P1(x481)+P1(f6(x481,x482)) % 0.56/0.72 [49]~P1(x492)+~P1(x491)+P1(f7(x491,x492)) % 0.56/0.72 [51]~P1(x511)+~P2(x512,x511)+P1(f3(x511,x512)) % 0.56/0.72 [54]~P1(x542)+~P2(x541,x542)+E(f7(x541,f3(x542,x541)),x542) % 0.56/0.72 [53]~P1(x531)+~P1(x532)+P3(x532,x532,x531)+E(x531,a1) % 0.56/0.72 [55]~P1(x553)+~P1(x552)+~P1(x551)+E(f6(f6(x551,x552),x553),f6(x551,f6(x552,x553))) % 0.56/0.72 [56]~P1(x563)+~P1(x562)+~P1(x561)+E(f7(f7(x561,x562),x563),f7(x561,f7(x562,x563))) % 0.56/0.72 [57]~P1(x573)+~P1(x572)+~P1(x571)+E(f6(f7(x571,x572),f7(x571,x573)),f7(x571,f6(x572,x573))) % 0.56/0.72 [58]~P1(x582)+~P1(x583)+~P1(x581)+E(f6(f7(x581,x582),f7(x583,x582)),f7(f6(x581,x583),x582)) % 0.56/0.72 [45]~P1(x451)+~P1(x452)+E(x451,a1)+E(x452,a1)+~E(f7(x452,x451),a1) % 0.56/0.72 [61]~P1(x611)+~P1(x612)+~P1(x613)+~P3(x613,x612,x611)+P3(x612,x613,x611)+E(x611,a1) % 0.56/0.72 [52]~P1(x522)+~P1(x523)+~P1(x521)+P2(x521,x522)+E(x521,a1)+~E(f7(x521,x523),x522) % 0.56/0.72 [59]~P1(x593)+~P1(x592)+~P1(x591)+P3(x592,x593,x591)+E(x591,a1)+~P2(x591,f6(x592,f5(x593))) % 0.56/0.72 [60]~P1(x601)+~P1(x603)+~P1(x602)+~P3(x602,x603,x601)+E(x601,a1)+P2(x601,f6(x602,f5(x603))) % 0.56/0.72 %EqnAxiom % 0.56/0.72 [1]E(x11,x11) % 0.56/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.72 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 0.56/0.72 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53)) % 0.56/0.72 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62)) % 0.56/0.72 [7]~E(x71,x72)+E(f7(x71,x73),f7(x72,x73)) % 0.56/0.72 [8]~E(x81,x82)+E(f7(x83,x81),f7(x83,x82)) % 0.56/0.72 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93)) % 0.56/0.72 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102)) % 0.56/0.72 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.56/0.72 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.56/0.72 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.56/0.72 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.56/0.72 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 0.56/0.72 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 0.56/0.72 % 0.56/0.72 %------------------------------------------- % 0.56/0.72 cnf(66,plain, % 0.56/0.72 ($false), % 0.56/0.72 inference(scs_inference,[],[23,25,27,2,16,50]), % 0.56/0.72 ['proof']). % 0.56/0.72 % SZS output end Proof % 0.56/0.72 % Total time :0.000000s %------------------------------------------------------------------------------