%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM432+3 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n023.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 0.46s 0.66s % Output : CNFRefutation 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : NUM432+3 : TPTP v8.2.0. Released v4.0.0. % 0.06/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n023.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sat Jun 22 22:11:08 EDT 2024 % 0.11/0.32 % CPUTime : % 0.18/0.50 start to proof:theBenchmark % 0.46/0.65 %------------------------------------------- % 0.46/0.65 % File :CSE---1.7 % 0.46/0.65 % Problem :theBenchmark % 0.46/0.65 % Transform :cnf % 0.46/0.65 % Format :tptp:raw % 0.46/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.46/0.65 % 0.46/0.65 % Result :Theorem 0.000000s % 0.46/0.65 % Output :CNFRefutation 0.000000s % 0.46/0.65 %------------------------------------------- % 0.46/0.65 %------------------------------------------------------------------------------ % 0.46/0.65 % File : NUM432+3 : TPTP v8.2.0. Released v4.0.0. % 0.46/0.65 % Domain : Number Theory % 0.46/0.65 % Problem : Fuerstenberg's infinitude of primes 05_04, 02 expansion % 0.46/0.65 % Version : Especial. % 0.46/0.65 % English : % 0.46/0.65 % 0.46/0.65 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.46/0.65 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.46/0.65 % Source : [Pas08] % 0.46/0.65 % Names : fuerst_05_04.02 [Pas08] % 0.46/0.65 % 0.46/0.65 % Status : Theorem % 0.46/0.65 % Rating : 0.11 v8.2.0, 0.14 v8.1.0, 0.11 v7.5.0, 0.09 v7.4.0, 0.13 v7.3.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.33 v5.0.0, 0.38 v4.1.0, 0.43 v4.0.1, 0.70 v4.0.0 % 0.46/0.65 % Syntax : Number of formulae : 27 ( 3 unt; 2 def) % 0.46/0.65 % Number of atoms : 95 ( 31 equ) % 0.46/0.65 % Maximal formula atoms : 8 ( 3 avg) % 0.46/0.65 % Number of connectives : 73 ( 5 ~; 3 |; 42 &) % 0.46/0.65 % ( 2 <=>; 21 =>; 0 <=; 0 <~>) % 0.46/0.65 % Maximal formula depth : 9 ( 5 avg) % 0.46/0.65 % Maximal term depth : 3 ( 1 avg) % 0.46/0.65 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty) % 0.46/0.65 % Number of functors : 11 ( 11 usr; 8 con; 0-2 aty) % 0.46/0.65 % Number of variables : 40 ( 36 !; 4 ?) % 0.46/0.65 % SPC : FOF_THM_RFO_SEQ % 0.46/0.65 % 0.46/0.65 % Comments : Problem generated by the SAD system [VLP07] % 0.46/0.65 %------------------------------------------------------------------------------ % 0.46/0.65 fof(mIntegers,axiom, % 0.46/0.65 ! [W0] : % 0.46/0.65 ( aInteger0(W0) % 0.46/0.65 => $true ) ). % 0.46/0.65 % 0.46/0.65 fof(mIntZero,axiom, % 0.46/0.65 aInteger0(sz00) ). % 0.46/0.65 % 0.46/0.65 fof(mIntOne,axiom, % 0.46/0.65 aInteger0(sz10) ). % 0.46/0.65 % 0.46/0.65 fof(mIntNeg,axiom, % 0.46/0.65 ! [W0] : % 0.46/0.65 ( aInteger0(W0) % 0.46/0.65 => aInteger0(smndt0(W0)) ) ). % 0.46/0.65 % 0.46/0.65 fof(mIntPlus,axiom, % 0.46/0.65 ! [W0,W1] : % 0.46/0.65 ( ( aInteger0(W0) % 0.46/0.65 & aInteger0(W1) ) % 0.46/0.65 => aInteger0(sdtpldt0(W0,W1)) ) ). % 0.46/0.65 % 0.46/0.65 fof(mIntMult,axiom, % 0.46/0.65 ! [W0,W1] : % 0.46/0.65 ( ( aInteger0(W0) % 0.46/0.65 & aInteger0(W1) ) % 0.46/0.65 => aInteger0(sdtasdt0(W0,W1)) ) ). % 0.46/0.65 % 0.46/0.65 fof(mAddAsso,axiom, % 0.46/0.65 ! [W0,W1,W2] : % 0.46/0.65 ( ( aInteger0(W0) % 0.46/0.65 & aInteger0(W1) % 0.46/0.65 & aInteger0(W2) ) % 0.46/0.65 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ). % 0.46/0.65 % 0.46/0.65 fof(mAddComm,axiom, % 0.46/0.65 ! [W0,W1] : % 0.46/0.65 ( ( aInteger0(W0) % 0.46/0.65 & aInteger0(W1) ) % 0.46/0.65 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.46/0.65 % 0.46/0.66 fof(mAddZero,axiom, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ( sdtpldt0(W0,sz00) = W0 % 0.46/0.66 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mAddNeg,axiom, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ( sdtpldt0(W0,smndt0(W0)) = sz00 % 0.46/0.66 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mMulAsso,axiom, % 0.46/0.66 ! [W0,W1,W2] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) % 0.46/0.66 & aInteger0(W2) ) % 0.46/0.66 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ). % 0.46/0.66 % 0.46/0.66 fof(mMulComm,axiom, % 0.46/0.66 ! [W0,W1] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) ) % 0.46/0.66 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.46/0.66 % 0.46/0.66 fof(mMulOne,axiom, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ( sdtasdt0(W0,sz10) = W0 % 0.46/0.66 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mDistrib,axiom, % 0.46/0.66 ! [W0,W1,W2] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) % 0.46/0.66 & aInteger0(W2) ) % 0.46/0.66 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.46/0.66 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mMulZero,axiom, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ( sdtasdt0(W0,sz00) = sz00 % 0.46/0.66 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mMulMinOne,axiom, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) % 0.46/0.66 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mZeroDiv,axiom, % 0.46/0.66 ! [W0,W1] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) ) % 0.46/0.66 => ( sdtasdt0(W0,W1) = sz00 % 0.46/0.66 => ( W0 = sz00 % 0.46/0.66 | W1 = sz00 ) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mDivisor,definition, % 0.46/0.66 ! [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 => ! [W1] : % 0.46/0.66 ( aDivisorOf0(W1,W0) % 0.46/0.66 <=> ( aInteger0(W1) % 0.46/0.66 & W1 != sz00 % 0.46/0.66 & ? [W2] : % 0.46/0.66 ( aInteger0(W2) % 0.46/0.66 & sdtasdt0(W1,W2) = W0 ) ) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mEquMod,definition, % 0.46/0.66 ! [W0,W1,W2] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) % 0.46/0.66 & aInteger0(W2) % 0.46/0.66 & W2 != sz00 ) % 0.46/0.66 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.46/0.66 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(mEquModRef,axiom, % 0.46/0.66 ! [W0,W1] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) % 0.46/0.66 & W1 != sz00 ) % 0.46/0.66 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ). % 0.46/0.66 % 0.46/0.66 fof(mEquModSym,axiom, % 0.46/0.66 ! [W0,W1,W2] : % 0.46/0.66 ( ( aInteger0(W0) % 0.46/0.66 & aInteger0(W1) % 0.46/0.66 & aInteger0(W2) % 0.46/0.66 & W2 != sz00 ) % 0.46/0.66 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.46/0.66 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ). % 0.46/0.66 % 0.46/0.66 fof(m__818,hypothesis, % 0.46/0.66 ( aInteger0(xa) % 0.46/0.66 & aInteger0(xb) % 0.46/0.66 & aInteger0(xq) % 0.46/0.66 & xq != sz00 % 0.46/0.66 & aInteger0(xc) ) ). % 0.46/0.66 % 0.46/0.66 fof(m__853,hypothesis, % 0.46/0.66 ( ? [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) % 0.46/0.66 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) % 0.46/0.66 & sdteqdtlpzmzozddtrp0(xa,xb,xq) % 0.46/0.66 & ? [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) % 0.46/0.66 & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))) % 0.46/0.66 & sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ). % 0.46/0.66 % 0.46/0.66 fof(m__876,hypothesis, % 0.46/0.66 ( aInteger0(xn) % 0.46/0.66 & sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ). % 0.46/0.66 % 0.46/0.66 fof(m__899,hypothesis, % 0.46/0.66 ( aInteger0(xm) % 0.46/0.66 & sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ) ). % 0.46/0.66 % 0.46/0.66 fof(m__924,hypothesis, % 0.46/0.66 sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)) ). % 0.46/0.66 % 0.46/0.66 fof(m__,conjecture, % 0.46/0.66 ( ? [W0] : % 0.46/0.66 ( aInteger0(W0) % 0.46/0.66 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) % 0.46/0.66 | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) % 0.46/0.66 | sdteqdtlpzmzozddtrp0(xa,xc,xq) ) ). % 0.46/0.66 % 0.46/0.66 %------------------------------------------------------------------------------ % 0.46/0.66 %------------------------------------------- % 0.46/0.66 % Proof found % 0.46/0.66 % SZS status Theorem for theBenchmark % 0.46/0.66 % SZS output start Proof % 0.46/0.66 %ClaNum:68(EqnAxiom:16) % 0.46/0.66 %VarNum:161(SingletonVarNum:56) % 0.46/0.66 %MaxLitNum:6 % 0.46/0.66 %MaxfuncDepth:2 % 0.46/0.66 %SharedTerms:44 % 0.46/0.66 %goalClause: 37 38 57 % 0.46/0.66 %singleGoalClaCount:2 % 0.46/0.66 [17]P1(a1) % 0.46/0.66 [18]P1(a8) % 0.46/0.66 [19]P1(a9) % 0.46/0.66 [20]P1(a10) % 0.46/0.66 [21]P1(a11) % 0.46/0.66 [22]P1(a12) % 0.46/0.66 [23]P1(a13) % 0.46/0.66 [24]P1(a14) % 0.46/0.66 [25]P1(a2) % 0.46/0.66 [26]P1(a4) % 0.46/0.66 [34]P3(a9,a10,a11) % 0.46/0.66 [35]P3(a10,a12,a11) % 0.46/0.66 [36]~E(a1,a11) % 0.46/0.66 [38]~P3(a9,a12,a11) % 0.46/0.66 [27]E(f6(a9,f5(a10)),f7(a11,a13)) % 0.46/0.66 [28]E(f6(a10,f5(a12)),f7(a11,a14)) % 0.46/0.66 [29]E(f6(a9,f5(a10)),f7(a11,a2)) % 0.46/0.66 [30]E(f6(a10,f5(a12)),f7(a11,a4)) % 0.46/0.66 [31]P2(a11,f6(a9,f5(a10))) % 0.46/0.66 [32]P2(a11,f6(a10,f5(a12))) % 0.46/0.66 [33]E(f7(a11,f6(a13,a14)),f6(a9,f5(a12))) % 0.46/0.66 [37]~P2(a11,f6(a9,f5(a12))) % 0.46/0.66 [39]~P1(x391)+P1(f5(x391)) % 0.46/0.66 [40]~P1(x401)+E(f7(a1,x401),a1) % 0.46/0.66 [41]~P1(x411)+E(f7(x411,a1),a1) % 0.46/0.66 [42]~P1(x421)+E(f6(a1,x421),x421) % 0.46/0.66 [43]~P1(x431)+E(f7(a8,x431),x431) % 0.46/0.66 [44]~P1(x441)+E(f6(x441,a1),x441) % 0.46/0.66 [45]~P1(x451)+E(f7(x451,a8),x451) % 0.46/0.66 [46]~P1(x461)+E(f6(f5(x461),x461),a1) % 0.46/0.66 [47]~P1(x471)+E(f6(x471,f5(x471)),a1) % 0.46/0.66 [48]~P1(x481)+E(f7(x481,f5(a8)),f5(x481)) % 0.46/0.66 [49]~P1(x491)+E(f7(f5(a8),x491),f5(x491)) % 0.46/0.66 [57]~P1(x571)+~E(f7(a11,x571),f6(a9,f5(a12))) % 0.46/0.66 [50]~P2(x501,x502)+~P1(x502)+~E(x501,a1) % 0.46/0.66 [51]~P2(x511,x512)+P1(x511)+~P1(x512) % 0.46/0.66 [53]~P1(x532)+~P1(x531)+E(f6(x531,x532),f6(x532,x531)) % 0.46/0.66 [54]~P1(x542)+~P1(x541)+E(f7(x541,x542),f7(x542,x541)) % 0.46/0.66 [55]~P1(x552)+~P1(x551)+P1(f6(x551,x552)) % 0.46/0.66 [56]~P1(x562)+~P1(x561)+P1(f7(x561,x562)) % 0.46/0.66 [58]~P1(x581)+~P2(x582,x581)+P1(f3(x581,x582)) % 0.46/0.66 [61]~P1(x612)+~P2(x611,x612)+E(f7(x611,f3(x612,x611)),x612) % 0.46/0.66 [60]~P1(x601)+~P1(x602)+P3(x602,x602,x601)+E(x601,a1) % 0.46/0.66 [62]~P1(x623)+~P1(x622)+~P1(x621)+E(f6(f6(x621,x622),x623),f6(x621,f6(x622,x623))) % 0.46/0.66 [63]~P1(x633)+~P1(x632)+~P1(x631)+E(f7(f7(x631,x632),x633),f7(x631,f7(x632,x633))) % 0.46/0.66 [64]~P1(x643)+~P1(x642)+~P1(x641)+E(f6(f7(x641,x642),f7(x641,x643)),f7(x641,f6(x642,x643))) % 0.46/0.66 [65]~P1(x652)+~P1(x653)+~P1(x651)+E(f6(f7(x651,x652),f7(x653,x652)),f7(f6(x651,x653),x652)) % 0.46/0.66 [52]~P1(x521)+~P1(x522)+E(x521,a1)+E(x522,a1)+~E(f7(x522,x521),a1) % 0.46/0.66 [68]~P1(x681)+~P1(x682)+~P1(x683)+~P3(x683,x682,x681)+P3(x682,x683,x681)+E(x681,a1) % 0.46/0.66 [59]~P1(x592)+~P1(x593)+~P1(x591)+P2(x591,x592)+E(x591,a1)+~E(f7(x591,x593),x592) % 0.46/0.66 [66]~P1(x663)+~P1(x662)+~P1(x661)+P3(x662,x663,x661)+E(x661,a1)+~P2(x661,f6(x662,f5(x663))) % 0.46/0.66 [67]~P1(x671)+~P1(x673)+~P1(x672)+~P3(x672,x673,x671)+E(x671,a1)+P2(x671,f6(x672,f5(x673))) % 0.46/0.66 %EqnAxiom % 0.46/0.66 [1]E(x11,x11) % 0.46/0.66 [2]E(x22,x21)+~E(x21,x22) % 0.46/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.46/0.66 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 0.46/0.66 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53)) % 0.46/0.66 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62)) % 0.46/0.66 [7]~E(x71,x72)+E(f7(x71,x73),f7(x72,x73)) % 0.46/0.66 [8]~E(x81,x82)+E(f7(x83,x81),f7(x83,x82)) % 0.46/0.66 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93)) % 0.46/0.66 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102)) % 0.46/0.66 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.46/0.66 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.46/0.66 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.46/0.66 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.46/0.66 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 0.46/0.66 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 0.46/0.66 % 0.46/0.66 %------------------------------------------- % 0.46/0.66 cnf(76,plain, % 0.46/0.66 ($false), % 0.46/0.66 inference(scs_inference,[],[17,23,24,33,57,2,51,55]), % 0.46/0.66 ['proof']). % 0.46/0.66 % SZS output end Proof % 0.46/0.66 % Total time :0.000000s %------------------------------------------------------------------------------