%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM425+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 : n018.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 12:24:11 EDT 2024 % Result : Theorem 0.58s 0.63s % Output : CNFRefutation 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM425+3 : TPTP v8.2.0. Released v4.0.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n018.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 : Sun Jun 23 01:54:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 0.56/0.62 %------------------------------------------- % 0.56/0.62 % File :CSE---1.7 % 0.56/0.62 % Problem :theBenchmark % 0.56/0.62 % Transform :cnf % 0.56/0.62 % Format :tptp:raw % 0.56/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.62 % 0.56/0.62 % Result :Theorem 0.000000s % 0.56/0.62 % Output :CNFRefutation 0.000000s % 0.56/0.62 %------------------------------------------- % 0.56/0.63 %------------------------------------------------------------------------------ % 0.56/0.63 % File : NUM425+3 : TPTP v8.2.0. Released v4.0.0. % 0.56/0.63 % Domain : Number Theory % 0.56/0.63 % Problem : Fuerstenberg's infinitude of primes 04_01, 02 expansion % 0.56/0.63 % Version : Especial. % 0.56/0.63 % English : % 0.56/0.63 % 0.56/0.63 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.56/0.63 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.56/0.63 % Source : [Pas08] % 0.56/0.63 % Names : fuerst_04_01.02 [Pas08] % 0.56/0.63 % 0.56/0.63 % Status : Theorem % 0.56/0.63 % Rating : 0.03 v8.1.0, 0.00 v7.3.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.04 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.30 v4.0.1, 0.52 v4.0.0 % 0.56/0.63 % Syntax : Number of formulae : 23 ( 2 unt; 2 def) % 0.56/0.63 % Number of atoms : 77 ( 26 equ) % 0.56/0.63 % Maximal formula atoms : 6 ( 3 avg) % 0.56/0.63 % Number of connectives : 58 ( 4 ~; 1 |; 32 &) % 0.56/0.63 % ( 2 <=>; 19 =>; 0 <=; 0 <~>) % 0.56/0.63 % Maximal formula depth : 9 ( 5 avg) % 0.56/0.63 % Maximal term depth : 3 ( 1 avg) % 0.56/0.63 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty) % 0.56/0.63 % Number of functors : 8 ( 8 usr; 5 con; 0-2 aty) % 0.56/0.63 % Number of variables : 36 ( 33 !; 3 ?) % 0.56/0.63 % SPC : FOF_THM_RFO_SEQ % 0.56/0.63 % 0.56/0.63 % Comments : Problem generated by the SAD system [VLP07] % 0.56/0.63 %------------------------------------------------------------------------------ % 0.56/0.63 fof(mIntegers,axiom, % 0.56/0.63 ! [W0] : % 0.56/0.63 ( aInteger0(W0) % 0.56/0.63 => $true ) ). % 0.56/0.63 % 0.56/0.63 fof(mIntZero,axiom, % 0.56/0.63 aInteger0(sz00) ). % 0.56/0.63 % 0.56/0.63 fof(mIntOne,axiom, % 0.56/0.63 aInteger0(sz10) ). % 0.56/0.63 % 0.56/0.63 fof(mIntNeg,axiom, % 0.56/0.63 ! [W0] : % 0.56/0.63 ( aInteger0(W0) % 0.56/0.63 => aInteger0(smndt0(W0)) ) ). % 0.56/0.63 % 0.56/0.63 fof(mIntPlus,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aInteger0(W0) % 0.56/0.63 & aInteger0(W1) ) % 0.56/0.63 => aInteger0(sdtpldt0(W0,W1)) ) ). % 0.56/0.63 % 0.56/0.63 fof(mIntMult,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aInteger0(W0) % 0.56/0.63 & aInteger0(W1) ) % 0.56/0.63 => aInteger0(sdtasdt0(W0,W1)) ) ). % 0.56/0.63 % 0.56/0.63 fof(mAddAsso,axiom, % 0.56/0.63 ! [W0,W1,W2] : % 0.56/0.63 ( ( aInteger0(W0) % 0.56/0.63 & aInteger0(W1) % 0.56/0.63 & aInteger0(W2) ) % 0.58/0.63 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ). % 0.58/0.63 % 0.58/0.63 fof(mAddComm,axiom, % 0.58/0.63 ! [W0,W1] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) ) % 0.58/0.63 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.58/0.63 % 0.58/0.63 fof(mAddZero,axiom, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ( sdtpldt0(W0,sz00) = W0 % 0.58/0.63 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mAddNeg,axiom, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ( sdtpldt0(W0,smndt0(W0)) = sz00 % 0.58/0.63 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mMulAsso,axiom, % 0.58/0.63 ! [W0,W1,W2] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) % 0.58/0.63 & aInteger0(W2) ) % 0.58/0.63 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ). % 0.58/0.63 % 0.58/0.63 fof(mMulComm,axiom, % 0.58/0.63 ! [W0,W1] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) ) % 0.58/0.63 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.58/0.63 % 0.58/0.63 fof(mMulOne,axiom, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ( sdtasdt0(W0,sz10) = W0 % 0.58/0.63 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mDistrib,axiom, % 0.58/0.63 ! [W0,W1,W2] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) % 0.58/0.63 & aInteger0(W2) ) % 0.58/0.63 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.58/0.63 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mMulZero,axiom, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ( sdtasdt0(W0,sz00) = sz00 % 0.58/0.63 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mMulMinOne,axiom, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) % 0.58/0.63 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mZeroDiv,axiom, % 0.58/0.63 ! [W0,W1] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) ) % 0.58/0.63 => ( sdtasdt0(W0,W1) = sz00 % 0.58/0.63 => ( W0 = sz00 % 0.58/0.63 | W1 = sz00 ) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mDivisor,definition, % 0.58/0.63 ! [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 => ! [W1] : % 0.58/0.63 ( aDivisorOf0(W1,W0) % 0.58/0.63 <=> ( aInteger0(W1) % 0.58/0.63 & W1 != sz00 % 0.58/0.63 & ? [W2] : % 0.58/0.63 ( aInteger0(W2) % 0.58/0.63 & sdtasdt0(W1,W2) = W0 ) ) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mEquMod,definition, % 0.58/0.63 ! [W0,W1,W2] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) % 0.58/0.63 & aInteger0(W2) % 0.58/0.63 & W2 != sz00 ) % 0.58/0.63 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.58/0.63 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ). % 0.58/0.63 % 0.58/0.63 fof(mEquModRef,axiom, % 0.58/0.63 ! [W0,W1] : % 0.58/0.63 ( ( aInteger0(W0) % 0.58/0.63 & aInteger0(W1) % 0.58/0.63 & W1 != sz00 ) % 0.58/0.63 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ). % 0.58/0.63 % 0.58/0.63 fof(m__704,hypothesis, % 0.58/0.63 ( aInteger0(xa) % 0.58/0.63 & aInteger0(xb) % 0.58/0.63 & aInteger0(xq) % 0.58/0.63 & xq != sz00 ) ). % 0.58/0.63 % 0.58/0.63 fof(m__724,hypothesis, % 0.58/0.63 ( ? [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) % 0.58/0.63 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) % 0.58/0.63 & sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ). % 0.58/0.63 % 0.58/0.63 fof(m__,conjecture, % 0.58/0.63 ? [W0] : % 0.58/0.63 ( aInteger0(W0) % 0.58/0.63 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) ). % 0.58/0.63 % 0.58/0.63 %------------------------------------------------------------------------------ % 0.58/0.63 %------------------------------------------- % 0.58/0.63 % Proof found % 0.58/0.63 % SZS status Theorem for theBenchmark % 0.58/0.63 % SZS output start Proof % 0.58/0.64 %ClaNum:55(EqnAxiom:16) % 0.58/0.64 %VarNum:151(SingletonVarNum:53) % 0.58/0.64 %MaxLitNum:6 % 0.58/0.64 %MaxfuncDepth:2 % 0.58/0.64 %SharedTerms:20 % 0.58/0.64 %goalClause: 45 % 0.58/0.64 [17]P1(a1) % 0.58/0.64 [18]P1(a7) % 0.58/0.64 [19]P1(a8) % 0.58/0.64 [20]P1(a9) % 0.58/0.64 [21]P1(a10) % 0.58/0.64 [22]P1(a2) % 0.58/0.64 [25]P3(a8,a9,a10) % 0.58/0.64 [26]~E(a1,a10) % 0.58/0.64 [23]E(f5(a8,f4(a9)),f6(a10,a2)) % 0.58/0.64 [24]P2(a10,f5(a8,f4(a9))) % 0.58/0.64 [27]~P1(x271)+P1(f4(x271)) % 0.58/0.64 [28]~P1(x281)+E(f6(a1,x281),a1) % 0.58/0.64 [29]~P1(x291)+E(f6(x291,a1),a1) % 0.58/0.64 [30]~P1(x301)+E(f5(a1,x301),x301) % 0.58/0.64 [31]~P1(x311)+E(f6(a7,x311),x311) % 0.58/0.64 [32]~P1(x321)+E(f5(x321,a1),x321) % 0.58/0.64 [33]~P1(x331)+E(f6(x331,a7),x331) % 0.58/0.64 [34]~P1(x341)+E(f5(f4(x341),x341),a1) % 0.58/0.64 [35]~P1(x351)+E(f5(x351,f4(x351)),a1) % 0.58/0.64 [36]~P1(x361)+E(f6(x361,f4(a7)),f4(x361)) % 0.58/0.64 [37]~P1(x371)+E(f6(f4(a7),x371),f4(x371)) % 0.58/0.64 [45]~P1(x451)+~E(f6(a10,x451),f5(a8,f4(a9))) % 0.58/0.64 [38]~P2(x381,x382)+~P1(x382)+~E(x381,a1) % 0.58/0.64 [39]~P2(x391,x392)+P1(x391)+~P1(x392) % 0.58/0.64 [41]~P1(x412)+~P1(x411)+E(f5(x411,x412),f5(x412,x411)) % 0.58/0.64 [42]~P1(x422)+~P1(x421)+E(f6(x421,x422),f6(x422,x421)) % 0.58/0.64 [43]~P1(x432)+~P1(x431)+P1(f5(x431,x432)) % 0.58/0.64 [44]~P1(x442)+~P1(x441)+P1(f6(x441,x442)) % 0.58/0.64 [46]~P1(x461)+~P2(x462,x461)+P1(f3(x461,x462)) % 0.58/0.64 [49]~P1(x492)+~P2(x491,x492)+E(f6(x491,f3(x492,x491)),x492) % 0.58/0.64 [48]~P1(x481)+~P1(x482)+P3(x482,x482,x481)+E(x481,a1) % 0.58/0.64 [50]~P1(x503)+~P1(x502)+~P1(x501)+E(f5(f5(x501,x502),x503),f5(x501,f5(x502,x503))) % 0.58/0.64 [51]~P1(x513)+~P1(x512)+~P1(x511)+E(f6(f6(x511,x512),x513),f6(x511,f6(x512,x513))) % 0.58/0.64 [52]~P1(x523)+~P1(x522)+~P1(x521)+E(f5(f6(x521,x522),f6(x521,x523)),f6(x521,f5(x522,x523))) % 0.58/0.64 [53]~P1(x532)+~P1(x533)+~P1(x531)+E(f5(f6(x531,x532),f6(x533,x532)),f6(f5(x531,x533),x532)) % 0.58/0.64 [40]~P1(x401)+~P1(x402)+E(x401,a1)+E(x402,a1)+~E(f6(x402,x401),a1) % 0.58/0.64 [47]~P1(x472)+~P1(x473)+~P1(x471)+P2(x471,x472)+E(x471,a1)+~E(f6(x471,x473),x472) % 0.58/0.64 [54]~P1(x543)+~P1(x542)+~P1(x541)+P3(x542,x543,x541)+E(x541,a1)+~P2(x541,f5(x542,f4(x543))) % 0.58/0.64 [55]~P1(x551)+~P1(x553)+~P1(x552)+~P3(x552,x553,x551)+E(x551,a1)+P2(x551,f5(x552,f4(x553))) % 0.58/0.64 %EqnAxiom % 0.58/0.64 [1]E(x11,x11) % 0.58/0.64 [2]E(x22,x21)+~E(x21,x22) % 0.58/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.58/0.64 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 0.58/0.64 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53)) % 0.58/0.64 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62)) % 0.58/0.64 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73)) % 0.58/0.64 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82)) % 0.58/0.64 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93)) % 0.58/0.64 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102)) % 0.58/0.64 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.58/0.64 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.58/0.64 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.58/0.64 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.58/0.64 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 0.58/0.64 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 0.58/0.64 % 0.58/0.64 %------------------------------------------- % 0.58/0.64 cnf(60,plain, % 0.58/0.64 ($false), % 0.58/0.64 inference(scs_inference,[],[22,23,24,2,16,45]), % 0.58/0.64 ['proof']). % 0.58/0.64 % SZS output end Proof % 0.58/0.64 % Total time :0.000000s %------------------------------------------------------------------------------