%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM530+1 : 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 : n028.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 12:24:51 EDT 2024 % Result : Theorem 0.60s 0.65s % Output : CNFRefutation 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM530+1 : TPTP v8.2.0. Released v4.0.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n028.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 21:04:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 0.60/0.64 %------------------------------------------- % 0.60/0.64 % File :CSE---1.7 % 0.60/0.64 % Problem :theBenchmark % 0.60/0.64 % Transform :cnf % 0.60/0.64 % Format :tptp:raw % 0.60/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.60/0.64 % 0.60/0.64 % Result :Theorem 0.010000s % 0.60/0.64 % Output :CNFRefutation 0.010000s % 0.60/0.64 %------------------------------------------- % 0.60/0.64 %------------------------------------------------------------------------------ % 0.60/0.64 % File : NUM530+1 : TPTP v8.2.0. Released v4.0.0. % 0.60/0.64 % Domain : Number Theory % 0.60/0.64 % Problem : Square root of a prime is irrational 15_06, 00 expansion % 0.60/0.64 % Version : Especial. % 0.60/0.64 % English : % 0.60/0.64 % 0.60/0.64 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.60/0.64 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.60/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.60/0.64 % Source : [Pas08] % 0.60/0.64 % Names : primes_15_06.00 [Pas08] % 0.60/0.64 % 0.60/0.64 % Status : ContradictoryAxioms % 0.60/0.64 % Rating : 0.14 v8.2.0, 0.08 v7.5.0, 0.03 v7.4.0, 0.29 v7.3.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.17 v4.1.0, 0.26 v4.0.1, 0.61 v4.0.0 % 0.60/0.64 % Syntax : Number of formulae : 49 ( 7 unt; 5 def) % 0.60/0.64 % Number of atoms : 215 ( 67 equ) % 0.60/0.64 % Maximal formula atoms : 10 ( 4 avg) % 0.60/0.64 % Number of connectives : 195 ( 29 ~; 8 |; 89 &) % 0.60/0.64 % ( 5 <=>; 64 =>; 0 <=; 0 <~>) % 0.60/0.64 % Maximal formula depth : 11 ( 6 avg) % 0.60/0.64 % Maximal term depth : 3 ( 1 avg) % 0.60/0.64 % Number of predicates : 8 ( 5 usr; 2 prp; 0-2 aty) % 0.60/0.64 % Number of functors : 10 ( 10 usr; 6 con; 0-2 aty) % 0.60/0.64 % Number of variables : 88 ( 85 !; 3 ?) % 0.60/0.64 % SPC : FOF_CAX_RFO_SEQ % 0.60/0.64 % 0.60/0.64 % Comments : Problem generated by the SAD system [VLP07] % 0.60/0.64 %------------------------------------------------------------------------------ % 0.60/0.64 fof(mNatSort,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => $true ) ). % 0.60/0.64 % 0.60/0.64 fof(mSortsC,axiom, % 0.60/0.64 aNaturalNumber0(sz00) ). % 0.60/0.64 % 0.60/0.64 fof(mSortsC_01,axiom, % 0.60/0.64 ( aNaturalNumber0(sz10) % 0.60/0.64 & sz10 != sz00 ) ). % 0.60/0.64 % 0.60/0.64 fof(mSortsB,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.60/0.64 % 0.60/0.64 fof(mSortsB_02,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.60/0.64 % 0.60/0.64 fof(mAddComm,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.60/0.64 % 0.60/0.64 fof(mAddAsso,axiom, % 0.60/0.64 ! [W0,W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) % 0.60/0.64 & aNaturalNumber0(W2) ) % 0.60/0.64 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.60/0.64 % 0.60/0.64 fof(m_AddZero,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => ( sdtpldt0(W0,sz00) = W0 % 0.60/0.64 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mMulComm,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.60/0.64 % 0.60/0.64 fof(mMulAsso,axiom, % 0.60/0.64 ! [W0,W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) % 0.60/0.64 & aNaturalNumber0(W2) ) % 0.60/0.64 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.60/0.64 % 0.60/0.64 fof(m_MulUnit,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => ( sdtasdt0(W0,sz10) = W0 % 0.60/0.64 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(m_MulZero,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => ( sdtasdt0(W0,sz00) = sz00 % 0.60/0.64 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mAMDistr,axiom, % 0.60/0.64 ! [W0,W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) % 0.60/0.64 & aNaturalNumber0(W2) ) % 0.60/0.64 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.60/0.64 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mAddCanc,axiom, % 0.60/0.64 ! [W0,W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) % 0.60/0.64 & aNaturalNumber0(W2) ) % 0.60/0.64 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.60/0.64 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.60/0.64 => W1 = W2 ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mMulCanc,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => ( W0 != sz00 % 0.60/0.64 => ! [W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W1) % 0.60/0.64 & aNaturalNumber0(W2) ) % 0.60/0.64 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.60/0.64 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.60/0.64 => W1 = W2 ) ) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mZeroAdd,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => ( sdtpldt0(W0,W1) = sz00 % 0.60/0.64 => ( W0 = sz00 % 0.60/0.64 & W1 = sz00 ) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mZeroMul,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => ( sdtasdt0(W0,W1) = sz00 % 0.60/0.64 => ( W0 = sz00 % 0.60/0.64 | W1 = sz00 ) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mDefLE,definition, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => ( sdtlseqdt0(W0,W1) % 0.60/0.64 <=> ? [W2] : % 0.60/0.64 ( aNaturalNumber0(W2) % 0.60/0.64 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mDefDiff,definition, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => ( sdtlseqdt0(W0,W1) % 0.60/0.64 => ! [W2] : % 0.60/0.64 ( W2 = sdtmndt0(W1,W0) % 0.60/0.64 <=> ( aNaturalNumber0(W2) % 0.60/0.64 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mLERefl,axiom, % 0.60/0.64 ! [W0] : % 0.60/0.64 ( aNaturalNumber0(W0) % 0.60/0.64 => sdtlseqdt0(W0,W0) ) ). % 0.60/0.64 % 0.60/0.64 fof(mLEAsym,axiom, % 0.60/0.64 ! [W0,W1] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.64 & aNaturalNumber0(W1) ) % 0.60/0.64 => ( ( sdtlseqdt0(W0,W1) % 0.60/0.64 & sdtlseqdt0(W1,W0) ) % 0.60/0.64 => W0 = W1 ) ) ). % 0.60/0.64 % 0.60/0.64 fof(mLETran,axiom, % 0.60/0.64 ! [W0,W1,W2] : % 0.60/0.64 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( sdtlseqdt0(W0,W1) % 0.60/0.65 & sdtlseqdt0(W1,W2) ) % 0.60/0.65 => sdtlseqdt0(W0,W2) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mLETotal,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( sdtlseqdt0(W0,W1) % 0.60/0.65 | ( W1 != W0 % 0.60/0.65 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mMonAdd,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( ( W0 != W1 % 0.60/0.65 & sdtlseqdt0(W0,W1) ) % 0.60/0.65 => ! [W2] : % 0.60/0.65 ( aNaturalNumber0(W2) % 0.60/0.65 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.60/0.65 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.60/0.65 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.60/0.65 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mMonMul,axiom, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( W0 != sz00 % 0.60/0.65 & W1 != W2 % 0.60/0.65 & sdtlseqdt0(W1,W2) ) % 0.60/0.65 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.60/0.65 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.60/0.65 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.60/0.65 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mLENTr,axiom, % 0.60/0.65 ! [W0] : % 0.60/0.65 ( aNaturalNumber0(W0) % 0.60/0.65 => ( W0 = sz00 % 0.60/0.65 | W0 = sz10 % 0.60/0.65 | ( sz10 != W0 % 0.60/0.65 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mMonMul2,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( W0 != sz00 % 0.60/0.65 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mIH,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( iLess0(W0,W1) % 0.60/0.65 => $true ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mIH_03,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( ( W0 != W1 % 0.60/0.65 & sdtlseqdt0(W0,W1) ) % 0.60/0.65 => iLess0(W0,W1) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDefDiv,definition, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( doDivides0(W0,W1) % 0.60/0.65 <=> ? [W2] : % 0.60/0.65 ( aNaturalNumber0(W2) % 0.60/0.65 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDefQuot,definition, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( ( W0 != sz00 % 0.60/0.65 & doDivides0(W0,W1) ) % 0.60/0.65 => ! [W2] : % 0.60/0.65 ( W2 = sdtsldt0(W1,W0) % 0.60/0.65 <=> ( aNaturalNumber0(W2) % 0.60/0.65 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDivTrans,axiom, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( doDivides0(W0,W1) % 0.60/0.65 & doDivides0(W1,W2) ) % 0.60/0.65 => doDivides0(W0,W2) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDivSum,axiom, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( doDivides0(W0,W1) % 0.60/0.65 & doDivides0(W0,W2) ) % 0.60/0.65 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDivMin,axiom, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( doDivides0(W0,W1) % 0.60/0.65 & doDivides0(W0,sdtpldt0(W1,W2)) ) % 0.60/0.65 => doDivides0(W0,W2) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDivLE,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( ( doDivides0(W0,W1) % 0.60/0.65 & W1 != sz00 ) % 0.60/0.65 => sdtlseqdt0(W0,W1) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDivAsso,axiom, % 0.60/0.65 ! [W0,W1] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) ) % 0.60/0.65 => ( ( W0 != sz00 % 0.60/0.65 & doDivides0(W0,W1) ) % 0.60/0.65 => ! [W2] : % 0.60/0.65 ( aNaturalNumber0(W2) % 0.60/0.65 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mDefPrime,definition, % 0.60/0.65 ! [W0] : % 0.60/0.65 ( aNaturalNumber0(W0) % 0.60/0.65 => ( isPrime0(W0) % 0.60/0.65 <=> ( W0 != sz00 % 0.60/0.65 & W0 != sz10 % 0.60/0.65 & ! [W1] : % 0.60/0.65 ( ( aNaturalNumber0(W1) % 0.60/0.65 & doDivides0(W1,W0) ) % 0.60/0.65 => ( W1 = sz10 % 0.60/0.65 | W1 = W0 ) ) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mPrimDiv,axiom, % 0.60/0.65 ! [W0] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & W0 != sz00 % 0.60/0.65 & W0 != sz10 ) % 0.60/0.65 => ? [W1] : % 0.60/0.65 ( aNaturalNumber0(W1) % 0.60/0.65 & doDivides0(W1,W0) % 0.60/0.65 & isPrime0(W1) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(mPDP,axiom, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) ) % 0.60/0.65 => ( ( isPrime0(W2) % 0.60/0.65 & doDivides0(W2,sdtasdt0(W0,W1)) ) % 0.60/0.65 => ( doDivides0(W2,W0) % 0.60/0.65 | doDivides0(W2,W1) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(m__2987,hypothesis, % 0.60/0.65 ( aNaturalNumber0(xn) % 0.60/0.65 & aNaturalNumber0(xm) % 0.60/0.65 & aNaturalNumber0(xp) % 0.60/0.65 & xn != sz00 % 0.60/0.65 & xm != sz00 % 0.60/0.65 & xp != sz00 ) ). % 0.60/0.65 % 0.60/0.65 fof(m__2963,hypothesis, % 0.60/0.65 ! [W0,W1,W2] : % 0.60/0.65 ( ( aNaturalNumber0(W0) % 0.60/0.65 & aNaturalNumber0(W1) % 0.60/0.65 & aNaturalNumber0(W2) % 0.60/0.65 & W0 != sz00 % 0.60/0.65 & W1 != sz00 % 0.60/0.65 & W2 != sz00 ) % 0.60/0.65 => ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) % 0.60/0.65 => ( iLess0(W0,xn) % 0.60/0.65 => ~ isPrime0(W2) ) ) ) ). % 0.60/0.65 % 0.60/0.65 fof(m__3014,hypothesis, % 0.60/0.65 sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ). % 0.60/0.65 % 0.60/0.65 fof(m__3025,hypothesis, % 0.60/0.65 isPrime0(xp) ). % 0.60/0.65 % 0.60/0.65 fof(m__3046,hypothesis, % 0.60/0.65 ( doDivides0(xp,sdtasdt0(xn,xn)) % 0.60/0.65 & doDivides0(xp,xn) ) ). % 0.60/0.65 % 0.60/0.65 fof(m__3059,hypothesis, % 0.60/0.65 xq = sdtsldt0(xn,xp) ). % 0.60/0.65 % 0.60/0.65 fof(m__3082,hypothesis, % 0.60/0.65 sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ). % 0.60/0.65 % 0.60/0.65 fof(m__3124,hypothesis, % 0.60/0.65 ( xm != xn % 0.60/0.65 & sdtlseqdt0(xm,xn) ) ). % 0.60/0.65 % 0.60/0.65 fof(m__3161,hypothesis, % 0.60/0.65 ~ isPrime0(xp) ). % 0.60/0.65 % 0.60/0.65 fof(m__,conjecture, % 0.60/0.65 $false ). % 0.60/0.65 % 0.60/0.65 %------------------------------------------------------------------------------ % 0.60/0.65 %------------------------------------------- % 0.60/0.65 % Proof found % 0.60/0.65 % SZS status Theorem for theBenchmark % 0.60/0.65 % SZS output start Proof % 0.60/0.65 %ClaNum:109(EqnAxiom:25) % 0.60/0.65 %VarNum:450(SingletonVarNum:134) % 0.60/0.65 %MaxLitNum:9 % 0.60/0.65 %MaxfuncDepth:2 % 0.60/0.65 %SharedTerms:30 % 0.60/0.65 [26]P1(a1) % 0.60/0.65 [27]P1(a10) % 0.60/0.65 [28]P1(a11) % 0.60/0.65 [29]P1(a12) % 0.60/0.65 [30]P1(a13) % 0.60/0.65 [31]P2(a13) % 0.60/0.65 [33]P5(a12,a11) % 0.60/0.65 [34]P3(a13,a11) % 0.60/0.65 [38]~E(a1,a10) % 0.60/0.65 [39]~E(a1,a11) % 0.60/0.65 [40]~E(a1,a12) % 0.60/0.65 [41]~E(a12,a11) % 0.60/0.65 [42]~E(a1,a13) % 0.60/0.65 [43]~P2(a13) % 0.60/0.65 [32]E(f2(a11,a13),a14) % 0.60/0.65 [35]P3(a13,f3(a11,a11)) % 0.60/0.65 [36]E(f3(a13,f3(a14,a14)),f3(a12,a12)) % 0.60/0.65 [37]E(f3(a13,f3(a12,a12)),f3(a11,a11)) % 0.60/0.65 [54]~P1(x541)+P5(x541,x541) % 0.60/0.65 [46]~P1(x461)+E(f3(a1,x461),a1) % 0.60/0.65 [47]~P1(x471)+E(f3(x471,a1),a1) % 0.60/0.65 [48]~P1(x481)+E(f8(a1,x481),x481) % 0.60/0.65 [49]~P1(x491)+E(f3(a10,x491),x491) % 0.60/0.65 [50]~P1(x501)+E(f8(x501,a1),x501) % 0.60/0.65 [51]~P1(x511)+E(f3(x511,a10),x511) % 0.60/0.65 [44]~P1(x441)+~P2(x441)+~E(x441,a1) % 0.60/0.65 [45]~P1(x451)+~P2(x451)+~E(x451,a10) % 0.60/0.65 [65]~P1(x652)+~P1(x651)+E(f8(x651,x652),f8(x652,x651)) % 0.60/0.65 [66]~P1(x662)+~P1(x661)+E(f3(x661,x662),f3(x662,x661)) % 0.60/0.65 [68]~P1(x682)+~P1(x681)+P1(f8(x681,x682)) % 0.60/0.65 [69]~P1(x692)+~P1(x691)+P1(f3(x691,x692)) % 0.60/0.65 [56]~P1(x561)+E(x561,a10)+P5(a10,x561)+E(x561,a1) % 0.60/0.65 [52]~P1(x521)+E(x521,a10)+E(x521,a1)+P1(f4(x521)) % 0.60/0.65 [53]~P1(x531)+E(x531,a10)+E(x531,a1)+P2(f4(x531)) % 0.60/0.65 [59]~P1(x591)+E(x591,a10)+P3(f4(x591),x591)+E(x591,a1) % 0.60/0.65 [60]~E(x602,x601)+~P1(x601)+~P1(x602)+P5(x601,x602) % 0.60/0.65 [67]P5(x672,x671)+~P1(x671)+~P1(x672)+P5(x671,x672) % 0.60/0.65 [62]~P1(x622)+~P1(x621)+E(x621,a1)+~E(f8(x622,x621),a1) % 0.60/0.65 [63]~P1(x632)+~P1(x631)+E(x631,a1)+~E(f8(x631,x632),a1) % 0.60/0.65 [73]~P1(x732)+~P1(x731)+P5(x732,f3(x732,x731))+E(x731,a1) % 0.60/0.65 [79]~P1(x792)+~P1(x791)+~P5(x791,x792)+P1(f6(x791,x792)) % 0.60/0.65 [80]~P1(x802)+~P1(x801)+~P3(x801,x802)+P1(f7(x801,x802)) % 0.60/0.65 [87]~P1(x871)+~P1(x872)+~P3(x871,x872)+E(f3(x871,f7(x871,x872)),x872) % 0.60/0.65 [88]~P1(x882)+~P1(x881)+~P5(x881,x882)+E(f8(x881,f6(x881,x882)),x882) % 0.60/0.65 [97]~P1(x973)+~P1(x972)+~P1(x971)+E(f8(f8(x971,x972),x973),f8(x971,f8(x972,x973))) % 0.60/0.65 [98]~P1(x983)+~P1(x982)+~P1(x981)+E(f3(f3(x981,x982),x983),f3(x981,f3(x982,x983))) % 0.60/0.65 [107]~P1(x1073)+~P1(x1072)+~P1(x1071)+E(f8(f3(x1071,x1072),f3(x1071,x1073)),f3(x1071,f8(x1072,x1073))) % 0.60/0.65 [108]~P1(x1082)+~P1(x1083)+~P1(x1081)+E(f8(f3(x1081,x1082),f3(x1083,x1082)),f3(f8(x1081,x1083),x1082)) % 0.60/0.65 [55]P2(x551)+~P1(x551)+E(x551,a10)+E(x551,a1)+~E(f5(x551),a10) % 0.60/0.65 [57]P2(x571)+~P1(x571)+E(x571,a10)+~E(f5(x571),x571)+E(x571,a1) % 0.60/0.65 [58]P2(x581)+~P1(x581)+E(x581,a10)+E(x581,a1)+P1(f5(x581)) % 0.60/0.65 [61]P2(x611)+~P1(x611)+E(x611,a10)+P3(f5(x611),x611)+E(x611,a1) % 0.60/0.65 [71]~P1(x711)+~P1(x712)+~P3(x712,x711)+P5(x712,x711)+E(x711,a1) % 0.60/0.65 [72]P4(x721,x722)+~P1(x722)+~P1(x721)+~P5(x721,x722)+E(x721,x722) % 0.60/0.65 [76]~P1(x762)+~P1(x761)+~P5(x762,x761)+~P5(x761,x762)+E(x761,x762) % 0.60/0.65 [64]~P1(x641)+~P1(x642)+E(x641,a1)+E(x642,a1)+~E(f3(x642,x641),a1) % 0.60/0.65 [74]~P1(x741)+~P1(x742)+~P1(x743)+P3(x741,x742)+~E(x742,f3(x741,x743)) % 0.60/0.65 [75]~P1(x752)+~P1(x751)+~P1(x753)+P5(x751,x752)+~E(f8(x751,x753),x752) % 0.60/0.65 [77]~P1(x773)+~P1(x772)+~P5(x773,x772)+P1(x771)+~E(x771,f9(x772,x773)) % 0.60/0.65 [81]~P1(x812)+~P1(x811)+~P1(x813)+E(x811,x812)+~E(f8(x813,x811),f8(x813,x812)) % 0.60/0.65 [82]~P1(x822)+~P1(x823)+~P1(x821)+E(x821,x822)+~E(f8(x821,x823),f8(x822,x823)) % 0.60/0.65 [85]~P1(x853)+~P1(x851)+~P5(x851,x853)+~E(x852,f9(x853,x851))+E(f8(x851,x852),x853) % 0.60/0.65 [70]~P1(x702)+~P1(x701)+~P2(x702)+~P3(x701,x702)+E(x701,x702)+E(x701,a10) % 0.60/0.65 [89]~P1(x892)+~P1(x891)+~P5(x893,x892)+~P5(x891,x893)+P5(x891,x892)+~P1(x893) % 0.60/0.65 [90]~P1(x902)+~P1(x901)+~P3(x903,x902)+~P3(x901,x903)+P3(x901,x902)+~P1(x903) % 0.60/0.65 [78]~P1(x781)+~P1(x783)+~P3(x781,x783)+P1(x782)+E(x781,a1)+~E(x782,f2(x783,x781)) % 0.60/0.65 [83]~P1(x832)+~P1(x831)+~P1(x833)+E(x831,x832)+~E(f3(x833,x831),f3(x833,x832))+E(x833,a1) % 0.60/0.65 [84]~P1(x842)+~P1(x843)+~P1(x841)+E(x841,x842)+~E(f3(x841,x843),f3(x842,x843))+E(x843,a1) % 0.60/0.65 [86]~P1(x861)+~P1(x862)+~P3(x861,x862)+~E(x863,f2(x862,x861))+E(x861,a1)+E(x862,f3(x861,x863)) % 0.60/0.65 [91]~P1(x912)+~P1(x913)+~P1(x911)+~P5(x913,x912)+~E(f8(x913,x911),x912)+E(x911,f9(x912,x913)) % 0.60/0.65 [99]~P1(x993)+~P1(x992)+~P1(x991)+~P3(x991,x993)+~P3(x991,x992)+P3(x991,f8(x992,x993)) % 0.60/0.65 [100]~P1(x1002)+~P1(x1001)+~P1(x1003)+~P5(x1001,x1002)+E(x1001,x1002)+P5(f8(x1003,x1001),f8(x1003,x1002)) % 0.60/0.65 [101]~P1(x1012)+~P1(x1013)+~P1(x1011)+~P5(x1011,x1012)+E(x1011,x1012)+P5(f8(x1011,x1013),f8(x1012,x1013)) % 0.60/0.65 [105]~P1(x1052)+~P1(x1051)+~P3(x1051,x1053)+P3(x1051,x1052)+~P1(x1053)+~P3(x1051,f8(x1053,x1052)) % 0.60/0.65 [106]~P1(x1062)+~P1(x1063)+~P1(x1061)+~P3(x1061,x1063)+E(x1061,a1)+E(f3(x1062,f2(x1063,x1061)),f2(f3(x1062,x1063),x1061)) % 0.60/0.65 [92]~P1(x921)+~P1(x923)+~P1(x922)+~P3(x921,x923)+~E(x923,f3(x921,x922))+E(x921,a1)+E(x922,f2(x923,x921)) % 0.60/0.65 [102]~P1(x1022)+~P1(x1021)+~P1(x1023)+~P5(x1021,x1022)+E(x1021,x1022)+P5(f3(x1023,x1021),f3(x1023,x1022))+E(x1023,a1) % 0.60/0.65 [103]~P1(x1032)+~P1(x1033)+~P1(x1031)+~P5(x1031,x1032)+E(x1031,x1032)+P5(f3(x1031,x1033),f3(x1032,x1033))+E(x1033,a1) % 0.60/0.65 [104]~P1(x1041)+~P1(x1042)+~P1(x1043)+~P2(x1041)+P3(x1041,x1042)+P3(x1041,x1043)+~P3(x1041,f3(x1043,x1042)) % 0.60/0.65 [109]~P1(x1091)+~P1(x1092)+~P1(x1093)+~P2(x1091)+~P4(x1093,a11)+E(x1091,a1)+E(x1092,a1)+E(x1093,a1)+~E(f3(x1091,f3(x1092,x1092)),f3(x1093,x1093)) % 0.60/0.65 %EqnAxiom % 0.60/0.65 [1]E(x11,x11) % 0.60/0.65 [2]E(x22,x21)+~E(x21,x22) % 0.60/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.60/0.65 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.60/0.65 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.60/0.65 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.60/0.65 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.60/0.65 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 0.60/0.65 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 0.60/0.65 [10]~E(x101,x102)+E(f7(x101,x103),f7(x102,x103)) % 0.60/0.65 [11]~E(x111,x112)+E(f7(x113,x111),f7(x113,x112)) % 0.60/0.65 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123)) % 0.60/0.65 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132)) % 0.60/0.65 [14]~E(x141,x142)+E(f9(x141,x143),f9(x142,x143)) % 0.60/0.65 [15]~E(x151,x152)+E(f9(x153,x151),f9(x153,x152)) % 0.60/0.65 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 0.60/0.65 [17]~E(x171,x172)+E(f5(x171),f5(x172)) % 0.60/0.65 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.60/0.65 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193) % 0.60/0.65 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201) % 0.60/0.65 [21]~P2(x211)+P2(x212)+~E(x211,x212) % 0.60/0.65 [22]P3(x222,x223)+~E(x221,x222)+~P3(x221,x223) % 0.60/0.65 [23]P3(x233,x232)+~E(x231,x232)+~P3(x233,x231) % 0.60/0.65 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.60/0.65 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.60/0.65 % 0.60/0.65 %------------------------------------------- % 0.60/0.65 cnf(126,plain, % 0.60/0.65 ($false), % 0.60/0.65 inference(scs_inference,[],[31,43]), % 0.60/0.65 ['proof']). % 0.60/0.65 % SZS output end Proof % 0.60/0.65 % Total time :0.010000s %------------------------------------------------------------------------------