%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM520+1 : 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 : n020.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 12:24:48 EDT 2024 % Result : Theorem 0.53s 0.66s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM520+1 : TPTP v8.2.0. Released v4.0.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n020.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sat Jun 22 19:32:39 EDT 2024 % 0.11/0.33 % CPUTime : % 0.18/0.57 start to proof:theBenchmark % 0.53/0.64 %------------------------------------------- % 0.53/0.64 % File :CSE---1.7 % 0.53/0.64 % Problem :theBenchmark % 0.53/0.64 % Transform :cnf % 0.53/0.64 % Format :tptp:raw % 0.53/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.64 % 0.53/0.64 % Result :Theorem 0.000000s % 0.53/0.64 % Output :CNFRefutation 0.000000s % 0.53/0.64 %------------------------------------------- % 0.53/0.64 %------------------------------------------------------------------------------ % 0.53/0.64 % File : NUM520+1 : TPTP v8.2.0. Released v4.0.0. % 0.53/0.64 % Domain : Number Theory % 0.53/0.64 % Problem : Square root of a prime is irrational 14_03_04, 00 expansion % 0.53/0.64 % Version : Especial. % 0.53/0.64 % English : % 0.53/0.64 % 0.53/0.64 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.53/0.64 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.53/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.53/0.65 % Source : [Pas08] % 0.53/0.65 % Names : primes_14_03_04.00 [Pas08] % 0.53/0.65 % 0.53/0.65 % Status : ContradictoryAxioms % 0.53/0.65 % Rating : 0.17 v8.2.0, 0.11 v7.5.0, 0.09 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 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.1, 0.57 v4.0.0 % 0.53/0.65 % Syntax : Number of formulae : 48 ( 4 unt; 5 def) % 0.53/0.65 % Number of atoms : 209 ( 63 equ) % 0.53/0.65 % Maximal formula atoms : 10 ( 4 avg) % 0.53/0.65 % Number of connectives : 189 ( 28 ~; 10 |; 84 &) % 0.53/0.65 % ( 5 <=>; 62 =>; 0 <=; 0 <~>) % 0.53/0.65 % Maximal formula depth : 11 ( 6 avg) % 0.53/0.65 % Maximal term depth : 3 ( 1 avg) % 0.53/0.65 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.53/0.65 % Number of functors : 10 ( 10 usr; 6 con; 0-2 aty) % 0.53/0.65 % Number of variables : 85 ( 82 !; 3 ?) % 0.53/0.65 % SPC : FOF_CAX_RFO_SEQ % 0.53/0.65 % 0.53/0.65 % Comments : Problem generated by the SAD system [VLP07] % 0.53/0.65 %------------------------------------------------------------------------------ % 0.53/0.65 fof(mNatSort,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => $true ) ). % 0.53/0.65 % 0.53/0.65 fof(mSortsC,axiom, % 0.53/0.65 aNaturalNumber0(sz00) ). % 0.53/0.65 % 0.53/0.65 fof(mSortsC_01,axiom, % 0.53/0.65 ( aNaturalNumber0(sz10) % 0.53/0.65 & sz10 != sz00 ) ). % 0.53/0.65 % 0.53/0.65 fof(mSortsB,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.53/0.65 % 0.53/0.65 fof(mSortsB_02,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.53/0.65 % 0.53/0.65 fof(mAddComm,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.53/0.65 % 0.53/0.65 fof(mAddAsso,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.53/0.65 % 0.53/0.65 fof(m_AddZero,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => ( sdtpldt0(W0,sz00) = W0 % 0.53/0.65 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMulComm,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMulAsso,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.53/0.65 % 0.53/0.65 fof(m_MulUnit,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => ( sdtasdt0(W0,sz10) = W0 % 0.53/0.65 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(m_MulZero,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => ( sdtasdt0(W0,sz00) = sz00 % 0.53/0.65 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mAMDistr,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.53/0.65 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mAddCanc,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.53/0.65 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.53/0.65 => W1 = W2 ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMulCanc,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => ( W0 != sz00 % 0.53/0.65 => ! [W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.53/0.65 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.53/0.65 => W1 = W2 ) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mZeroAdd,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( sdtpldt0(W0,W1) = sz00 % 0.53/0.65 => ( W0 = sz00 % 0.53/0.65 & W1 = sz00 ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mZeroMul,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( sdtasdt0(W0,W1) = sz00 % 0.53/0.65 => ( W0 = sz00 % 0.53/0.65 | W1 = sz00 ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDefLE,definition, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( sdtlseqdt0(W0,W1) % 0.53/0.65 <=> ? [W2] : % 0.53/0.65 ( aNaturalNumber0(W2) % 0.53/0.65 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDefDiff,definition, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( sdtlseqdt0(W0,W1) % 0.53/0.65 => ! [W2] : % 0.53/0.65 ( W2 = sdtmndt0(W1,W0) % 0.53/0.65 <=> ( aNaturalNumber0(W2) % 0.53/0.65 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mLERefl,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => sdtlseqdt0(W0,W0) ) ). % 0.53/0.65 % 0.53/0.65 fof(mLEAsym,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.65 & sdtlseqdt0(W1,W0) ) % 0.53/0.65 => W0 = W1 ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mLETran,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.65 & sdtlseqdt0(W1,W2) ) % 0.53/0.65 => sdtlseqdt0(W0,W2) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mLETotal,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( sdtlseqdt0(W0,W1) % 0.53/0.65 | ( W1 != W0 % 0.53/0.65 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMonAdd,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( ( W0 != W1 % 0.53/0.65 & sdtlseqdt0(W0,W1) ) % 0.53/0.65 => ! [W2] : % 0.53/0.65 ( aNaturalNumber0(W2) % 0.53/0.65 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.53/0.65 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.53/0.65 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.53/0.65 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMonMul,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( ( W0 != sz00 % 0.53/0.65 & W1 != W2 % 0.53/0.65 & sdtlseqdt0(W1,W2) ) % 0.53/0.65 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.53/0.65 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.53/0.65 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.53/0.65 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mLENTr,axiom, % 0.53/0.65 ! [W0] : % 0.53/0.65 ( aNaturalNumber0(W0) % 0.53/0.65 => ( W0 = sz00 % 0.53/0.65 | W0 = sz10 % 0.53/0.65 | ( sz10 != W0 % 0.53/0.65 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mMonMul2,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( W0 != sz00 % 0.53/0.65 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mIH,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( iLess0(W0,W1) % 0.53/0.65 => $true ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mIH_03,axiom, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( ( W0 != W1 % 0.53/0.65 & sdtlseqdt0(W0,W1) ) % 0.53/0.65 => iLess0(W0,W1) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDefDiv,definition, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( doDivides0(W0,W1) % 0.53/0.65 <=> ? [W2] : % 0.53/0.65 ( aNaturalNumber0(W2) % 0.53/0.65 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDefQuot,definition, % 0.53/0.65 ! [W0,W1] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) ) % 0.53/0.65 => ( ( W0 != sz00 % 0.53/0.65 & doDivides0(W0,W1) ) % 0.53/0.65 => ! [W2] : % 0.53/0.65 ( W2 = sdtsldt0(W1,W0) % 0.53/0.65 <=> ( aNaturalNumber0(W2) % 0.53/0.65 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDivTrans,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.65 ( ( aNaturalNumber0(W0) % 0.53/0.65 & aNaturalNumber0(W1) % 0.53/0.65 & aNaturalNumber0(W2) ) % 0.53/0.65 => ( ( doDivides0(W0,W1) % 0.53/0.65 & doDivides0(W1,W2) ) % 0.53/0.65 => doDivides0(W0,W2) ) ) ). % 0.53/0.65 % 0.53/0.65 fof(mDivSum,axiom, % 0.53/0.65 ! [W0,W1,W2] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & aNaturalNumber0(W1) % 0.53/0.66 & aNaturalNumber0(W2) ) % 0.53/0.66 => ( ( doDivides0(W0,W1) % 0.53/0.66 & doDivides0(W0,W2) ) % 0.53/0.66 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(mDivMin,axiom, % 0.53/0.66 ! [W0,W1,W2] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & aNaturalNumber0(W1) % 0.53/0.66 & aNaturalNumber0(W2) ) % 0.53/0.66 => ( ( doDivides0(W0,W1) % 0.53/0.66 & doDivides0(W0,sdtpldt0(W1,W2)) ) % 0.53/0.66 => doDivides0(W0,W2) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(mDivLE,axiom, % 0.53/0.66 ! [W0,W1] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & aNaturalNumber0(W1) ) % 0.53/0.66 => ( ( doDivides0(W0,W1) % 0.53/0.66 & W1 != sz00 ) % 0.53/0.66 => sdtlseqdt0(W0,W1) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(mDivAsso,axiom, % 0.53/0.66 ! [W0,W1] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & aNaturalNumber0(W1) ) % 0.53/0.66 => ( ( W0 != sz00 % 0.53/0.66 & doDivides0(W0,W1) ) % 0.53/0.66 => ! [W2] : % 0.53/0.66 ( aNaturalNumber0(W2) % 0.53/0.66 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(mDefPrime,definition, % 0.53/0.66 ! [W0] : % 0.53/0.66 ( aNaturalNumber0(W0) % 0.53/0.66 => ( isPrime0(W0) % 0.53/0.66 <=> ( W0 != sz00 % 0.53/0.66 & W0 != sz10 % 0.53/0.66 & ! [W1] : % 0.53/0.66 ( ( aNaturalNumber0(W1) % 0.53/0.66 & doDivides0(W1,W0) ) % 0.53/0.66 => ( W1 = sz10 % 0.53/0.66 | W1 = W0 ) ) ) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(mPrimDiv,axiom, % 0.53/0.66 ! [W0] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & W0 != sz00 % 0.53/0.66 & W0 != sz10 ) % 0.53/0.66 => ? [W1] : % 0.53/0.66 ( aNaturalNumber0(W1) % 0.53/0.66 & doDivides0(W1,W0) % 0.53/0.66 & isPrime0(W1) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(m__1837,hypothesis, % 0.53/0.66 ( aNaturalNumber0(xn) % 0.53/0.66 & aNaturalNumber0(xm) % 0.53/0.66 & aNaturalNumber0(xp) ) ). % 0.53/0.66 % 0.53/0.66 fof(m__1799,hypothesis, % 0.53/0.66 ! [W0,W1,W2] : % 0.53/0.66 ( ( aNaturalNumber0(W0) % 0.53/0.66 & aNaturalNumber0(W1) % 0.53/0.66 & aNaturalNumber0(W2) ) % 0.53/0.66 => ( ( isPrime0(W2) % 0.53/0.66 & doDivides0(W2,sdtasdt0(W0,W1)) ) % 0.53/0.66 => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) % 0.53/0.66 => ( doDivides0(W2,W0) % 0.53/0.66 | doDivides0(W2,W1) ) ) ) ) ). % 0.53/0.66 % 0.53/0.66 fof(m__1860,hypothesis, % 0.53/0.66 ( isPrime0(xp) % 0.53/0.66 & doDivides0(xp,sdtasdt0(xn,xm)) ) ). % 0.53/0.66 % 0.53/0.66 fof(m__1870,hypothesis, % 0.53/0.66 ~ sdtlseqdt0(xp,xn) ). % 0.53/0.66 % 0.53/0.66 fof(m__2075,hypothesis, % 0.53/0.66 ~ sdtlseqdt0(xp,xm) ). % 0.53/0.66 % 0.53/0.66 fof(m__2287,hypothesis, % 0.53/0.66 ( xn != xp % 0.53/0.66 & sdtlseqdt0(xn,xp) % 0.53/0.66 & xm != xp % 0.53/0.66 & sdtlseqdt0(xm,xp) ) ). % 0.53/0.66 % 0.53/0.66 fof(m__2306,hypothesis, % 0.53/0.66 xk = sdtsldt0(sdtasdt0(xn,xm),xp) ). % 0.53/0.66 % 0.53/0.66 fof(m__2315,hypothesis, % 0.53/0.66 ~ ( xk = sz00 % 0.53/0.66 | xk = sz10 ) ). % 0.53/0.66 % 0.53/0.66 fof(m__2327,hypothesis, % 0.53/0.66 ~ ( xk != sz00 % 0.53/0.66 & xk != sz10 ) ). % 0.53/0.66 % 0.53/0.66 fof(m__,conjecture, % 0.53/0.66 ( doDivides0(xp,xn) % 0.53/0.66 | doDivides0(xp,xm) ) ). % 0.53/0.66 % 0.53/0.66 %------------------------------------------------------------------------------ % 0.53/0.66 %------------------------------------------- % 0.53/0.66 % Proof found % 0.53/0.66 % SZS status Theorem for theBenchmark % 0.53/0.66 % SZS output start Proof % 0.53/0.66 %ClaNum:110(EqnAxiom:25) % 0.53/0.66 %VarNum:440(SingletonVarNum:131) % 0.53/0.66 %MaxLitNum:8 % 0.53/0.66 %MaxfuncDepth:2 % 0.53/0.66 %SharedTerms:31 % 0.53/0.66 %goalClause: 43 44 % 0.53/0.66 %singleGoalClaCount:2 % 0.53/0.66 [26]P1(a1) % 0.53/0.66 [27]P1(a10) % 0.53/0.66 [28]P1(a11) % 0.53/0.66 [29]P1(a12) % 0.53/0.66 [30]P1(a14) % 0.53/0.66 [31]P2(a14) % 0.53/0.66 [32]P5(a11,a14) % 0.53/0.66 [33]P5(a12,a14) % 0.53/0.66 [36]~E(a1,a10) % 0.53/0.66 [37]~E(a14,a11) % 0.53/0.66 [38]~E(a14,a12) % 0.53/0.66 [39]~E(a1,a13) % 0.53/0.66 [40]~E(a13,a10) % 0.53/0.66 [41]~P5(a14,a11) % 0.53/0.66 [42]~P5(a14,a12) % 0.53/0.66 [43]~P3(a14,a11) % 0.53/0.66 [44]~P3(a14,a12) % 0.53/0.66 [35]P3(a14,f2(a11,a12)) % 0.53/0.66 [34]E(f7(f2(a11,a12),a14),a13) % 0.53/0.66 [45]E(a1,a13)+E(a13,a10) % 0.53/0.66 [56]~P1(x561)+P5(x561,x561) % 0.53/0.66 [48]~P1(x481)+E(f2(a1,x481),a1) % 0.53/0.66 [49]~P1(x491)+E(f2(x491,a1),a1) % 0.53/0.66 [50]~P1(x501)+E(f8(a1,x501),x501) % 0.53/0.66 [51]~P1(x511)+E(f2(a10,x511),x511) % 0.53/0.66 [52]~P1(x521)+E(f8(x521,a1),x521) % 0.53/0.66 [53]~P1(x531)+E(f2(x531,a10),x531) % 0.53/0.66 [46]~P1(x461)+~P2(x461)+~E(x461,a1) % 0.53/0.66 [47]~P1(x471)+~P2(x471)+~E(x471,a10) % 0.53/0.66 [67]~P1(x672)+~P1(x671)+E(f8(x671,x672),f8(x672,x671)) % 0.53/0.66 [68]~P1(x682)+~P1(x681)+E(f2(x681,x682),f2(x682,x681)) % 0.53/0.66 [70]~P1(x702)+~P1(x701)+P1(f8(x701,x702)) % 0.53/0.66 [71]~P1(x712)+~P1(x711)+P1(f2(x711,x712)) % 0.53/0.66 [58]~P1(x581)+E(x581,a10)+P5(a10,x581)+E(x581,a1) % 0.53/0.66 [54]~P1(x541)+E(x541,a10)+E(x541,a1)+P1(f3(x541)) % 0.53/0.66 [55]~P1(x551)+E(x551,a10)+E(x551,a1)+P2(f3(x551)) % 0.53/0.66 [61]~P1(x611)+E(x611,a10)+P3(f3(x611),x611)+E(x611,a1) % 0.53/0.66 [62]~E(x622,x621)+~P1(x621)+~P1(x622)+P5(x621,x622) % 0.53/0.66 [69]P5(x692,x691)+~P1(x691)+~P1(x692)+P5(x691,x692) % 0.53/0.66 [64]~P1(x642)+~P1(x641)+E(x641,a1)+~E(f8(x642,x641),a1) % 0.53/0.66 [65]~P1(x652)+~P1(x651)+E(x651,a1)+~E(f8(x651,x652),a1) % 0.53/0.66 [75]~P1(x752)+~P1(x751)+P5(x752,f2(x752,x751))+E(x751,a1) % 0.53/0.66 [81]~P1(x812)+~P1(x811)+~P5(x811,x812)+P1(f5(x811,x812)) % 0.53/0.66 [82]~P1(x822)+~P1(x821)+~P3(x821,x822)+P1(f6(x821,x822)) % 0.53/0.66 [89]~P1(x891)+~P1(x892)+~P3(x891,x892)+E(f2(x891,f6(x891,x892)),x892) % 0.53/0.66 [90]~P1(x902)+~P1(x901)+~P5(x901,x902)+E(f8(x901,f5(x901,x902)),x902) % 0.53/0.66 [99]~P1(x993)+~P1(x992)+~P1(x991)+E(f8(f8(x991,x992),x993),f8(x991,f8(x992,x993))) % 0.53/0.66 [100]~P1(x1003)+~P1(x1002)+~P1(x1001)+E(f2(f2(x1001,x1002),x1003),f2(x1001,f2(x1002,x1003))) % 0.53/0.66 [108]~P1(x1083)+~P1(x1082)+~P1(x1081)+E(f8(f2(x1081,x1082),f2(x1081,x1083)),f2(x1081,f8(x1082,x1083))) % 0.53/0.66 [109]~P1(x1092)+~P1(x1093)+~P1(x1091)+E(f8(f2(x1091,x1092),f2(x1093,x1092)),f2(f8(x1091,x1093),x1092)) % 0.53/0.66 [57]P2(x571)+~P1(x571)+E(x571,a10)+E(x571,a1)+~E(f4(x571),a10) % 0.53/0.66 [59]P2(x591)+~P1(x591)+E(x591,a10)+~E(f4(x591),x591)+E(x591,a1) % 0.53/0.66 [60]P2(x601)+~P1(x601)+E(x601,a10)+E(x601,a1)+P1(f4(x601)) % 0.53/0.66 [63]P2(x631)+~P1(x631)+E(x631,a10)+P3(f4(x631),x631)+E(x631,a1) % 0.53/0.66 [73]~P1(x731)+~P1(x732)+~P3(x732,x731)+P5(x732,x731)+E(x731,a1) % 0.53/0.66 [74]P4(x741,x742)+~P1(x742)+~P1(x741)+~P5(x741,x742)+E(x741,x742) % 0.53/0.66 [78]~P1(x782)+~P1(x781)+~P5(x782,x781)+~P5(x781,x782)+E(x781,x782) % 0.53/0.66 [66]~P1(x661)+~P1(x662)+E(x661,a1)+E(x662,a1)+~E(f2(x662,x661),a1) % 0.53/0.66 [76]~P1(x761)+~P1(x762)+~P1(x763)+P3(x761,x762)+~E(x762,f2(x761,x763)) % 0.53/0.66 [77]~P1(x772)+~P1(x771)+~P1(x773)+P5(x771,x772)+~E(f8(x771,x773),x772) % 0.53/0.66 [79]~P1(x793)+~P1(x792)+~P5(x793,x792)+P1(x791)+~E(x791,f9(x792,x793)) % 0.53/0.66 [83]~P1(x832)+~P1(x831)+~P1(x833)+E(x831,x832)+~E(f8(x833,x831),f8(x833,x832)) % 0.53/0.66 [84]~P1(x842)+~P1(x843)+~P1(x841)+E(x841,x842)+~E(f8(x841,x843),f8(x842,x843)) % 0.53/0.66 [87]~P1(x873)+~P1(x871)+~P5(x871,x873)+~E(x872,f9(x873,x871))+E(f8(x871,x872),x873) % 0.53/0.66 [72]~P1(x722)+~P1(x721)+~P2(x722)+~P3(x721,x722)+E(x721,x722)+E(x721,a10) % 0.53/0.66 [91]~P1(x912)+~P1(x911)+~P5(x913,x912)+~P5(x911,x913)+P5(x911,x912)+~P1(x913) % 0.53/0.66 [92]~P1(x922)+~P1(x921)+~P3(x923,x922)+~P3(x921,x923)+P3(x921,x922)+~P1(x923) % 0.53/0.66 [80]~P1(x801)+~P1(x803)+~P3(x801,x803)+P1(x802)+E(x801,a1)+~E(x802,f7(x803,x801)) % 0.53/0.66 [85]~P1(x852)+~P1(x851)+~P1(x853)+E(x851,x852)+~E(f2(x853,x851),f2(x853,x852))+E(x853,a1) % 0.53/0.66 [86]~P1(x862)+~P1(x863)+~P1(x861)+E(x861,x862)+~E(f2(x861,x863),f2(x862,x863))+E(x863,a1) % 0.53/0.66 [88]~P1(x881)+~P1(x882)+~P3(x881,x882)+~E(x883,f7(x882,x881))+E(x881,a1)+E(x882,f2(x881,x883)) % 0.53/0.66 [93]~P1(x932)+~P1(x933)+~P1(x931)+~P5(x933,x932)+~E(f8(x933,x931),x932)+E(x931,f9(x932,x933)) % 0.53/0.66 [101]~P1(x1013)+~P1(x1012)+~P1(x1011)+~P3(x1011,x1013)+~P3(x1011,x1012)+P3(x1011,f8(x1012,x1013)) % 0.53/0.66 [102]~P1(x1022)+~P1(x1021)+~P1(x1023)+~P5(x1021,x1022)+E(x1021,x1022)+P5(f8(x1023,x1021),f8(x1023,x1022)) % 0.53/0.66 [103]~P1(x1032)+~P1(x1033)+~P1(x1031)+~P5(x1031,x1032)+E(x1031,x1032)+P5(f8(x1031,x1033),f8(x1032,x1033)) % 0.53/0.66 [106]~P1(x1062)+~P1(x1061)+~P3(x1061,x1063)+P3(x1061,x1062)+~P1(x1063)+~P3(x1061,f8(x1063,x1062)) % 0.53/0.66 [107]~P1(x1072)+~P1(x1073)+~P1(x1071)+~P3(x1071,x1073)+E(x1071,a1)+E(f7(f2(x1072,x1073),x1071),f2(x1072,f7(x1073,x1071))) % 0.53/0.66 [94]~P1(x941)+~P1(x943)+~P1(x942)+~P3(x941,x943)+~E(x943,f2(x941,x942))+E(x941,a1)+E(x942,f7(x943,x941)) % 0.53/0.66 [104]~P1(x1042)+~P1(x1041)+~P1(x1043)+~P5(x1041,x1042)+E(x1041,x1042)+P5(f2(x1043,x1041),f2(x1043,x1042))+E(x1043,a1) % 0.53/0.66 [105]~P1(x1052)+~P1(x1053)+~P1(x1051)+~P5(x1051,x1052)+E(x1051,x1052)+P5(f2(x1051,x1053),f2(x1052,x1053))+E(x1053,a1) % 0.53/0.66 [110]~P1(x1101)+~P1(x1102)+~P1(x1103)+~P2(x1101)+P3(x1101,x1102)+P3(x1101,x1103)+~P3(x1101,f2(x1103,x1102))+~P4(f8(f8(x1103,x1102),x1101),f8(f8(a11,a12),a14)) % 0.53/0.66 %EqnAxiom % 0.53/0.66 [1]E(x11,x11) % 0.53/0.66 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.66 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.53/0.66 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.53/0.66 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 0.53/0.66 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 0.53/0.66 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 0.53/0.66 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 0.53/0.66 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.53/0.66 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.53/0.66 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123)) % 0.53/0.66 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132)) % 0.53/0.66 [14]~E(x141,x142)+E(f6(x141,x143),f6(x142,x143)) % 0.53/0.66 [15]~E(x151,x152)+E(f6(x153,x151),f6(x153,x152)) % 0.53/0.66 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 0.53/0.66 [17]~E(x171,x172)+E(f3(x171),f3(x172)) % 0.53/0.66 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.53/0.66 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193) % 0.53/0.66 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201) % 0.53/0.66 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213) % 0.53/0.66 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221) % 0.53/0.66 [23]~P2(x231)+P2(x232)+~E(x231,x232) % 0.53/0.66 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.53/0.66 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.53/0.66 % 0.53/0.66 %------------------------------------------- % 0.53/0.66 cnf(126,plain, % 0.53/0.66 ($false), % 0.53/0.66 inference(scs_inference,[],[39,40,45]), % 0.53/0.66 ['proof']). % 0.53/0.66 % SZS output end Proof % 0.53/0.66 % Total time :0.000000s %------------------------------------------------------------------------------