%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM519+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 : 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 12:24:47 EDT 2024 % Result : Theorem 0.57s 0.69s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : NUM519+1 : TPTP v8.2.0. Released v4.0.0. % 0.09/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n020.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sun Jun 23 01:27:09 EDT 2024 % 0.14/0.36 % CPUTime : % 0.56/0.61 start to proof:theBenchmark % 0.57/0.67 %------------------------------------------- % 0.57/0.67 % File :CSE---1.7 % 0.57/0.67 % Problem :theBenchmark % 0.57/0.67 % Transform :cnf % 0.57/0.67 % Format :tptp:raw % 0.57/0.67 % Command :java -jar mcs_scs.jar %d %s % 0.57/0.67 % 0.57/0.67 % Result :Theorem 0.010000s % 0.57/0.67 % Output :CNFRefutation 0.010000s % 0.57/0.67 %------------------------------------------- % 0.57/0.68 %------------------------------------------------------------------------------ % 0.57/0.68 % File : NUM519+1 : TPTP v8.2.0. Released v4.0.0. % 0.57/0.68 % Domain : Number Theory % 0.57/0.68 % Problem : Square root of a prime is irrational 14_03_03_07, 00 expansion % 0.57/0.68 % Version : Especial. % 0.57/0.68 % English : % 0.57/0.68 % 0.57/0.68 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.57/0.68 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.57/0.68 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.57/0.68 % Source : [Pas08] % 0.57/0.68 % Names : primes_14_03_03_07.00 [Pas08] % 0.57/0.68 % 0.57/0.68 % Status : ContradictoryAxioms % 0.57/0.68 % Rating : 0.19 v8.2.0, 0.14 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, 0.21 v4.1.0, 0.26 v4.0.1, 0.57 v4.0.0 % 0.57/0.68 % Syntax : Number of formulae : 54 ( 6 unt; 5 def) % 0.57/0.68 % Number of atoms : 220 ( 64 equ) % 0.57/0.68 % Maximal formula atoms : 10 ( 4 avg) % 0.57/0.68 % Number of connectives : 196 ( 30 ~; 11 |; 88 &) % 0.57/0.68 % ( 5 <=>; 62 =>; 0 <=; 0 <~>) % 0.57/0.68 % Maximal formula depth : 11 ( 5 avg) % 0.57/0.68 % Maximal term depth : 3 ( 1 avg) % 0.57/0.68 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.57/0.68 % Number of functors : 11 ( 11 usr; 7 con; 0-2 aty) % 0.57/0.68 % Number of variables : 85 ( 82 !; 3 ?) % 0.57/0.68 % SPC : FOF_CAX_RFO_SEQ % 0.57/0.68 % 0.57/0.68 % Comments : Problem generated by the SAD system [VLP07] % 0.57/0.68 %------------------------------------------------------------------------------ % 0.57/0.68 fof(mNatSort,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => $true ) ). % 0.57/0.68 % 0.57/0.68 fof(mSortsC,axiom, % 0.57/0.68 aNaturalNumber0(sz00) ). % 0.57/0.68 % 0.57/0.68 fof(mSortsC_01,axiom, % 0.57/0.68 ( aNaturalNumber0(sz10) % 0.57/0.68 & sz10 != sz00 ) ). % 0.57/0.68 % 0.57/0.68 fof(mSortsB,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.57/0.68 % 0.57/0.68 fof(mSortsB_02,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.57/0.68 % 0.57/0.68 fof(mAddComm,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.57/0.68 % 0.57/0.68 fof(mAddAsso,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.57/0.68 % 0.57/0.68 fof(m_AddZero,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => ( sdtpldt0(W0,sz00) = W0 % 0.57/0.68 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMulComm,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMulAsso,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.57/0.68 % 0.57/0.68 fof(m_MulUnit,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => ( sdtasdt0(W0,sz10) = W0 % 0.57/0.68 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(m_MulZero,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => ( sdtasdt0(W0,sz00) = sz00 % 0.57/0.68 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mAMDistr,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.57/0.68 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mAddCanc,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.57/0.68 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.57/0.68 => W1 = W2 ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMulCanc,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => ( W0 != sz00 % 0.57/0.68 => ! [W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.57/0.68 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.57/0.68 => W1 = W2 ) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mZeroAdd,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( sdtpldt0(W0,W1) = sz00 % 0.57/0.68 => ( W0 = sz00 % 0.57/0.68 & W1 = sz00 ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mZeroMul,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( sdtasdt0(W0,W1) = sz00 % 0.57/0.68 => ( W0 = sz00 % 0.57/0.68 | W1 = sz00 ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mDefLE,definition, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( sdtlseqdt0(W0,W1) % 0.57/0.68 <=> ? [W2] : % 0.57/0.68 ( aNaturalNumber0(W2) % 0.57/0.68 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mDefDiff,definition, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( sdtlseqdt0(W0,W1) % 0.57/0.68 => ! [W2] : % 0.57/0.68 ( W2 = sdtmndt0(W1,W0) % 0.57/0.68 <=> ( aNaturalNumber0(W2) % 0.57/0.68 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mLERefl,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => sdtlseqdt0(W0,W0) ) ). % 0.57/0.68 % 0.57/0.68 fof(mLEAsym,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( ( sdtlseqdt0(W0,W1) % 0.57/0.68 & sdtlseqdt0(W1,W0) ) % 0.57/0.68 => W0 = W1 ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mLETran,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => ( ( sdtlseqdt0(W0,W1) % 0.57/0.68 & sdtlseqdt0(W1,W2) ) % 0.57/0.68 => sdtlseqdt0(W0,W2) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mLETotal,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( sdtlseqdt0(W0,W1) % 0.57/0.68 | ( W1 != W0 % 0.57/0.68 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMonAdd,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.68 => ( ( W0 != W1 % 0.57/0.68 & sdtlseqdt0(W0,W1) ) % 0.57/0.68 => ! [W2] : % 0.57/0.68 ( aNaturalNumber0(W2) % 0.57/0.68 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.57/0.68 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.57/0.68 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.57/0.68 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMonMul,axiom, % 0.57/0.68 ! [W0,W1,W2] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) % 0.57/0.68 & aNaturalNumber0(W2) ) % 0.57/0.68 => ( ( W0 != sz00 % 0.57/0.68 & W1 != W2 % 0.57/0.68 & sdtlseqdt0(W1,W2) ) % 0.57/0.68 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.57/0.68 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.57/0.68 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.57/0.68 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mLENTr,axiom, % 0.57/0.68 ! [W0] : % 0.57/0.68 ( aNaturalNumber0(W0) % 0.57/0.68 => ( W0 = sz00 % 0.57/0.68 | W0 = sz10 % 0.57/0.68 | ( sz10 != W0 % 0.57/0.68 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.57/0.68 % 0.57/0.68 fof(mMonMul2,axiom, % 0.57/0.68 ! [W0,W1] : % 0.57/0.68 ( ( aNaturalNumber0(W0) % 0.57/0.68 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( W0 != sz00 % 0.57/0.69 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mIH,axiom, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( iLess0(W0,W1) % 0.57/0.69 => $true ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mIH_03,axiom, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( ( W0 != W1 % 0.57/0.69 & sdtlseqdt0(W0,W1) ) % 0.57/0.69 => iLess0(W0,W1) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDefDiv,definition, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( doDivides0(W0,W1) % 0.57/0.69 <=> ? [W2] : % 0.57/0.69 ( aNaturalNumber0(W2) % 0.57/0.69 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDefQuot,definition, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( ( W0 != sz00 % 0.57/0.69 & doDivides0(W0,W1) ) % 0.57/0.69 => ! [W2] : % 0.57/0.69 ( W2 = sdtsldt0(W1,W0) % 0.57/0.69 <=> ( aNaturalNumber0(W2) % 0.57/0.69 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDivTrans,axiom, % 0.57/0.69 ! [W0,W1,W2] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) % 0.57/0.69 & aNaturalNumber0(W2) ) % 0.57/0.69 => ( ( doDivides0(W0,W1) % 0.57/0.69 & doDivides0(W1,W2) ) % 0.57/0.69 => doDivides0(W0,W2) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDivSum,axiom, % 0.57/0.69 ! [W0,W1,W2] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) % 0.57/0.69 & aNaturalNumber0(W2) ) % 0.57/0.69 => ( ( doDivides0(W0,W1) % 0.57/0.69 & doDivides0(W0,W2) ) % 0.57/0.69 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDivMin,axiom, % 0.57/0.69 ! [W0,W1,W2] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) % 0.57/0.69 & aNaturalNumber0(W2) ) % 0.57/0.69 => ( ( doDivides0(W0,W1) % 0.57/0.69 & doDivides0(W0,sdtpldt0(W1,W2)) ) % 0.57/0.69 => doDivides0(W0,W2) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDivLE,axiom, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( ( doDivides0(W0,W1) % 0.57/0.69 & W1 != sz00 ) % 0.57/0.69 => sdtlseqdt0(W0,W1) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDivAsso,axiom, % 0.57/0.69 ! [W0,W1] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) ) % 0.57/0.69 => ( ( W0 != sz00 % 0.57/0.69 & doDivides0(W0,W1) ) % 0.57/0.69 => ! [W2] : % 0.57/0.69 ( aNaturalNumber0(W2) % 0.57/0.69 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mDefPrime,definition, % 0.57/0.69 ! [W0] : % 0.57/0.69 ( aNaturalNumber0(W0) % 0.57/0.69 => ( isPrime0(W0) % 0.57/0.69 <=> ( W0 != sz00 % 0.57/0.69 & W0 != sz10 % 0.57/0.69 & ! [W1] : % 0.57/0.69 ( ( aNaturalNumber0(W1) % 0.57/0.69 & doDivides0(W1,W0) ) % 0.57/0.69 => ( W1 = sz10 % 0.57/0.69 | W1 = W0 ) ) ) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(mPrimDiv,axiom, % 0.57/0.69 ! [W0] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & W0 != sz00 % 0.57/0.69 & W0 != sz10 ) % 0.57/0.69 => ? [W1] : % 0.57/0.69 ( aNaturalNumber0(W1) % 0.57/0.69 & doDivides0(W1,W0) % 0.57/0.69 & isPrime0(W1) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__1837,hypothesis, % 0.57/0.69 ( aNaturalNumber0(xn) % 0.57/0.69 & aNaturalNumber0(xm) % 0.57/0.69 & aNaturalNumber0(xp) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__1799,hypothesis, % 0.57/0.69 ! [W0,W1,W2] : % 0.57/0.69 ( ( aNaturalNumber0(W0) % 0.57/0.69 & aNaturalNumber0(W1) % 0.57/0.69 & aNaturalNumber0(W2) ) % 0.57/0.69 => ( ( isPrime0(W2) % 0.57/0.69 & doDivides0(W2,sdtasdt0(W0,W1)) ) % 0.57/0.69 => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) % 0.57/0.69 => ( doDivides0(W2,W0) % 0.57/0.69 | doDivides0(W2,W1) ) ) ) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__1860,hypothesis, % 0.57/0.69 ( isPrime0(xp) % 0.57/0.69 & doDivides0(xp,sdtasdt0(xn,xm)) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__1870,hypothesis, % 0.57/0.69 ~ sdtlseqdt0(xp,xn) ). % 0.57/0.69 % 0.57/0.69 fof(m__2075,hypothesis, % 0.57/0.69 ~ sdtlseqdt0(xp,xm) ). % 0.57/0.69 % 0.57/0.69 fof(m__2287,hypothesis, % 0.57/0.69 ( xn != xp % 0.57/0.69 & sdtlseqdt0(xn,xp) % 0.57/0.69 & xm != xp % 0.57/0.69 & sdtlseqdt0(xm,xp) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2306,hypothesis, % 0.57/0.69 xk = sdtsldt0(sdtasdt0(xn,xm),xp) ). % 0.57/0.69 % 0.57/0.69 fof(m__2315,hypothesis, % 0.57/0.69 ~ ( xk = sz00 % 0.57/0.69 | xk = sz10 ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2327,hypothesis, % 0.57/0.69 ( xk != sz00 % 0.57/0.69 & xk != sz10 ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2342,hypothesis, % 0.57/0.69 ( aNaturalNumber0(xr) % 0.57/0.69 & doDivides0(xr,xk) % 0.57/0.69 & isPrime0(xr) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2362,hypothesis, % 0.57/0.69 ( sdtlseqdt0(xr,xk) % 0.57/0.69 & doDivides0(xr,sdtasdt0(xn,xm)) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2377,hypothesis, % 0.57/0.69 ( xk != xp % 0.57/0.69 & sdtlseqdt0(xk,xp) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2449,hypothesis, % 0.57/0.69 ( doDivides0(xr,xn) % 0.57/0.69 | doDivides0(xr,xm) ) ). % 0.57/0.69 % 0.57/0.69 fof(m__2487,hypothesis, % 0.57/0.69 ~ doDivides0(xr,xn) ). % 0.57/0.69 % 0.57/0.69 fof(m__2698,hypothesis, % 0.57/0.69 ~ doDivides0(xr,xm) ). % 0.57/0.69 % 0.57/0.69 fof(m__,conjecture, % 0.57/0.69 ( doDivides0(xp,xn) % 0.57/0.69 | doDivides0(xp,xm) ) ). % 0.57/0.69 % 0.57/0.69 %------------------------------------------------------------------------------ % 0.57/0.69 %------------------------------------------- % 0.57/0.69 % Proof found % 0.57/0.69 % SZS status Theorem for theBenchmark % 0.57/0.69 % SZS output start Proof % 0.57/0.69 %ClaNum:121(EqnAxiom:25) % 0.57/0.69 %VarNum:440(SingletonVarNum:131) % 0.57/0.69 %MaxLitNum:8 % 0.57/0.69 %MaxfuncDepth:2 % 0.57/0.69 %SharedTerms:41 % 0.57/0.69 %goalClause: 52 53 % 0.57/0.69 %singleGoalClaCount:2 % 0.57/0.69 [26]P1(a1) % 0.57/0.69 [27]P1(a10) % 0.57/0.69 [28]P1(a11) % 0.57/0.69 [29]P1(a12) % 0.57/0.69 [30]P1(a14) % 0.57/0.69 [31]P1(a15) % 0.57/0.69 [32]P2(a14) % 0.57/0.69 [33]P2(a15) % 0.57/0.69 [34]P5(a11,a14) % 0.57/0.69 [35]P5(a12,a14) % 0.57/0.69 [36]P5(a13,a14) % 0.57/0.69 [37]P5(a15,a13) % 0.57/0.69 [38]P3(a15,a13) % 0.57/0.69 [42]~E(a1,a10) % 0.57/0.69 [43]~E(a14,a11) % 0.57/0.69 [44]~E(a14,a12) % 0.57/0.69 [46]~E(a1,a13) % 0.57/0.69 [48]~E(a13,a10) % 0.57/0.69 [49]~E(a13,a14) % 0.57/0.69 [50]~P5(a14,a11) % 0.57/0.69 [51]~P5(a14,a12) % 0.57/0.69 [52]~P3(a14,a11) % 0.57/0.69 [53]~P3(a14,a12) % 0.57/0.69 [54]~P3(a15,a11) % 0.57/0.69 [55]~P3(a15,a12) % 0.57/0.69 [40]P3(a14,f2(a11,a12)) % 0.57/0.69 [41]P3(a15,f2(a11,a12)) % 0.57/0.69 [39]E(f7(f2(a11,a12),a14),a13) % 0.57/0.69 [68]P3(a15,a11)+P3(a15,a12) % 0.57/0.69 [66]~P1(x661)+P5(x661,x661) % 0.57/0.69 [58]~P1(x581)+E(f2(a1,x581),a1) % 0.57/0.69 [59]~P1(x591)+E(f2(x591,a1),a1) % 0.57/0.69 [60]~P1(x601)+E(f8(a1,x601),x601) % 0.57/0.69 [61]~P1(x611)+E(f2(a10,x611),x611) % 0.57/0.69 [62]~P1(x621)+E(f8(x621,a1),x621) % 0.57/0.69 [63]~P1(x631)+E(f2(x631,a10),x631) % 0.57/0.69 [56]~P1(x561)+~P2(x561)+~E(x561,a1) % 0.57/0.69 [57]~P1(x571)+~P2(x571)+~E(x571,a10) % 0.57/0.69 [78]~P1(x782)+~P1(x781)+E(f8(x781,x782),f8(x782,x781)) % 0.57/0.69 [79]~P1(x792)+~P1(x791)+E(f2(x791,x792),f2(x792,x791)) % 0.57/0.69 [81]~P1(x812)+~P1(x811)+P1(f8(x811,x812)) % 0.57/0.69 [82]~P1(x822)+~P1(x821)+P1(f2(x821,x822)) % 0.57/0.69 [69]~P1(x691)+E(x691,a10)+P5(a10,x691)+E(x691,a1) % 0.57/0.69 [64]~P1(x641)+E(x641,a10)+E(x641,a1)+P1(f3(x641)) % 0.57/0.69 [65]~P1(x651)+E(x651,a10)+E(x651,a1)+P2(f3(x651)) % 0.57/0.69 [72]~P1(x721)+E(x721,a10)+P3(f3(x721),x721)+E(x721,a1) % 0.57/0.69 [73]~E(x732,x731)+~P1(x731)+~P1(x732)+P5(x731,x732) % 0.57/0.69 [80]P5(x802,x801)+~P1(x801)+~P1(x802)+P5(x801,x802) % 0.57/0.69 [75]~P1(x752)+~P1(x751)+E(x751,a1)+~E(f8(x752,x751),a1) % 0.57/0.69 [76]~P1(x762)+~P1(x761)+E(x761,a1)+~E(f8(x761,x762),a1) % 0.57/0.69 [86]~P1(x862)+~P1(x861)+P5(x862,f2(x862,x861))+E(x861,a1) % 0.57/0.69 [92]~P1(x922)+~P1(x921)+~P5(x921,x922)+P1(f5(x921,x922)) % 0.57/0.69 [93]~P1(x932)+~P1(x931)+~P3(x931,x932)+P1(f6(x931,x932)) % 0.57/0.69 [100]~P1(x1001)+~P1(x1002)+~P3(x1001,x1002)+E(f2(x1001,f6(x1001,x1002)),x1002) % 0.57/0.69 [101]~P1(x1012)+~P1(x1011)+~P5(x1011,x1012)+E(f8(x1011,f5(x1011,x1012)),x1012) % 0.57/0.69 [110]~P1(x1103)+~P1(x1102)+~P1(x1101)+E(f8(f8(x1101,x1102),x1103),f8(x1101,f8(x1102,x1103))) % 0.57/0.69 [111]~P1(x1113)+~P1(x1112)+~P1(x1111)+E(f2(f2(x1111,x1112),x1113),f2(x1111,f2(x1112,x1113))) % 0.57/0.69 [119]~P1(x1193)+~P1(x1192)+~P1(x1191)+E(f8(f2(x1191,x1192),f2(x1191,x1193)),f2(x1191,f8(x1192,x1193))) % 0.57/0.69 [120]~P1(x1202)+~P1(x1203)+~P1(x1201)+E(f8(f2(x1201,x1202),f2(x1203,x1202)),f2(f8(x1201,x1203),x1202)) % 0.57/0.69 [67]P2(x671)+~P1(x671)+E(x671,a10)+E(x671,a1)+~E(f4(x671),a10) % 0.57/0.69 [70]P2(x701)+~P1(x701)+E(x701,a10)+~E(f4(x701),x701)+E(x701,a1) % 0.57/0.69 [71]P2(x711)+~P1(x711)+E(x711,a10)+E(x711,a1)+P1(f4(x711)) % 0.57/0.69 [74]P2(x741)+~P1(x741)+E(x741,a10)+P3(f4(x741),x741)+E(x741,a1) % 0.57/0.69 [84]~P1(x841)+~P1(x842)+~P3(x842,x841)+P5(x842,x841)+E(x841,a1) % 0.57/0.69 [85]P4(x851,x852)+~P1(x852)+~P1(x851)+~P5(x851,x852)+E(x851,x852) % 0.57/0.69 [89]~P1(x892)+~P1(x891)+~P5(x892,x891)+~P5(x891,x892)+E(x891,x892) % 0.57/0.69 [77]~P1(x771)+~P1(x772)+E(x771,a1)+E(x772,a1)+~E(f2(x772,x771),a1) % 0.57/0.69 [87]~P1(x871)+~P1(x872)+~P1(x873)+P3(x871,x872)+~E(x872,f2(x871,x873)) % 0.57/0.69 [88]~P1(x882)+~P1(x881)+~P1(x883)+P5(x881,x882)+~E(f8(x881,x883),x882) % 0.57/0.69 [90]~P1(x903)+~P1(x902)+~P5(x903,x902)+P1(x901)+~E(x901,f9(x902,x903)) % 0.57/0.69 [94]~P1(x942)+~P1(x941)+~P1(x943)+E(x941,x942)+~E(f8(x943,x941),f8(x943,x942)) % 0.57/0.69 [95]~P1(x952)+~P1(x953)+~P1(x951)+E(x951,x952)+~E(f8(x951,x953),f8(x952,x953)) % 0.57/0.69 [98]~P1(x983)+~P1(x981)+~P5(x981,x983)+~E(x982,f9(x983,x981))+E(f8(x981,x982),x983) % 0.57/0.69 [83]~P1(x832)+~P1(x831)+~P2(x832)+~P3(x831,x832)+E(x831,x832)+E(x831,a10) % 0.57/0.69 [102]~P1(x1022)+~P1(x1021)+~P5(x1023,x1022)+~P5(x1021,x1023)+P5(x1021,x1022)+~P1(x1023) % 0.57/0.69 [103]~P1(x1032)+~P1(x1031)+~P3(x1033,x1032)+~P3(x1031,x1033)+P3(x1031,x1032)+~P1(x1033) % 0.57/0.69 [91]~P1(x911)+~P1(x913)+~P3(x911,x913)+P1(x912)+E(x911,a1)+~E(x912,f7(x913,x911)) % 0.57/0.69 [96]~P1(x962)+~P1(x961)+~P1(x963)+E(x961,x962)+~E(f2(x963,x961),f2(x963,x962))+E(x963,a1) % 0.57/0.69 [97]~P1(x972)+~P1(x973)+~P1(x971)+E(x971,x972)+~E(f2(x971,x973),f2(x972,x973))+E(x973,a1) % 0.57/0.69 [99]~P1(x991)+~P1(x992)+~P3(x991,x992)+~E(x993,f7(x992,x991))+E(x991,a1)+E(x992,f2(x991,x993)) % 0.57/0.69 [104]~P1(x1042)+~P1(x1043)+~P1(x1041)+~P5(x1043,x1042)+~E(f8(x1043,x1041),x1042)+E(x1041,f9(x1042,x1043)) % 0.57/0.69 [112]~P1(x1123)+~P1(x1122)+~P1(x1121)+~P3(x1121,x1123)+~P3(x1121,x1122)+P3(x1121,f8(x1122,x1123)) % 0.57/0.69 [113]~P1(x1132)+~P1(x1131)+~P1(x1133)+~P5(x1131,x1132)+E(x1131,x1132)+P5(f8(x1133,x1131),f8(x1133,x1132)) % 0.57/0.69 [114]~P1(x1142)+~P1(x1143)+~P1(x1141)+~P5(x1141,x1142)+E(x1141,x1142)+P5(f8(x1141,x1143),f8(x1142,x1143)) % 0.57/0.69 [117]~P1(x1172)+~P1(x1171)+~P3(x1171,x1173)+P3(x1171,x1172)+~P1(x1173)+~P3(x1171,f8(x1173,x1172)) % 0.57/0.69 [118]~P1(x1182)+~P1(x1183)+~P1(x1181)+~P3(x1181,x1183)+E(x1181,a1)+E(f7(f2(x1182,x1183),x1181),f2(x1182,f7(x1183,x1181))) % 0.57/0.69 [105]~P1(x1051)+~P1(x1053)+~P1(x1052)+~P3(x1051,x1053)+~E(x1053,f2(x1051,x1052))+E(x1051,a1)+E(x1052,f7(x1053,x1051)) % 0.57/0.69 [115]~P1(x1152)+~P1(x1151)+~P1(x1153)+~P5(x1151,x1152)+E(x1151,x1152)+P5(f2(x1153,x1151),f2(x1153,x1152))+E(x1153,a1) % 0.57/0.69 [116]~P1(x1162)+~P1(x1163)+~P1(x1161)+~P5(x1161,x1162)+E(x1161,x1162)+P5(f2(x1161,x1163),f2(x1162,x1163))+E(x1163,a1) % 0.57/0.69 [121]~P1(x1211)+~P1(x1212)+~P1(x1213)+~P2(x1211)+P3(x1211,x1212)+P3(x1211,x1213)+~P3(x1211,f2(x1213,x1212))+~P4(f8(f8(x1213,x1212),x1211),f8(f8(a11,a12),a14)) % 0.57/0.69 %EqnAxiom % 0.57/0.69 [1]E(x11,x11) % 0.57/0.69 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.69 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.57/0.69 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.57/0.69 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 0.57/0.69 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 0.57/0.69 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 0.57/0.69 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 0.57/0.69 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.57/0.69 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.57/0.69 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123)) % 0.57/0.69 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132)) % 0.57/0.69 [14]~E(x141,x142)+E(f6(x141,x143),f6(x142,x143)) % 0.57/0.69 [15]~E(x151,x152)+E(f6(x153,x151),f6(x153,x152)) % 0.57/0.69 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 0.57/0.69 [17]~E(x171,x172)+E(f3(x171),f3(x172)) % 0.57/0.69 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.57/0.69 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193) % 0.57/0.69 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201) % 0.57/0.69 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213) % 0.57/0.69 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221) % 0.57/0.69 [23]~P2(x231)+P2(x232)+~E(x231,x232) % 0.57/0.69 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.57/0.69 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.57/0.69 % 0.57/0.69 %------------------------------------------- % 0.57/0.70 cnf(137,plain, % 0.57/0.70 ($false), % 0.57/0.70 inference(scs_inference,[],[54,55,68]), % 0.57/0.70 ['proof']). % 0.57/0.70 % SZS output end Proof % 0.57/0.70 % Total time :0.010000s %------------------------------------------------------------------------------