%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM489+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 : n025.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 12:24:32 EDT 2024 % Result : Theorem 0.54s 0.63s % Output : CNFRefutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM489+1 : TPTP v8.2.0. Released v4.0.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n025.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 : Sun Jun 23 02:43:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.19/0.55 start to proof:theBenchmark % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % File :CSE---1.7 % 0.54/0.61 % Problem :theBenchmark % 0.54/0.61 % Transform :cnf % 0.54/0.61 % Format :tptp:raw % 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.61 % 0.54/0.61 % Result :Theorem 0.010000s % 0.54/0.61 % Output :CNFRefutation 0.010000s % 0.54/0.61 %------------------------------------------- % 0.54/0.62 %------------------------------------------------------------------------------ % 0.54/0.62 % File : NUM489+1 : TPTP v8.2.0. Released v4.0.0. % 0.54/0.62 % Domain : Number Theory % 0.54/0.62 % Problem : Square root of a prime is irrational 14_01_03_01, 00 expansion % 0.54/0.62 % Version : Especial. % 0.54/0.62 % English : % 0.54/0.62 % 0.54/0.62 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.54/0.62 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.54/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.54/0.62 % Source : [Pas08] % 0.54/0.62 % Names : primes_14_01_03_01.00 [Pas08] % 0.54/0.62 % 0.54/0.62 % Status : Theorem % 0.54/0.62 % Rating : 0.17 v8.2.0, 0.19 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.37 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.39 v5.3.0, 0.44 v5.2.0, 0.25 v5.1.0, 0.38 v5.0.0, 0.42 v4.1.0, 0.48 v4.0.1, 0.78 v4.0.0 % 0.54/0.62 % Syntax : Number of formulae : 45 ( 4 unt; 5 def) % 0.54/0.62 % Number of atoms : 201 ( 59 equ) % 0.54/0.62 % Maximal formula atoms : 10 ( 4 avg) % 0.54/0.62 % Number of connectives : 177 ( 21 ~; 8 |; 81 &) % 0.54/0.62 % ( 5 <=>; 62 =>; 0 <=; 0 <~>) % 0.54/0.62 % Maximal formula depth : 11 ( 6 avg) % 0.54/0.62 % Maximal term depth : 3 ( 1 avg) % 0.54/0.62 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.54/0.62 % Number of functors : 10 ( 10 usr; 6 con; 0-2 aty) % 0.54/0.62 % Number of variables : 85 ( 82 !; 3 ?) % 0.54/0.62 % SPC : FOF_THM_RFO_SEQ % 0.54/0.62 % 0.54/0.62 % Comments : Problem generated by the SAD system [VLP07] % 0.54/0.62 %------------------------------------------------------------------------------ % 0.54/0.62 fof(mNatSort,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => $true ) ). % 0.54/0.62 % 0.54/0.62 fof(mSortsC,axiom, % 0.54/0.62 aNaturalNumber0(sz00) ). % 0.54/0.62 % 0.54/0.62 fof(mSortsC_01,axiom, % 0.54/0.62 ( aNaturalNumber0(sz10) % 0.54/0.62 & sz10 != sz00 ) ). % 0.54/0.62 % 0.54/0.62 fof(mSortsB,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.54/0.62 % 0.54/0.62 fof(mSortsB_02,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.54/0.62 % 0.54/0.62 fof(mAddComm,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.54/0.62 % 0.54/0.62 fof(mAddAsso,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.54/0.62 % 0.54/0.62 fof(m_AddZero,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => ( sdtpldt0(W0,sz00) = W0 % 0.54/0.62 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMulComm,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMulAsso,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.54/0.62 % 0.54/0.62 fof(m_MulUnit,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => ( sdtasdt0(W0,sz10) = W0 % 0.54/0.62 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(m_MulZero,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => ( sdtasdt0(W0,sz00) = sz00 % 0.54/0.62 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mAMDistr,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.54/0.62 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mAddCanc,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.54/0.62 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.54/0.62 => W1 = W2 ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMulCanc,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => ( W0 != sz00 % 0.54/0.62 => ! [W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.54/0.62 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.54/0.62 => W1 = W2 ) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mZeroAdd,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( sdtpldt0(W0,W1) = sz00 % 0.54/0.62 => ( W0 = sz00 % 0.54/0.62 & W1 = sz00 ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mZeroMul,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( sdtasdt0(W0,W1) = sz00 % 0.54/0.62 => ( W0 = sz00 % 0.54/0.62 | W1 = sz00 ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mDefLE,definition, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( sdtlseqdt0(W0,W1) % 0.54/0.62 <=> ? [W2] : % 0.54/0.62 ( aNaturalNumber0(W2) % 0.54/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mDefDiff,definition, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( sdtlseqdt0(W0,W1) % 0.54/0.62 => ! [W2] : % 0.54/0.62 ( W2 = sdtmndt0(W1,W0) % 0.54/0.62 <=> ( aNaturalNumber0(W2) % 0.54/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mLERefl,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => sdtlseqdt0(W0,W0) ) ). % 0.54/0.62 % 0.54/0.62 fof(mLEAsym,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( ( sdtlseqdt0(W0,W1) % 0.54/0.62 & sdtlseqdt0(W1,W0) ) % 0.54/0.62 => W0 = W1 ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mLETran,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => ( ( sdtlseqdt0(W0,W1) % 0.54/0.62 & sdtlseqdt0(W1,W2) ) % 0.54/0.62 => sdtlseqdt0(W0,W2) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mLETotal,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( sdtlseqdt0(W0,W1) % 0.54/0.62 | ( W1 != W0 % 0.54/0.62 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMonAdd,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( ( W0 != W1 % 0.54/0.62 & sdtlseqdt0(W0,W1) ) % 0.54/0.62 => ! [W2] : % 0.54/0.62 ( aNaturalNumber0(W2) % 0.54/0.62 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.54/0.62 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.54/0.62 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.54/0.62 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMonMul,axiom, % 0.54/0.62 ! [W0,W1,W2] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) % 0.54/0.62 & aNaturalNumber0(W2) ) % 0.54/0.62 => ( ( W0 != sz00 % 0.54/0.62 & W1 != W2 % 0.54/0.62 & sdtlseqdt0(W1,W2) ) % 0.54/0.62 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.54/0.62 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.54/0.62 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.54/0.62 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mLENTr,axiom, % 0.54/0.62 ! [W0] : % 0.54/0.62 ( aNaturalNumber0(W0) % 0.54/0.62 => ( W0 = sz00 % 0.54/0.62 | W0 = sz10 % 0.54/0.62 | ( sz10 != W0 % 0.54/0.62 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mMonMul2,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( W0 != sz00 % 0.54/0.62 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mIH,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.62 ( ( aNaturalNumber0(W0) % 0.54/0.62 & aNaturalNumber0(W1) ) % 0.54/0.62 => ( iLess0(W0,W1) % 0.54/0.62 => $true ) ) ). % 0.54/0.62 % 0.54/0.62 fof(mIH_03,axiom, % 0.54/0.62 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( ( W0 != W1 % 0.54/0.63 & sdtlseqdt0(W0,W1) ) % 0.54/0.63 => iLess0(W0,W1) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefDiv,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( doDivides0(W0,W1) % 0.54/0.63 <=> ? [W2] : % 0.54/0.63 ( aNaturalNumber0(W2) % 0.54/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefQuot,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( ( W0 != sz00 % 0.54/0.63 & doDivides0(W0,W1) ) % 0.54/0.63 => ! [W2] : % 0.54/0.63 ( W2 = sdtsldt0(W1,W0) % 0.54/0.63 <=> ( aNaturalNumber0(W2) % 0.54/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivTrans,axiom, % 0.54/0.63 ! [W0,W1,W2] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) % 0.54/0.63 & aNaturalNumber0(W2) ) % 0.54/0.63 => ( ( doDivides0(W0,W1) % 0.54/0.63 & doDivides0(W1,W2) ) % 0.54/0.63 => doDivides0(W0,W2) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivSum,axiom, % 0.54/0.63 ! [W0,W1,W2] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) % 0.54/0.63 & aNaturalNumber0(W2) ) % 0.54/0.63 => ( ( doDivides0(W0,W1) % 0.54/0.63 & doDivides0(W0,W2) ) % 0.54/0.63 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivMin,axiom, % 0.54/0.63 ! [W0,W1,W2] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) % 0.54/0.63 & aNaturalNumber0(W2) ) % 0.54/0.63 => ( ( doDivides0(W0,W1) % 0.54/0.63 & doDivides0(W0,sdtpldt0(W1,W2)) ) % 0.54/0.63 => doDivides0(W0,W2) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivLE,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( ( doDivides0(W0,W1) % 0.54/0.63 & W1 != sz00 ) % 0.54/0.63 => sdtlseqdt0(W0,W1) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivAsso,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( ( W0 != sz00 % 0.54/0.63 & doDivides0(W0,W1) ) % 0.54/0.63 => ! [W2] : % 0.54/0.63 ( aNaturalNumber0(W2) % 0.54/0.63 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefPrime,definition, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( aNaturalNumber0(W0) % 0.54/0.63 => ( isPrime0(W0) % 0.54/0.63 <=> ( W0 != sz00 % 0.54/0.63 & W0 != sz10 % 0.54/0.63 & ! [W1] : % 0.54/0.63 ( ( aNaturalNumber0(W1) % 0.54/0.63 & doDivides0(W1,W0) ) % 0.54/0.63 => ( W1 = sz10 % 0.54/0.63 | W1 = W0 ) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mPrimDiv,axiom, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & W0 != sz00 % 0.54/0.63 & W0 != sz10 ) % 0.54/0.63 => ? [W1] : % 0.54/0.63 ( aNaturalNumber0(W1) % 0.54/0.63 & doDivides0(W1,W0) % 0.54/0.63 & isPrime0(W1) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__1837,hypothesis, % 0.54/0.63 ( aNaturalNumber0(xn) % 0.54/0.63 & aNaturalNumber0(xm) % 0.54/0.63 & aNaturalNumber0(xp) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__1799,hypothesis, % 0.54/0.63 ! [W0,W1,W2] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) % 0.54/0.63 & aNaturalNumber0(W2) ) % 0.54/0.63 => ( ( isPrime0(W2) % 0.54/0.63 & doDivides0(W2,sdtasdt0(W0,W1)) ) % 0.54/0.63 => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) % 0.54/0.63 => ( doDivides0(W2,W0) % 0.54/0.63 | doDivides0(W2,W1) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__1860,hypothesis, % 0.54/0.63 ( isPrime0(xp) % 0.54/0.63 & doDivides0(xp,sdtasdt0(xn,xm)) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__1870,hypothesis, % 0.54/0.63 sdtlseqdt0(xp,xn) ). % 0.54/0.63 % 0.54/0.63 fof(m__1883,hypothesis, % 0.54/0.63 xr = sdtmndt0(xn,xp) ). % 0.54/0.63 % 0.54/0.63 fof(m__1894,hypothesis, % 0.54/0.63 ( xr != xn % 0.54/0.63 & sdtlseqdt0(xr,xn) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__,conjecture, % 0.54/0.63 xn = sdtpldt0(xp,xr) ). % 0.54/0.63 % 0.54/0.63 %------------------------------------------------------------------------------ % 0.54/0.63 %------------------------------------------- % 0.54/0.63 % Proof found % 0.54/0.63 % SZS status Theorem for theBenchmark % 0.54/0.63 % SZS output start Proof % 0.54/0.63 %ClaNum:103(EqnAxiom:25) % 0.54/0.63 %VarNum:440(SingletonVarNum:131) % 0.54/0.63 %MaxLitNum:8 % 0.54/0.63 %MaxfuncDepth:2 % 0.54/0.63 %SharedTerms:24 % 0.54/0.63 %goalClause: 38 % 0.54/0.63 %singleGoalClaCount:1 % 0.54/0.63 [26]P1(a1) % 0.54/0.63 [27]P1(a10) % 0.54/0.63 [28]P1(a11) % 0.54/0.63 [29]P1(a12) % 0.54/0.63 [30]P1(a13) % 0.54/0.63 [31]P2(a13) % 0.54/0.63 [33]P5(a13,a11) % 0.54/0.63 [34]P5(a14,a11) % 0.54/0.63 [36]~E(a1,a10) % 0.54/0.63 [37]~E(a14,a11) % 0.54/0.63 [32]E(f2(a11,a13),a14) % 0.54/0.63 [35]P3(a13,f3(a11,a12)) % 0.54/0.63 [38]~E(f8(a13,a14),a11) % 0.54/0.63 [49]~P1(x491)+P5(x491,x491) % 0.54/0.63 [41]~P1(x411)+E(f3(a1,x411),a1) % 0.54/0.63 [42]~P1(x421)+E(f3(x421,a1),a1) % 0.54/0.63 [43]~P1(x431)+E(f8(a1,x431),x431) % 0.54/0.63 [44]~P1(x441)+E(f3(a10,x441),x441) % 0.54/0.63 [45]~P1(x451)+E(f8(x451,a1),x451) % 0.54/0.63 [46]~P1(x461)+E(f3(x461,a10),x461) % 0.54/0.63 [39]~P1(x391)+~P2(x391)+~E(x391,a1) % 0.54/0.63 [40]~P1(x401)+~P2(x401)+~E(x401,a10) % 0.54/0.63 [60]~P1(x602)+~P1(x601)+E(f8(x601,x602),f8(x602,x601)) % 0.54/0.63 [61]~P1(x612)+~P1(x611)+E(f3(x611,x612),f3(x612,x611)) % 0.54/0.63 [63]~P1(x632)+~P1(x631)+P1(f8(x631,x632)) % 0.54/0.63 [64]~P1(x642)+~P1(x641)+P1(f3(x641,x642)) % 0.54/0.63 [51]~P1(x511)+E(x511,a10)+P5(a10,x511)+E(x511,a1) % 0.54/0.63 [47]~P1(x471)+E(x471,a10)+E(x471,a1)+P1(f4(x471)) % 0.54/0.63 [48]~P1(x481)+E(x481,a10)+E(x481,a1)+P2(f4(x481)) % 0.54/0.63 [54]~P1(x541)+E(x541,a10)+P3(f4(x541),x541)+E(x541,a1) % 0.54/0.63 [55]~E(x552,x551)+~P1(x551)+~P1(x552)+P5(x551,x552) % 0.54/0.63 [62]P5(x622,x621)+~P1(x621)+~P1(x622)+P5(x621,x622) % 0.54/0.63 [57]~P1(x572)+~P1(x571)+E(x571,a1)+~E(f8(x572,x571),a1) % 0.54/0.63 [58]~P1(x582)+~P1(x581)+E(x581,a1)+~E(f8(x581,x582),a1) % 0.54/0.63 [68]~P1(x682)+~P1(x681)+P5(x682,f3(x682,x681))+E(x681,a1) % 0.54/0.63 [74]~P1(x742)+~P1(x741)+~P5(x741,x742)+P1(f6(x741,x742)) % 0.54/0.63 [75]~P1(x752)+~P1(x751)+~P3(x751,x752)+P1(f7(x751,x752)) % 0.54/0.63 [82]~P1(x821)+~P1(x822)+~P3(x821,x822)+E(f3(x821,f7(x821,x822)),x822) % 0.54/0.63 [83]~P1(x832)+~P1(x831)+~P5(x831,x832)+E(f8(x831,f6(x831,x832)),x832) % 0.54/0.63 [92]~P1(x923)+~P1(x922)+~P1(x921)+E(f8(f8(x921,x922),x923),f8(x921,f8(x922,x923))) % 0.54/0.63 [93]~P1(x933)+~P1(x932)+~P1(x931)+E(f3(f3(x931,x932),x933),f3(x931,f3(x932,x933))) % 0.54/0.63 [101]~P1(x1013)+~P1(x1012)+~P1(x1011)+E(f8(f3(x1011,x1012),f3(x1011,x1013)),f3(x1011,f8(x1012,x1013))) % 0.54/0.63 [102]~P1(x1022)+~P1(x1023)+~P1(x1021)+E(f8(f3(x1021,x1022),f3(x1023,x1022)),f3(f8(x1021,x1023),x1022)) % 0.54/0.63 [50]P2(x501)+~P1(x501)+E(x501,a10)+E(x501,a1)+~E(f5(x501),a10) % 0.54/0.63 [52]P2(x521)+~P1(x521)+E(x521,a10)+~E(f5(x521),x521)+E(x521,a1) % 0.54/0.63 [53]P2(x531)+~P1(x531)+E(x531,a10)+E(x531,a1)+P1(f5(x531)) % 0.54/0.63 [56]P2(x561)+~P1(x561)+E(x561,a10)+P3(f5(x561),x561)+E(x561,a1) % 0.54/0.63 [66]~P1(x661)+~P1(x662)+~P3(x662,x661)+P5(x662,x661)+E(x661,a1) % 0.54/0.63 [67]P4(x671,x672)+~P1(x672)+~P1(x671)+~P5(x671,x672)+E(x671,x672) % 0.54/0.63 [71]~P1(x712)+~P1(x711)+~P5(x712,x711)+~P5(x711,x712)+E(x711,x712) % 0.54/0.63 [59]~P1(x591)+~P1(x592)+E(x591,a1)+E(x592,a1)+~E(f3(x592,x591),a1) % 0.54/0.63 [69]~P1(x691)+~P1(x692)+~P1(x693)+P3(x691,x692)+~E(x692,f3(x691,x693)) % 0.54/0.63 [70]~P1(x702)+~P1(x701)+~P1(x703)+P5(x701,x702)+~E(f8(x701,x703),x702) % 0.54/0.63 [72]~P1(x723)+~P1(x722)+~P5(x723,x722)+P1(x721)+~E(x721,f2(x722,x723)) % 0.54/0.63 [76]~P1(x762)+~P1(x761)+~P1(x763)+E(x761,x762)+~E(f8(x763,x761),f8(x763,x762)) % 0.54/0.63 [77]~P1(x772)+~P1(x773)+~P1(x771)+E(x771,x772)+~E(f8(x771,x773),f8(x772,x773)) % 0.54/0.63 [80]~P1(x803)+~P1(x801)+~P5(x801,x803)+~E(x802,f2(x803,x801))+E(f8(x801,x802),x803) % 0.54/0.63 [65]~P1(x652)+~P1(x651)+~P2(x652)+~P3(x651,x652)+E(x651,x652)+E(x651,a10) % 0.54/0.63 [84]~P1(x842)+~P1(x841)+~P5(x843,x842)+~P5(x841,x843)+P5(x841,x842)+~P1(x843) % 0.54/0.63 [85]~P1(x852)+~P1(x851)+~P3(x853,x852)+~P3(x851,x853)+P3(x851,x852)+~P1(x853) % 0.54/0.63 [73]~P1(x731)+~P1(x733)+~P3(x731,x733)+P1(x732)+E(x731,a1)+~E(x732,f9(x733,x731)) % 0.54/0.63 [78]~P1(x782)+~P1(x781)+~P1(x783)+E(x781,x782)+~E(f3(x783,x781),f3(x783,x782))+E(x783,a1) % 0.54/0.63 [79]~P1(x792)+~P1(x793)+~P1(x791)+E(x791,x792)+~E(f3(x791,x793),f3(x792,x793))+E(x793,a1) % 0.54/0.63 [81]~P1(x811)+~P1(x812)+~P3(x811,x812)+~E(x813,f9(x812,x811))+E(x811,a1)+E(x812,f3(x811,x813)) % 0.54/0.63 [86]~P1(x862)+~P1(x863)+~P1(x861)+~P5(x863,x862)+~E(f8(x863,x861),x862)+E(x861,f2(x862,x863)) % 0.54/0.63 [94]~P1(x943)+~P1(x942)+~P1(x941)+~P3(x941,x943)+~P3(x941,x942)+P3(x941,f8(x942,x943)) % 0.54/0.63 [95]~P1(x952)+~P1(x951)+~P1(x953)+~P5(x951,x952)+E(x951,x952)+P5(f8(x953,x951),f8(x953,x952)) % 0.54/0.63 [96]~P1(x962)+~P1(x963)+~P1(x961)+~P5(x961,x962)+E(x961,x962)+P5(f8(x961,x963),f8(x962,x963)) % 0.54/0.63 [99]~P1(x992)+~P1(x991)+~P3(x991,x993)+P3(x991,x992)+~P1(x993)+~P3(x991,f8(x993,x992)) % 0.54/0.63 [100]~P1(x1002)+~P1(x1003)+~P1(x1001)+~P3(x1001,x1003)+E(x1001,a1)+E(f9(f3(x1002,x1003),x1001),f3(x1002,f9(x1003,x1001))) % 0.54/0.63 [87]~P1(x871)+~P1(x873)+~P1(x872)+~P3(x871,x873)+~E(x873,f3(x871,x872))+E(x871,a1)+E(x872,f9(x873,x871)) % 0.54/0.63 [97]~P1(x972)+~P1(x971)+~P1(x973)+~P5(x971,x972)+E(x971,x972)+P5(f3(x973,x971),f3(x973,x972))+E(x973,a1) % 0.54/0.63 [98]~P1(x982)+~P1(x983)+~P1(x981)+~P5(x981,x982)+E(x981,x982)+P5(f3(x981,x983),f3(x982,x983))+E(x983,a1) % 0.54/0.63 [103]~P1(x1031)+~P1(x1032)+~P1(x1033)+~P2(x1031)+P3(x1031,x1032)+P3(x1031,x1033)+~P3(x1031,f3(x1033,x1032))+~P4(f8(f8(x1033,x1032),x1031),f8(f8(a11,a12),a13)) % 0.54/0.63 %EqnAxiom % 0.54/0.63 [1]E(x11,x11) % 0.54/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.63 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.61/0.63 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.61/0.63 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.61/0.63 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.61/0.63 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 0.61/0.63 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 0.61/0.63 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.61/0.63 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.61/0.63 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123)) % 0.61/0.63 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132)) % 0.61/0.63 [14]~E(x141,x142)+E(f7(x141,x143),f7(x142,x143)) % 0.61/0.63 [15]~E(x151,x152)+E(f7(x153,x151),f7(x153,x152)) % 0.61/0.63 [16]~E(x161,x162)+E(f5(x161),f5(x162)) % 0.61/0.63 [17]~E(x171,x172)+E(f4(x171),f4(x172)) % 0.61/0.63 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.61/0.63 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193) % 0.61/0.63 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201) % 0.61/0.63 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213) % 0.61/0.63 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221) % 0.61/0.63 [23]~P2(x231)+P2(x232)+~E(x231,x232) % 0.61/0.63 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.61/0.63 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.61/0.63 % 0.61/0.63 %------------------------------------------- % 0.61/0.63 cnf(109,plain, % 0.61/0.63 (~P5(x1091,x1092)+~P1(x1091)+~P1(x1092)+P1(f2(x1092,x1091))), % 0.61/0.63 inference(equality_inference,[],[72])). % 0.61/0.63 cnf(127,plain, % 0.61/0.63 ($false), % 0.61/0.63 inference(scs_inference,[],[38,26,28,30,33,34,32,2,24,62,109,80]), % 0.61/0.63 ['proof']). % 0.61/0.63 % SZS output end Proof % 0.61/0.63 % Total time :0.010000s %------------------------------------------------------------------------------