%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM484+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 : n001.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 12:24:30 EDT 2024 % Result : Theorem 0.56s 0.63s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM484+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 % 0.13/0.33 % Computer : n001.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Jun 23 02:30:24 EDT 2024 % 0.13/0.33 % CPUTime : % 0.20/0.56 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 0.010000s % 0.56/0.62 % Output :CNFRefutation 0.010000s % 0.56/0.62 %------------------------------------------- % 0.56/0.62 %------------------------------------------------------------------------------ % 0.56/0.62 % File : NUM484+1 : TPTP v8.2.0. Released v4.0.0. % 0.56/0.62 % Domain : Number Theory % 0.56/0.62 % Problem : Square root of a prime is irrational 13_03, 00 expansion % 0.56/0.62 % Version : Especial. % 0.56/0.62 % English : % 0.56/0.62 % 0.56/0.62 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.56/0.62 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.56/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.56/0.62 % Source : [Pas08] % 0.56/0.62 % Names : primes_13_03.00 [Pas08] % 0.56/0.62 % 0.56/0.62 % Status : ContradictoryAxioms % 0.56/0.62 % Rating : 0.08 v8.2.0, 0.06 v7.5.0, 0.00 v7.4.0, 0.29 v7.3.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.61 v4.0.0 % 0.56/0.62 % Syntax : Number of formulae : 43 ( 4 unt; 5 def) % 0.56/0.62 % Number of atoms : 192 ( 58 equ) % 0.56/0.62 % Maximal formula atoms : 10 ( 4 avg) % 0.56/0.62 % Number of connectives : 174 ( 25 ~; 7 |; 77 &) % 0.56/0.62 % ( 5 <=>; 60 =>; 0 <=; 0 <~>) % 0.56/0.62 % Maximal formula depth : 11 ( 6 avg) % 0.56/0.62 % Maximal term depth : 3 ( 1 avg) % 0.56/0.62 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.56/0.62 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty) % 0.56/0.62 % Number of variables : 83 ( 79 !; 4 ?) % 0.56/0.62 % SPC : FOF_CAX_RFO_SEQ % 0.56/0.62 % 0.56/0.62 % Comments : Problem generated by the SAD system [VLP07] % 0.56/0.62 %------------------------------------------------------------------------------ % 0.56/0.62 fof(mNatSort,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => $true ) ). % 0.56/0.62 % 0.56/0.62 fof(mSortsC,axiom, % 0.56/0.62 aNaturalNumber0(sz00) ). % 0.56/0.62 % 0.56/0.62 fof(mSortsC_01,axiom, % 0.56/0.62 ( aNaturalNumber0(sz10) % 0.56/0.62 & sz10 != sz00 ) ). % 0.56/0.62 % 0.56/0.62 fof(mSortsB,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.56/0.62 % 0.56/0.62 fof(mSortsB_02,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.56/0.62 % 0.56/0.62 fof(mAddComm,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.56/0.62 % 0.56/0.62 fof(mAddAsso,axiom, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.56/0.62 % 0.56/0.62 fof(m_AddZero,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => ( sdtpldt0(W0,sz00) = W0 % 0.56/0.62 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mMulComm,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.56/0.62 % 0.56/0.62 fof(mMulAsso,axiom, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.56/0.62 % 0.56/0.62 fof(m_MulUnit,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => ( sdtasdt0(W0,sz10) = W0 % 0.56/0.62 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(m_MulZero,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => ( sdtasdt0(W0,sz00) = sz00 % 0.56/0.62 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mAMDistr,axiom, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.56/0.62 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mAddCanc,axiom, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.56/0.62 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.56/0.62 => W1 = W2 ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mMulCanc,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => ( W0 != sz00 % 0.56/0.62 => ! [W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.56/0.62 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.56/0.62 => W1 = W2 ) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mZeroAdd,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( sdtpldt0(W0,W1) = sz00 % 0.56/0.62 => ( W0 = sz00 % 0.56/0.62 & W1 = sz00 ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mZeroMul,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( sdtasdt0(W0,W1) = sz00 % 0.56/0.62 => ( W0 = sz00 % 0.56/0.62 | W1 = sz00 ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mDefLE,definition, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( sdtlseqdt0(W0,W1) % 0.56/0.62 <=> ? [W2] : % 0.56/0.62 ( aNaturalNumber0(W2) % 0.56/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mDefDiff,definition, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( sdtlseqdt0(W0,W1) % 0.56/0.62 => ! [W2] : % 0.56/0.62 ( W2 = sdtmndt0(W1,W0) % 0.56/0.62 <=> ( aNaturalNumber0(W2) % 0.56/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mLERefl,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aNaturalNumber0(W0) % 0.56/0.62 => sdtlseqdt0(W0,W0) ) ). % 0.56/0.62 % 0.56/0.62 fof(mLEAsym,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( ( sdtlseqdt0(W0,W1) % 0.56/0.62 & sdtlseqdt0(W1,W0) ) % 0.56/0.62 => W0 = W1 ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mLETran,axiom, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) % 0.56/0.62 & aNaturalNumber0(W2) ) % 0.56/0.62 => ( ( sdtlseqdt0(W0,W1) % 0.56/0.62 & sdtlseqdt0(W1,W2) ) % 0.56/0.62 => sdtlseqdt0(W0,W2) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mLETotal,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( sdtlseqdt0(W0,W1) % 0.56/0.62 | ( W1 != W0 % 0.56/0.62 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mMonAdd,axiom, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aNaturalNumber0(W0) % 0.56/0.62 & aNaturalNumber0(W1) ) % 0.56/0.62 => ( ( W0 != W1 % 0.56/0.62 & sdtlseqdt0(W0,W1) ) % 0.56/0.62 => ! [W2] : % 0.56/0.62 ( aNaturalNumber0(W2) % 0.56/0.62 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.56/0.63 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.56/0.63 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.56/0.63 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mMonMul,axiom, % 0.56/0.63 ! [W0,W1,W2] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) % 0.56/0.63 & aNaturalNumber0(W2) ) % 0.56/0.63 => ( ( W0 != sz00 % 0.56/0.63 & W1 != W2 % 0.56/0.63 & sdtlseqdt0(W1,W2) ) % 0.56/0.63 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.56/0.63 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.56/0.63 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.56/0.63 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mLENTr,axiom, % 0.56/0.63 ! [W0] : % 0.56/0.63 ( aNaturalNumber0(W0) % 0.56/0.63 => ( W0 = sz00 % 0.56/0.63 | W0 = sz10 % 0.56/0.63 | ( sz10 != W0 % 0.56/0.63 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mMonMul2,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( W0 != sz00 % 0.56/0.63 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mIH,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( iLess0(W0,W1) % 0.56/0.63 => $true ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mIH_03,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( ( W0 != W1 % 0.56/0.63 & sdtlseqdt0(W0,W1) ) % 0.56/0.63 => iLess0(W0,W1) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDefDiv,definition, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( doDivides0(W0,W1) % 0.56/0.63 <=> ? [W2] : % 0.56/0.63 ( aNaturalNumber0(W2) % 0.56/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDefQuot,definition, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( ( W0 != sz00 % 0.56/0.63 & doDivides0(W0,W1) ) % 0.56/0.63 => ! [W2] : % 0.56/0.63 ( W2 = sdtsldt0(W1,W0) % 0.56/0.63 <=> ( aNaturalNumber0(W2) % 0.56/0.63 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDivTrans,axiom, % 0.56/0.63 ! [W0,W1,W2] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) % 0.56/0.63 & aNaturalNumber0(W2) ) % 0.56/0.63 => ( ( doDivides0(W0,W1) % 0.56/0.63 & doDivides0(W1,W2) ) % 0.56/0.63 => doDivides0(W0,W2) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDivSum,axiom, % 0.56/0.63 ! [W0,W1,W2] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) % 0.56/0.63 & aNaturalNumber0(W2) ) % 0.56/0.63 => ( ( doDivides0(W0,W1) % 0.56/0.63 & doDivides0(W0,W2) ) % 0.56/0.63 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDivMin,axiom, % 0.56/0.63 ! [W0,W1,W2] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) % 0.56/0.63 & aNaturalNumber0(W2) ) % 0.56/0.63 => ( ( doDivides0(W0,W1) % 0.56/0.63 & doDivides0(W0,sdtpldt0(W1,W2)) ) % 0.56/0.63 => doDivides0(W0,W2) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDivLE,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( ( doDivides0(W0,W1) % 0.56/0.63 & W1 != sz00 ) % 0.56/0.63 => sdtlseqdt0(W0,W1) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDivAsso,axiom, % 0.56/0.63 ! [W0,W1] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & aNaturalNumber0(W1) ) % 0.56/0.63 => ( ( W0 != sz00 % 0.56/0.63 & doDivides0(W0,W1) ) % 0.56/0.63 => ! [W2] : % 0.56/0.63 ( aNaturalNumber0(W2) % 0.56/0.63 => sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(mDefPrime,definition, % 0.56/0.63 ! [W0] : % 0.56/0.63 ( aNaturalNumber0(W0) % 0.56/0.63 => ( isPrime0(W0) % 0.56/0.63 <=> ( W0 != sz00 % 0.56/0.63 & W0 != sz10 % 0.56/0.63 & ! [W1] : % 0.56/0.63 ( ( aNaturalNumber0(W1) % 0.56/0.63 & doDivides0(W1,W0) ) % 0.56/0.63 => ( W1 = sz10 % 0.56/0.63 | W1 = W0 ) ) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(m__1716,hypothesis, % 0.56/0.63 aNaturalNumber0(xk) ). % 0.56/0.63 % 0.56/0.63 fof(m__1700,hypothesis, % 0.56/0.63 ! [W0] : % 0.56/0.63 ( ( aNaturalNumber0(W0) % 0.56/0.63 & W0 != sz00 % 0.56/0.63 & W0 != sz10 ) % 0.56/0.63 => ( iLess0(W0,xk) % 0.56/0.63 => ? [W1] : % 0.56/0.63 ( aNaturalNumber0(W1) % 0.56/0.63 & doDivides0(W1,W0) % 0.56/0.63 & isPrime0(W1) ) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(m__1716_04,hypothesis, % 0.56/0.63 ( xk != sz00 % 0.56/0.63 & xk != sz10 ) ). % 0.56/0.63 % 0.56/0.63 fof(m__1725,hypothesis, % 0.56/0.63 ~ isPrime0(xk) ). % 0.56/0.63 % 0.56/0.63 fof(m__1737,hypothesis, % 0.56/0.63 ~ ~ isPrime0(xk) ). % 0.56/0.63 % 0.56/0.63 fof(m__,conjecture, % 0.56/0.63 ? [W0] : % 0.56/0.63 ( aNaturalNumber0(W0) % 0.56/0.63 & doDivides0(W0,xk) % 0.56/0.63 & isPrime0(W0) ) ). % 0.56/0.63 % 0.56/0.63 %------------------------------------------------------------------------------ % 0.56/0.63 %------------------------------------------- % 0.56/0.63 % Proof found % 0.56/0.63 % SZS status Theorem for theBenchmark % 0.56/0.63 % SZS output start Proof % 0.56/0.63 %ClaNum:98(EqnAxiom:25) % 0.56/0.63 %VarNum:432(SingletonVarNum:129) % 0.56/0.63 %MaxLitNum:7 % 0.56/0.63 %MaxfuncDepth:2 % 0.56/0.63 %SharedTerms:11 % 0.56/0.63 %goalClause: 48 % 0.56/0.63 [26]P1(a1) % 0.56/0.63 [27]P1(a10) % 0.56/0.63 [28]P1(a11) % 0.56/0.63 [29]P2(a11) % 0.56/0.63 [30]~E(a1,a10) % 0.56/0.63 [31]~E(a1,a11) % 0.56/0.63 [32]~E(a11,a10) % 0.56/0.63 [33]~P2(a11) % 0.56/0.63 [42]~P1(x421)+P5(x421,x421) % 0.56/0.63 [36]~P1(x361)+E(f2(a1,x361),a1) % 0.56/0.63 [37]~P1(x371)+E(f2(x371,a1),a1) % 0.56/0.63 [38]~P1(x381)+E(f7(a1,x381),x381) % 0.56/0.63 [39]~P1(x391)+E(f2(a10,x391),x391) % 0.56/0.63 [40]~P1(x401)+E(f7(x401,a1),x401) % 0.56/0.63 [41]~P1(x411)+E(f2(x411,a10),x411) % 0.56/0.63 [34]~P1(x341)+~P2(x341)+~E(x341,a1) % 0.56/0.63 [35]~P1(x351)+~P2(x351)+~E(x351,a10) % 0.56/0.63 [48]~P2(x481)+~P1(x481)+~P3(x481,a11) % 0.56/0.63 [55]~P1(x552)+~P1(x551)+E(f7(x551,x552),f7(x552,x551)) % 0.56/0.63 [56]~P1(x562)+~P1(x561)+E(f2(x561,x562),f2(x562,x561)) % 0.56/0.63 [58]~P1(x582)+~P1(x581)+P1(f7(x581,x582)) % 0.56/0.63 [59]~P1(x592)+~P1(x591)+P1(f2(x591,x592)) % 0.56/0.63 [44]~P1(x441)+E(x441,a10)+P5(a10,x441)+E(x441,a1) % 0.56/0.63 [47]~E(x472,x471)+~P1(x471)+~P1(x472)+P5(x471,x472) % 0.56/0.63 [57]P5(x572,x571)+~P1(x571)+~P1(x572)+P5(x571,x572) % 0.56/0.63 [50]~P1(x502)+~P1(x501)+E(x501,a1)+~E(f7(x502,x501),a1) % 0.56/0.63 [51]~P1(x512)+~P1(x511)+E(x511,a1)+~E(f7(x511,x512),a1) % 0.56/0.63 [64]~P1(x642)+~P1(x641)+P5(x642,f2(x642,x641))+E(x641,a1) % 0.56/0.63 [70]~P1(x702)+~P1(x701)+~P5(x701,x702)+P1(f4(x701,x702)) % 0.56/0.63 [71]~P1(x712)+~P1(x711)+~P3(x711,x712)+P1(f5(x711,x712)) % 0.56/0.63 [78]~P1(x781)+~P1(x782)+~P3(x781,x782)+E(f2(x781,f5(x781,x782)),x782) % 0.56/0.63 [79]~P1(x792)+~P1(x791)+~P5(x791,x792)+E(f7(x791,f4(x791,x792)),x792) % 0.56/0.63 [88]~P1(x883)+~P1(x882)+~P1(x881)+E(f7(f7(x881,x882),x883),f7(x881,f7(x882,x883))) % 0.56/0.63 [89]~P1(x893)+~P1(x892)+~P1(x891)+E(f2(f2(x891,x892),x893),f2(x891,f2(x892,x893))) % 0.56/0.63 [97]~P1(x973)+~P1(x972)+~P1(x971)+E(f7(f2(x971,x972),f2(x971,x973)),f2(x971,f7(x972,x973))) % 0.56/0.63 [98]~P1(x982)+~P1(x983)+~P1(x981)+E(f7(f2(x981,x982),f2(x983,x982)),f2(f7(x981,x983),x982)) % 0.56/0.63 [43]P2(x431)+~P1(x431)+E(x431,a10)+E(x431,a1)+~E(f3(x431),a10) % 0.56/0.63 [45]P2(x451)+~P1(x451)+E(x451,a10)+~E(f3(x451),x451)+E(x451,a1) % 0.56/0.63 [46]P2(x461)+~P1(x461)+E(x461,a10)+E(x461,a1)+P1(f3(x461)) % 0.56/0.63 [49]P2(x491)+~P1(x491)+E(x491,a10)+P3(f3(x491),x491)+E(x491,a1) % 0.56/0.63 [53]~P1(x531)+E(x531,a10)+~P4(x531,a11)+E(x531,a1)+P1(f6(x531)) % 0.56/0.63 [54]~P1(x541)+E(x541,a10)+~P4(x541,a11)+E(x541,a1)+P2(f6(x541)) % 0.56/0.63 [61]~P1(x611)+E(x611,a10)+P3(f6(x611),x611)+~P4(x611,a11)+E(x611,a1) % 0.56/0.63 [62]~P1(x621)+~P1(x622)+~P3(x622,x621)+P5(x622,x621)+E(x621,a1) % 0.56/0.63 [63]P4(x631,x632)+~P1(x632)+~P1(x631)+~P5(x631,x632)+E(x631,x632) % 0.56/0.63 [67]~P1(x672)+~P1(x671)+~P5(x672,x671)+~P5(x671,x672)+E(x671,x672) % 0.56/0.63 [52]~P1(x521)+~P1(x522)+E(x521,a1)+E(x522,a1)+~E(f2(x522,x521),a1) % 0.56/0.63 [65]~P1(x651)+~P1(x652)+~P1(x653)+P3(x651,x652)+~E(x652,f2(x651,x653)) % 0.56/0.63 [66]~P1(x662)+~P1(x661)+~P1(x663)+P5(x661,x662)+~E(f7(x661,x663),x662) % 0.56/0.63 [68]~P1(x683)+~P1(x682)+~P5(x683,x682)+P1(x681)+~E(x681,f8(x682,x683)) % 0.56/0.63 [72]~P1(x722)+~P1(x721)+~P1(x723)+E(x721,x722)+~E(f7(x723,x721),f7(x723,x722)) % 0.56/0.63 [73]~P1(x732)+~P1(x733)+~P1(x731)+E(x731,x732)+~E(f7(x731,x733),f7(x732,x733)) % 0.56/0.63 [76]~P1(x763)+~P1(x761)+~P5(x761,x763)+~E(x762,f8(x763,x761))+E(f7(x761,x762),x763) % 0.56/0.63 [60]~P1(x602)+~P1(x601)+~P2(x602)+~P3(x601,x602)+E(x601,x602)+E(x601,a10) % 0.56/0.63 [80]~P1(x802)+~P1(x801)+~P5(x803,x802)+~P5(x801,x803)+P5(x801,x802)+~P1(x803) % 0.56/0.63 [81]~P1(x812)+~P1(x811)+~P3(x813,x812)+~P3(x811,x813)+P3(x811,x812)+~P1(x813) % 0.56/0.63 [69]~P1(x691)+~P1(x693)+~P3(x691,x693)+P1(x692)+E(x691,a1)+~E(x692,f9(x693,x691)) % 0.56/0.63 [74]~P1(x742)+~P1(x741)+~P1(x743)+E(x741,x742)+~E(f2(x743,x741),f2(x743,x742))+E(x743,a1) % 0.56/0.63 [75]~P1(x752)+~P1(x753)+~P1(x751)+E(x751,x752)+~E(f2(x751,x753),f2(x752,x753))+E(x753,a1) % 0.56/0.63 [77]~P1(x771)+~P1(x772)+~P3(x771,x772)+~E(x773,f9(x772,x771))+E(x771,a1)+E(x772,f2(x771,x773)) % 0.56/0.63 [82]~P1(x822)+~P1(x823)+~P1(x821)+~P5(x823,x822)+~E(f7(x823,x821),x822)+E(x821,f8(x822,x823)) % 0.56/0.63 [90]~P1(x903)+~P1(x902)+~P1(x901)+~P3(x901,x903)+~P3(x901,x902)+P3(x901,f7(x902,x903)) % 0.56/0.63 [91]~P1(x912)+~P1(x911)+~P1(x913)+~P5(x911,x912)+E(x911,x912)+P5(f7(x913,x911),f7(x913,x912)) % 0.56/0.63 [92]~P1(x922)+~P1(x923)+~P1(x921)+~P5(x921,x922)+E(x921,x922)+P5(f7(x921,x923),f7(x922,x923)) % 0.56/0.63 [95]~P1(x952)+~P1(x951)+~P3(x951,x953)+P3(x951,x952)+~P1(x953)+~P3(x951,f7(x953,x952)) % 0.56/0.63 [96]~P1(x962)+~P1(x963)+~P1(x961)+~P3(x961,x963)+E(x961,a1)+E(f9(f2(x962,x963),x961),f2(x962,f9(x963,x961))) % 0.56/0.63 [83]~P1(x831)+~P1(x833)+~P1(x832)+~P3(x831,x833)+~E(x833,f2(x831,x832))+E(x831,a1)+E(x832,f9(x833,x831)) % 0.56/0.63 [93]~P1(x932)+~P1(x931)+~P1(x933)+~P5(x931,x932)+E(x931,x932)+P5(f2(x933,x931),f2(x933,x932))+E(x933,a1) % 0.56/0.63 [94]~P1(x942)+~P1(x943)+~P1(x941)+~P5(x941,x942)+E(x941,x942)+P5(f2(x941,x943),f2(x942,x943))+E(x943,a1) % 0.56/0.63 %EqnAxiom % 0.56/0.63 [1]E(x11,x11) % 0.56/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.63 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.56/0.63 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.56/0.63 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 0.56/0.63 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 0.56/0.63 [8]~E(x81,x82)+E(f9(x81,x83),f9(x82,x83)) % 0.56/0.63 [9]~E(x91,x92)+E(f9(x93,x91),f9(x93,x92)) % 0.56/0.63 [10]~E(x101,x102)+E(f8(x101,x103),f8(x102,x103)) % 0.56/0.63 [11]~E(x111,x112)+E(f8(x113,x111),f8(x113,x112)) % 0.56/0.63 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123)) % 0.56/0.63 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132)) % 0.56/0.63 [14]~E(x141,x142)+E(f5(x141,x143),f5(x142,x143)) % 0.56/0.63 [15]~E(x151,x152)+E(f5(x153,x151),f5(x153,x152)) % 0.56/0.63 [16]~E(x161,x162)+E(f3(x161),f3(x162)) % 0.56/0.63 [17]~E(x171,x172)+E(f6(x171),f6(x172)) % 0.56/0.63 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.56/0.63 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193) % 0.56/0.63 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201) % 0.56/0.63 [21]P4(x212,x213)+~E(x211,x212)+~P4(x211,x213) % 0.56/0.63 [22]P4(x223,x222)+~E(x221,x222)+~P4(x223,x221) % 0.56/0.63 [23]~P2(x231)+P2(x232)+~E(x231,x232) % 0.56/0.63 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.56/0.63 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.56/0.63 % 0.56/0.63 %------------------------------------------- % 0.56/0.63 cnf(114,plain, % 0.56/0.63 ($false), % 0.56/0.63 inference(scs_inference,[],[29,33]), % 0.56/0.63 ['proof']). % 0.56/0.63 % SZS output end Proof % 0.56/0.63 % Total time :0.010000s %------------------------------------------------------------------------------