%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM472+2 : 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 12:24:26 EDT 2024 % Result : Theorem 0.58s 0.67s % Output : CNFRefutation 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : NUM472+2 : TPTP v8.2.0. Released v4.0.0. % 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.35 % DateTime : Sun Jun 23 02:48:09 EDT 2024 % 0.12/0.35 % CPUTime : % 0.20/0.58 start to proof:theBenchmark % 0.58/0.65 %------------------------------------------- % 0.58/0.65 % File :CSE---1.7 % 0.58/0.65 % Problem :theBenchmark % 0.58/0.65 % Transform :cnf % 0.58/0.65 % Format :tptp:raw % 0.58/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.58/0.65 % 0.58/0.65 % Result :Theorem 0.010000s % 0.58/0.65 % Output :CNFRefutation 0.010000s % 0.58/0.65 %------------------------------------------- % 0.58/0.66 %------------------------------------------------------------------------------ % 0.58/0.66 % File : NUM472+2 : TPTP v8.2.0. Released v4.0.0. % 0.58/0.66 % Domain : Number Theory % 0.58/0.66 % Problem : Square root of a prime is irrational 10_03_01, 01 expansion % 0.58/0.66 % Version : Especial. % 0.58/0.66 % English : % 0.58/0.66 % 0.58/0.66 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.58/0.66 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.58/0.66 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.58/0.66 % Source : [Pas08] % 0.58/0.66 % Names : primes_10_03_01.01 [Pas08] % 0.58/0.66 % 0.58/0.66 % Status : Theorem % 0.58/0.66 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.04 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0 % 0.58/0.66 % Syntax : Number of formulae : 39 ( 2 unt; 4 def) % 0.58/0.66 % Number of atoms : 171 ( 55 equ) % 0.58/0.66 % Maximal formula atoms : 10 ( 4 avg) % 0.58/0.66 % Number of connectives : 147 ( 15 ~; 7 |; 72 &) % 0.58/0.66 % ( 4 <=>; 49 =>; 0 <=; 0 <~>) % 0.58/0.66 % Maximal formula depth : 11 ( 6 avg) % 0.58/0.66 % Maximal term depth : 3 ( 1 avg) % 0.58/0.66 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty) % 0.58/0.66 % Number of functors : 11 ( 11 usr; 7 con; 0-2 aty) % 0.58/0.66 % Number of variables : 73 ( 68 !; 5 ?) % 0.58/0.66 % SPC : FOF_THM_RFO_SEQ % 0.58/0.66 % 0.58/0.66 % Comments : Problem generated by the SAD system [VLP07] % 0.58/0.66 %------------------------------------------------------------------------------ % 0.58/0.66 fof(mNatSort,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => $true ) ). % 0.58/0.66 % 0.58/0.66 fof(mSortsC,axiom, % 0.58/0.66 aNaturalNumber0(sz00) ). % 0.58/0.66 % 0.58/0.66 fof(mSortsC_01,axiom, % 0.58/0.66 ( aNaturalNumber0(sz10) % 0.58/0.66 & sz10 != sz00 ) ). % 0.58/0.66 % 0.58/0.66 fof(mSortsB,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.58/0.66 % 0.58/0.66 fof(mSortsB_02,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.58/0.66 % 0.58/0.66 fof(mAddComm,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.58/0.66 % 0.58/0.66 fof(mAddAsso,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.58/0.66 % 0.58/0.66 fof(m_AddZero,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => ( sdtpldt0(W0,sz00) = W0 % 0.58/0.66 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mMulComm,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.58/0.66 % 0.58/0.66 fof(mMulAsso,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.58/0.66 % 0.58/0.66 fof(m_MulUnit,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => ( sdtasdt0(W0,sz10) = W0 % 0.58/0.66 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(m_MulZero,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => ( sdtasdt0(W0,sz00) = sz00 % 0.58/0.66 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mAMDistr,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.58/0.66 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mAddCanc,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.58/0.66 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.58/0.66 => W1 = W2 ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mMulCanc,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => ( W0 != sz00 % 0.58/0.66 => ! [W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.58/0.66 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.58/0.66 => W1 = W2 ) ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mZeroAdd,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( sdtpldt0(W0,W1) = sz00 % 0.58/0.66 => ( W0 = sz00 % 0.58/0.66 & W1 = sz00 ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mZeroMul,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( sdtasdt0(W0,W1) = sz00 % 0.58/0.66 => ( W0 = sz00 % 0.58/0.66 | W1 = sz00 ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mDefLE,definition, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( sdtlseqdt0(W0,W1) % 0.58/0.66 <=> ? [W2] : % 0.58/0.66 ( aNaturalNumber0(W2) % 0.58/0.66 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mDefDiff,definition, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( sdtlseqdt0(W0,W1) % 0.58/0.66 => ! [W2] : % 0.58/0.66 ( W2 = sdtmndt0(W1,W0) % 0.58/0.66 <=> ( aNaturalNumber0(W2) % 0.58/0.66 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mLERefl,axiom, % 0.58/0.66 ! [W0] : % 0.58/0.66 ( aNaturalNumber0(W0) % 0.58/0.66 => sdtlseqdt0(W0,W0) ) ). % 0.58/0.66 % 0.58/0.66 fof(mLEAsym,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( ( sdtlseqdt0(W0,W1) % 0.58/0.66 & sdtlseqdt0(W1,W0) ) % 0.58/0.66 => W0 = W1 ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mLETran,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.66 & aNaturalNumber0(W2) ) % 0.58/0.66 => ( ( sdtlseqdt0(W0,W1) % 0.58/0.66 & sdtlseqdt0(W1,W2) ) % 0.58/0.66 => sdtlseqdt0(W0,W2) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mLETotal,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( sdtlseqdt0(W0,W1) % 0.58/0.66 | ( W1 != W0 % 0.58/0.66 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mMonAdd,axiom, % 0.58/0.66 ! [W0,W1] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) ) % 0.58/0.66 => ( ( W0 != W1 % 0.58/0.66 & sdtlseqdt0(W0,W1) ) % 0.58/0.66 => ! [W2] : % 0.58/0.66 ( aNaturalNumber0(W2) % 0.58/0.66 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.58/0.66 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.58/0.66 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.58/0.66 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.58/0.66 % 0.58/0.66 fof(mMonMul,axiom, % 0.58/0.66 ! [W0,W1,W2] : % 0.58/0.66 ( ( aNaturalNumber0(W0) % 0.58/0.66 & aNaturalNumber0(W1) % 0.58/0.67 & aNaturalNumber0(W2) ) % 0.58/0.67 => ( ( W0 != sz00 % 0.58/0.67 & W1 != W2 % 0.58/0.67 & sdtlseqdt0(W1,W2) ) % 0.58/0.67 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.58/0.67 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.58/0.67 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.58/0.67 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mLENTr,axiom, % 0.58/0.67 ! [W0] : % 0.58/0.67 ( aNaturalNumber0(W0) % 0.58/0.67 => ( W0 = sz00 % 0.58/0.67 | W0 = sz10 % 0.58/0.67 | ( sz10 != W0 % 0.58/0.67 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mMonMul2,axiom, % 0.58/0.67 ! [W0,W1] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) ) % 0.58/0.67 => ( W0 != sz00 % 0.58/0.67 => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mIH,axiom, % 0.58/0.67 ! [W0,W1] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) ) % 0.58/0.67 => ( iLess0(W0,W1) % 0.58/0.67 => $true ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mIH_03,axiom, % 0.58/0.67 ! [W0,W1] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) ) % 0.58/0.67 => ( ( W0 != W1 % 0.58/0.67 & sdtlseqdt0(W0,W1) ) % 0.58/0.67 => iLess0(W0,W1) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mDefDiv,definition, % 0.58/0.67 ! [W0,W1] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) ) % 0.58/0.67 => ( doDivides0(W0,W1) % 0.58/0.67 <=> ? [W2] : % 0.58/0.67 ( aNaturalNumber0(W2) % 0.58/0.67 & W1 = sdtasdt0(W0,W2) ) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mDefQuot,definition, % 0.58/0.67 ! [W0,W1] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) ) % 0.58/0.67 => ( ( W0 != sz00 % 0.58/0.67 & doDivides0(W0,W1) ) % 0.58/0.67 => ! [W2] : % 0.58/0.67 ( W2 = sdtsldt0(W1,W0) % 0.58/0.67 <=> ( aNaturalNumber0(W2) % 0.58/0.67 & W1 = sdtasdt0(W0,W2) ) ) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mDivTrans,axiom, % 0.58/0.67 ! [W0,W1,W2] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) % 0.58/0.67 & aNaturalNumber0(W2) ) % 0.58/0.67 => ( ( doDivides0(W0,W1) % 0.58/0.67 & doDivides0(W1,W2) ) % 0.58/0.67 => doDivides0(W0,W2) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(mDivSum,axiom, % 0.58/0.67 ! [W0,W1,W2] : % 0.58/0.67 ( ( aNaturalNumber0(W0) % 0.58/0.67 & aNaturalNumber0(W1) % 0.58/0.67 & aNaturalNumber0(W2) ) % 0.58/0.67 => ( ( doDivides0(W0,W1) % 0.58/0.67 & doDivides0(W0,W2) ) % 0.58/0.67 => doDivides0(W0,sdtpldt0(W1,W2)) ) ) ). % 0.58/0.67 % 0.58/0.67 fof(m__1324,hypothesis, % 0.58/0.67 ( aNaturalNumber0(xl) % 0.58/0.67 & aNaturalNumber0(xm) % 0.58/0.67 & aNaturalNumber0(xn) ) ). % 0.58/0.67 % 0.58/0.67 fof(m__1324_04,hypothesis, % 0.58/0.67 ( ? [W0] : % 0.58/0.67 ( aNaturalNumber0(W0) % 0.58/0.67 & xm = sdtasdt0(xl,W0) ) % 0.58/0.67 & doDivides0(xl,xm) % 0.58/0.67 & ? [W0] : % 0.58/0.67 ( aNaturalNumber0(W0) % 0.58/0.67 & sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ) % 0.58/0.67 & doDivides0(xl,sdtpldt0(xm,xn)) ) ). % 0.58/0.67 % 0.58/0.67 fof(m__1347,hypothesis, % 0.58/0.67 xl != sz00 ). % 0.58/0.67 % 0.58/0.67 fof(m__1360,hypothesis, % 0.58/0.67 ( aNaturalNumber0(xp) % 0.58/0.67 & xm = sdtasdt0(xl,xp) % 0.58/0.67 & xp = sdtsldt0(xm,xl) ) ). % 0.58/0.67 % 0.58/0.67 fof(m__1379,hypothesis, % 0.58/0.67 ( aNaturalNumber0(xq) % 0.58/0.67 & sdtpldt0(xm,xn) = sdtasdt0(xl,xq) % 0.58/0.67 & xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ). % 0.58/0.67 % 0.58/0.67 fof(m__,conjecture, % 0.58/0.67 ( ? [W0] : % 0.58/0.67 ( aNaturalNumber0(W0) % 0.58/0.67 & sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) % 0.58/0.67 | sdtlseqdt0(xm,sdtpldt0(xm,xn)) ) ). % 0.58/0.67 % 0.58/0.67 %------------------------------------------------------------------------------ % 0.58/0.67 %------------------------------------------- % 0.58/0.67 % Proof found % 0.58/0.67 % SZS status Theorem for theBenchmark % 0.58/0.67 % SZS output start Proof % 0.58/0.67 %ClaNum:94(EqnAxiom:22) % 0.58/0.67 %VarNum:350(SingletonVarNum:110) % 0.58/0.67 %MaxLitNum:7 % 0.58/0.67 %MaxfuncDepth:2 % 0.58/0.67 %SharedTerms:36 % 0.58/0.67 %goalClause: 42 58 % 0.58/0.67 %singleGoalClaCount:1 % 0.58/0.67 [23]P1(a1) % 0.58/0.67 [24]P1(a10) % 0.58/0.67 [25]P1(a11) % 0.58/0.67 [26]P1(a12) % 0.58/0.67 [27]P1(a13) % 0.58/0.67 [28]P1(a14) % 0.58/0.67 [29]P1(a15) % 0.58/0.67 [30]P1(a2) % 0.58/0.67 [31]P1(a5) % 0.58/0.67 [35]P2(a11,a12) % 0.58/0.67 [40]~E(a1,a10) % 0.58/0.67 [41]~E(a1,a11) % 0.58/0.67 [32]E(f6(a11,a14),a12) % 0.58/0.67 [33]E(f6(a11,a2),a12) % 0.58/0.67 [34]E(f7(a12,a11),a14) % 0.58/0.67 [36]E(f8(a12,a13),f6(a11,a15)) % 0.58/0.67 [37]E(f8(a12,a13),f6(a11,a5)) % 0.58/0.67 [39]P2(a11,f8(a12,a13)) % 0.58/0.67 [42]~P3(a12,f8(a12,a13)) % 0.58/0.67 [38]E(f7(f8(a12,a13),a11),a15) % 0.58/0.67 [49]~P1(x491)+P3(x491,x491) % 0.58/0.67 [43]~P1(x431)+E(f6(a1,x431),a1) % 0.58/0.67 [44]~P1(x441)+E(f6(x441,a1),a1) % 0.58/0.67 [45]~P1(x451)+E(f8(a1,x451),x451) % 0.58/0.67 [46]~P1(x461)+E(f6(a10,x461),x461) % 0.58/0.67 [47]~P1(x471)+E(f8(x471,a1),x471) % 0.58/0.67 [48]~P1(x481)+E(f6(x481,a10),x481) % 0.58/0.67 [58]~P1(x581)+~E(f8(a12,x581),f8(a12,a13)) % 0.58/0.67 [55]~P1(x552)+~P1(x551)+E(f8(x551,x552),f8(x552,x551)) % 0.58/0.67 [56]~P1(x562)+~P1(x561)+E(f6(x561,x562),f6(x562,x561)) % 0.58/0.67 [59]~P1(x592)+~P1(x591)+P1(f8(x591,x592)) % 0.58/0.67 [60]~P1(x602)+~P1(x601)+P1(f6(x601,x602)) % 0.58/0.67 [50]~P1(x501)+E(x501,a10)+P3(a10,x501)+E(x501,a1) % 0.58/0.67 [51]~E(x512,x511)+~P1(x511)+~P1(x512)+P3(x511,x512) % 0.58/0.67 [57]P3(x572,x571)+~P1(x571)+~P1(x572)+P3(x571,x572) % 0.58/0.67 [52]~P1(x522)+~P1(x521)+E(x521,a1)+~E(f8(x522,x521),a1) % 0.58/0.67 [53]~P1(x532)+~P1(x531)+E(x531,a1)+~E(f8(x531,x532),a1) % 0.58/0.67 [62]~P1(x622)+~P1(x621)+P3(x622,f6(x622,x621))+E(x621,a1) % 0.58/0.67 [68]~P1(x682)+~P1(x681)+~P3(x681,x682)+P1(f3(x681,x682)) % 0.58/0.67 [69]~P1(x692)+~P1(x691)+~P2(x691,x692)+P1(f4(x691,x692)) % 0.58/0.67 [76]~P1(x761)+~P1(x762)+~P2(x761,x762)+E(f6(x761,f4(x761,x762)),x762) % 0.58/0.67 [77]~P1(x772)+~P1(x771)+~P3(x771,x772)+E(f8(x771,f3(x771,x772)),x772) % 0.58/0.67 [86]~P1(x863)+~P1(x862)+~P1(x861)+E(f8(f8(x861,x862),x863),f8(x861,f8(x862,x863))) % 0.58/0.67 [87]~P1(x873)+~P1(x872)+~P1(x871)+E(f6(f6(x871,x872),x873),f6(x871,f6(x872,x873))) % 0.58/0.67 [93]~P1(x933)+~P1(x932)+~P1(x931)+E(f8(f6(x931,x932),f6(x931,x933)),f6(x931,f8(x932,x933))) % 0.58/0.67 [94]~P1(x942)+~P1(x943)+~P1(x941)+E(f8(f6(x941,x942),f6(x943,x942)),f6(f8(x941,x943),x942)) % 0.58/0.67 [61]P4(x611,x612)+~P1(x612)+~P1(x611)+~P3(x611,x612)+E(x611,x612) % 0.58/0.67 [65]~P1(x652)+~P1(x651)+~P3(x652,x651)+~P3(x651,x652)+E(x651,x652) % 0.58/0.67 [54]~P1(x541)+~P1(x542)+E(x541,a1)+E(x542,a1)+~E(f6(x542,x541),a1) % 0.58/0.67 [63]~P1(x631)+~P1(x632)+~P1(x633)+P2(x631,x632)+~E(x632,f6(x631,x633)) % 0.58/0.67 [64]~P1(x642)+~P1(x641)+~P1(x643)+P3(x641,x642)+~E(f8(x641,x643),x642) % 0.58/0.67 [66]~P1(x663)+~P1(x662)+~P3(x663,x662)+P1(x661)+~E(x661,f9(x662,x663)) % 0.58/0.67 [70]~P1(x702)+~P1(x701)+~P1(x703)+E(x701,x702)+~E(f8(x703,x701),f8(x703,x702)) % 0.58/0.67 [71]~P1(x712)+~P1(x713)+~P1(x711)+E(x711,x712)+~E(f8(x711,x713),f8(x712,x713)) % 0.58/0.67 [74]~P1(x743)+~P1(x741)+~P3(x741,x743)+~E(x742,f9(x743,x741))+E(f8(x741,x742),x743) % 0.58/0.67 [78]~P1(x782)+~P1(x781)+~P3(x783,x782)+~P3(x781,x783)+P3(x781,x782)+~P1(x783) % 0.58/0.67 [79]~P1(x792)+~P1(x791)+~P2(x793,x792)+~P2(x791,x793)+P2(x791,x792)+~P1(x793) % 0.58/0.67 [67]~P1(x671)+~P1(x673)+~P2(x671,x673)+P1(x672)+E(x671,a1)+~E(x672,f7(x673,x671)) % 0.58/0.67 [72]~P1(x722)+~P1(x721)+~P1(x723)+E(x721,x722)+~E(f6(x723,x721),f6(x723,x722))+E(x723,a1) % 0.58/0.67 [73]~P1(x732)+~P1(x733)+~P1(x731)+E(x731,x732)+~E(f6(x731,x733),f6(x732,x733))+E(x733,a1) % 0.58/0.67 [75]~P1(x751)+~P1(x752)+~P2(x751,x752)+~E(x753,f7(x752,x751))+E(x751,a1)+E(x752,f6(x751,x753)) % 0.58/0.67 [80]~P1(x802)+~P1(x803)+~P1(x801)+~P3(x803,x802)+~E(f8(x803,x801),x802)+E(x801,f9(x802,x803)) % 0.58/0.67 [88]~P1(x883)+~P1(x882)+~P1(x881)+~P2(x881,x883)+~P2(x881,x882)+P2(x881,f8(x882,x883)) % 0.58/0.67 [89]~P1(x892)+~P1(x891)+~P1(x893)+~P3(x891,x892)+E(x891,x892)+P3(f8(x893,x891),f8(x893,x892)) % 0.58/0.67 [90]~P1(x902)+~P1(x903)+~P1(x901)+~P3(x901,x902)+E(x901,x902)+P3(f8(x901,x903),f8(x902,x903)) % 0.58/0.67 [81]~P1(x811)+~P1(x813)+~P1(x812)+~P2(x811,x813)+~E(x813,f6(x811,x812))+E(x811,a1)+E(x812,f7(x813,x811)) % 0.58/0.67 [91]~P1(x912)+~P1(x911)+~P1(x913)+~P3(x911,x912)+E(x911,x912)+P3(f6(x913,x911),f6(x913,x912))+E(x913,a1) % 0.58/0.67 [92]~P1(x922)+~P1(x923)+~P1(x921)+~P3(x921,x922)+E(x921,x922)+P3(f6(x921,x923),f6(x922,x923))+E(x923,a1) % 0.58/0.67 %EqnAxiom % 0.58/0.67 [1]E(x11,x11) % 0.58/0.67 [2]E(x22,x21)+~E(x21,x22) % 0.58/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.58/0.67 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43)) % 0.58/0.67 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52)) % 0.58/0.67 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63)) % 0.58/0.67 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72)) % 0.58/0.67 [8]~E(x81,x82)+E(f7(x81,x83),f7(x82,x83)) % 0.58/0.67 [9]~E(x91,x92)+E(f7(x93,x91),f7(x93,x92)) % 0.58/0.67 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.58/0.67 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.58/0.67 [12]~E(x121,x122)+E(f3(x121,x123),f3(x122,x123)) % 0.58/0.67 [13]~E(x131,x132)+E(f3(x133,x131),f3(x133,x132)) % 0.58/0.67 [14]~E(x141,x142)+E(f4(x141,x143),f4(x142,x143)) % 0.58/0.67 [15]~E(x151,x152)+E(f4(x153,x151),f4(x153,x152)) % 0.58/0.67 [16]~P1(x161)+P1(x162)+~E(x161,x162) % 0.58/0.67 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173) % 0.58/0.67 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181) % 0.58/0.67 [19]P4(x192,x193)+~E(x191,x192)+~P4(x191,x193) % 0.58/0.67 [20]P4(x203,x202)+~E(x201,x202)+~P4(x203,x201) % 0.58/0.67 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213) % 0.58/0.67 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221) % 0.58/0.67 % 0.58/0.67 %------------------------------------------- % 0.58/0.67 cnf(96,plain, % 0.58/0.67 (~P1(a13)), % 0.58/0.67 inference(equality_inference,[],[58])). % 0.58/0.67 cnf(109,plain, % 0.58/0.67 ($false), % 0.58/0.67 inference(scs_inference,[],[96,27]), % 0.58/0.67 ['proof']). % 0.58/0.67 % SZS output end Proof % 0.58/0.67 % Total time :0.010000s %------------------------------------------------------------------------------