%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : RNG050+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 : n026.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 14:00:52 EDT 2024 % Result : Theorem 0.53s 0.64s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG050+1 : TPTP v8.2.0. Released v4.0.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n026.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Jun 18 14:16:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.49/0.56 start to proof:theBenchmark % 0.53/0.63 %------------------------------------------- % 0.53/0.63 % File :CSE---1.7 % 0.53/0.63 % Problem :theBenchmark % 0.53/0.63 % Transform :cnf % 0.53/0.63 % Format :tptp:raw % 0.53/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.63 % 0.53/0.63 % Result :Theorem 0.010000s % 0.53/0.63 % Output :CNFRefutation 0.010000s % 0.53/0.63 %------------------------------------------- % 0.53/0.64 %------------------------------------------------------------------------------ % 0.53/0.64 % File : RNG050+1 : TPTP v8.2.0. Released v4.0.0. % 0.53/0.64 % Domain : Ring Theory % 0.53/0.64 % Problem : Cauchy-Bouniakowsky-Schwarz inequality 04_04, 00 expansion % 0.53/0.64 % Version : Especial. % 0.53/0.64 % English : % 0.53/0.64 % 0.53/0.64 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.53/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.53/0.64 % Source : [Pas08] % 0.53/0.64 % Names : cauchy_04_04.00 [Pas08] % 0.53/0.64 % 0.53/0.64 % Status : Theorem % 0.53/0.64 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.04 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.78 v4.0.0 % 0.53/0.64 % Syntax : Number of formulae : 39 ( 3 unt; 1 def) % 0.53/0.64 % Number of atoms : 154 ( 41 equ) % 0.53/0.64 % Maximal formula atoms : 9 ( 3 avg) % 0.53/0.64 % Number of connectives : 121 ( 6 ~; 1 |; 60 &) % 0.53/0.64 % ( 1 <=>; 53 =>; 0 <=; 0 <~>) % 0.53/0.64 % Maximal formula depth : 10 ( 5 avg) % 0.53/0.64 % Maximal term depth : 5 ( 1 avg) % 0.53/0.64 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.53/0.64 % Number of functors : 11 ( 11 usr; 3 con; 0-2 aty) % 0.53/0.64 % Number of variables : 69 ( 68 !; 1 ?) % 0.53/0.64 % SPC : FOF_THM_RFO_SEQ % 0.53/0.64 % 0.53/0.64 % Comments : Problem generated by the SAD system [VLP07] % 0.53/0.64 %------------------------------------------------------------------------------ % 0.53/0.64 fof(mNatSort,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aNaturalNumber0(W0) % 0.53/0.64 => $true ) ). % 0.53/0.64 % 0.53/0.64 fof(mZeroNat,axiom, % 0.53/0.64 aNaturalNumber0(sz00) ). % 0.53/0.64 % 0.53/0.64 fof(mSuccNat,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aNaturalNumber0(W0) % 0.53/0.64 => ( aNaturalNumber0(szszuzczcdt0(W0)) % 0.53/0.64 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mNatExtr,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( ( aNaturalNumber0(W0) % 0.53/0.64 & W0 != sz00 ) % 0.53/0.64 => ? [W1] : % 0.53/0.64 ( aNaturalNumber0(W1) % 0.53/0.64 & W0 = szszuzczcdt0(W1) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mSuccEqu,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aNaturalNumber0(W0) % 0.53/0.64 & aNaturalNumber0(W1) ) % 0.53/0.64 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.53/0.64 => W0 = W1 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mIHOrd,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aNaturalNumber0(W0) % 0.53/0.64 & aNaturalNumber0(W1) ) % 0.53/0.64 => ( iLess0(W0,W1) % 0.53/0.64 => $true ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mIH,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aNaturalNumber0(W0) % 0.53/0.64 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mScSort,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aScalar0(W0) % 0.53/0.64 => $true ) ). % 0.53/0.64 % 0.53/0.64 fof(mSZeroSc,axiom, % 0.53/0.64 aScalar0(sz0z00) ). % 0.53/0.64 % 0.53/0.64 fof(mSumSc,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => aScalar0(sdtpldt0(W0,W1)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mMulSc,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => aScalar0(sdtasdt0(W0,W1)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mNegSc,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aScalar0(W0) % 0.53/0.64 => aScalar0(smndt0(W0)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mScZero,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aScalar0(W0) % 0.53/0.64 => ( sdtpldt0(W0,sz0z00) = W0 % 0.53/0.64 & sdtpldt0(sz0z00,W0) = W0 % 0.53/0.64 & sdtasdt0(W0,sz0z00) = sz0z00 % 0.53/0.64 & sdtasdt0(sz0z00,W0) = sz0z00 % 0.53/0.64 & sdtpldt0(W0,smndt0(W0)) = sz0z00 % 0.53/0.64 & sdtpldt0(smndt0(W0),W0) = sz0z00 % 0.53/0.64 & smndt0(smndt0(W0)) = W0 % 0.53/0.64 & smndt0(sz0z00) = sz0z00 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mArith,axiom, % 0.53/0.64 ! [W0,W1,W2] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) ) % 0.53/0.64 => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) % 0.53/0.64 & sdtpldt0(W0,W1) = sdtpldt0(W1,W0) % 0.53/0.64 & sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) % 0.53/0.64 & sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mDistr,axiom, % 0.53/0.64 ! [W0,W1,W2] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) ) % 0.53/0.64 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.53/0.64 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mDistr2,axiom, % 0.53/0.64 ! [W0,W1,W2,W3] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) % 0.53/0.64 & aScalar0(W3) ) % 0.53/0.64 => sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ). % 0.53/0.64 % 0.53/0.64 fof(mMNeg,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) % 0.53/0.64 & sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mMDNeg,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLess,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( sdtlseqdt0(W0,W1) % 0.53/0.64 => $true ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLERef,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aScalar0(W0) % 0.53/0.64 => sdtlseqdt0(W0,W0) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLEASm,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.64 & sdtlseqdt0(W1,W0) ) % 0.53/0.64 => W0 = W1 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLETrn,axiom, % 0.53/0.64 ! [W0,W1,W2] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) ) % 0.53/0.64 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.64 & sdtlseqdt0(W1,W2) ) % 0.53/0.64 => sdtlseqdt0(W0,W2) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLEMon,axiom, % 0.53/0.64 ! [W0,W1,W2,W3] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) % 0.53/0.64 & aScalar0(W3) ) % 0.53/0.64 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.64 & sdtlseqdt0(W2,W3) ) % 0.53/0.64 => sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLEMonM,axiom, % 0.53/0.64 ! [W0,W1,W2,W3] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) % 0.53/0.64 & aScalar0(W2) % 0.53/0.64 & aScalar0(W3) ) % 0.53/0.64 => ( ( sdtlseqdt0(W0,W1) % 0.53/0.64 & sdtlseqdt0(sz0z00,W2) % 0.53/0.64 & sdtlseqdt0(W2,W3) ) % 0.53/0.64 => sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mLETot,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( sdtlseqdt0(W0,W1) % 0.53/0.64 | sdtlseqdt0(W1,W0) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mPosMon,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( ( sdtlseqdt0(sz0z00,W0) % 0.53/0.64 & sdtlseqdt0(sz0z00,W1) ) % 0.53/0.64 => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) % 0.53/0.64 & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mSqPos,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aScalar0(W0) % 0.53/0.64 => sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mSqrt,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aScalar0(W0) % 0.53/0.64 & aScalar0(W1) ) % 0.53/0.64 => ( ( sdtlseqdt0(sz0z00,W0) % 0.53/0.64 & sdtlseqdt0(sz0z00,W1) % 0.53/0.64 & sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) % 0.53/0.64 => W0 = W1 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mVcSort,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aVector0(W0) % 0.53/0.64 => $true ) ). % 0.53/0.64 % 0.53/0.64 fof(mDimNat,axiom, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aVector0(W0) % 0.53/0.64 => aNaturalNumber0(aDimensionOf0(W0)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mElmSc,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aVector0(W0) % 0.53/0.64 & aNaturalNumber0(W1) ) % 0.53/0.64 => aScalar0(sdtlbdtrb0(W0,W1)) ) ). % 0.53/0.64 % 0.53/0.64 fof(mDefInit,definition, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aVector0(W0) % 0.53/0.64 => ( aDimensionOf0(W0) != sz00 % 0.53/0.64 => ! [W1] : % 0.53/0.64 ( W1 = sziznziztdt0(W0) % 0.53/0.64 <=> ( aVector0(W1) % 0.53/0.64 & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) % 0.53/0.64 & ! [W2] : % 0.53/0.64 ( aNaturalNumber0(W2) % 0.53/0.64 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mEqInit,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aVector0(W0) % 0.53/0.64 & aVector0(W1) ) % 0.53/0.64 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) % 0.53/0.64 & aDimensionOf0(W1) != sz00 ) % 0.53/0.64 => aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mScPr,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aVector0(W0) % 0.53/0.64 & aVector0(W1) ) % 0.53/0.64 => ( aDimensionOf0(W0) = aDimensionOf0(W1) % 0.53/0.64 => aScalar0(sdtasasdt0(W0,W1)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mDefSPZ,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aVector0(W0) % 0.53/0.64 & aVector0(W1) ) % 0.53/0.64 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) % 0.53/0.64 & aDimensionOf0(W1) = sz00 ) % 0.53/0.64 => sdtasasdt0(W0,W1) = sz0z00 ) ) ). % 0.53/0.64 % 0.53/0.64 fof(mDefSPN,axiom, % 0.53/0.64 ! [W0,W1] : % 0.53/0.64 ( ( aVector0(W0) % 0.53/0.64 & aVector0(W1) ) % 0.53/0.64 => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) % 0.53/0.64 & aDimensionOf0(W1) != sz00 ) % 0.53/0.64 => sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(m__1542,hypothesis, % 0.53/0.64 aVector0(xs) ). % 0.53/0.64 % 0.53/0.64 fof(m__1516,hypothesis, % 0.53/0.64 ! [W0] : % 0.53/0.64 ( aVector0(W0) % 0.53/0.64 => ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) % 0.53/0.64 => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ) ). % 0.53/0.64 % 0.53/0.64 fof(m__,conjecture, % 0.53/0.64 ( ( aDimensionOf0(xs) != sz00 % 0.53/0.64 => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) % 0.53/0.64 => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ). % 0.53/0.64 % 0.53/0.64 %------------------------------------------------------------------------------ % 0.53/0.64 %------------------------------------------- % 0.53/0.64 % Proof found % 0.53/0.64 % SZS status Theorem for theBenchmark % 0.53/0.64 % SZS output start Proof % 0.53/0.64 %ClaNum:79(EqnAxiom:25) % 0.53/0.64 %VarNum:297(SingletonVarNum:94) % 0.53/0.64 %MaxLitNum:8 % 0.53/0.64 %MaxfuncDepth:4 % 0.53/0.64 %SharedTerms:13 % 0.53/0.64 %goalClause: 29 49 % 0.53/0.65 %singleGoalClaCount:1 % 0.53/0.65 [26]P1(a1) % 0.53/0.65 [27]P2(a10) % 0.53/0.65 [28]P3(a11) % 0.53/0.65 [29]~P4(a10,f2(a11,a11)) % 0.53/0.65 [49]P4(a10,f2(a11,a11))+E(f3(a11),a1) % 0.53/0.65 [42]~P2(x421)+P4(x421,x421) % 0.53/0.65 [30]~P2(x301)+E(f6(a10),a10) % 0.53/0.65 [31]~P1(x311)+~E(f12(x311),a1) % 0.53/0.65 [32]~P1(x321)+P1(f12(x321)) % 0.53/0.65 [33]~P3(x331)+P1(f3(x331)) % 0.53/0.65 [34]~P2(x341)+P2(f6(x341)) % 0.53/0.65 [37]~P2(x371)+E(f7(x371,a10),a10) % 0.53/0.65 [38]~P2(x381)+E(f7(a10,x381),a10) % 0.53/0.65 [40]~P2(x401)+E(f8(x401,a10),x401) % 0.53/0.65 [41]~P2(x411)+E(f8(a10,x411),x411) % 0.53/0.65 [46]~P1(x461)+P5(x461,f12(x461)) % 0.53/0.65 [54]~P2(x541)+P4(a10,f7(x541,x541)) % 0.53/0.65 [35]~P2(x351)+E(f6(f6(x351)),x351) % 0.53/0.65 [44]~P2(x441)+E(f8(x441,f6(x441)),a10) % 0.53/0.65 [45]~P2(x451)+E(f8(f6(x451),x451),a10) % 0.53/0.65 [36]~P1(x361)+E(x361,a1)+P1(f4(x361)) % 0.53/0.65 [67]~P3(x671)+~P5(f3(x671),f3(a11))+P4(a10,f2(x671,x671)) % 0.53/0.65 [39]~P1(x391)+E(x391,a1)+E(f12(f4(x391)),x391) % 0.53/0.65 [51]~P2(x512)+~P2(x511)+P2(f8(x511,x512)) % 0.53/0.65 [52]~P2(x522)+~P2(x521)+P2(f7(x521,x522)) % 0.53/0.65 [53]~P1(x532)+~P3(x531)+P2(f9(x531,x532)) % 0.53/0.65 [59]~P2(x592)+~P2(x591)+E(f7(f6(x591),f6(x592)),f7(x591,x592)) % 0.53/0.65 [63]~P2(x632)+~P2(x631)+E(f6(f7(x631,x632)),f7(x631,f6(x632))) % 0.53/0.65 [64]~P2(x642)+~P2(x641)+E(f6(f7(x641,x642)),f7(f6(x641),x642)) % 0.53/0.65 [50]P4(x502,x501)+~P2(x501)+~P2(x502)+P4(x501,x502) % 0.53/0.65 [43]~P3(x431)+P3(x432)+~E(x432,f13(x431))+E(f3(x431),a1) % 0.53/0.65 [47]~P1(x472)+~P1(x471)+E(x471,x472)+~E(f12(x471),f12(x472)) % 0.53/0.65 [61]~P3(x612)+~P3(x611)+~E(f3(x611),f3(x612))+P2(f2(x611,x612)) % 0.53/0.65 [48]~P3(x481)+~E(x482,f13(x481))+E(f3(x481),a1)+E(f12(f3(x482)),f3(x481)) % 0.53/0.65 [56]~P2(x562)+~P2(x561)+~P2(x563)+E(f8(x561,x562),f8(x562,x561)) % 0.53/0.65 [57]~P2(x572)+~P2(x571)+~P2(x573)+E(f7(x571,x572),f7(x572,x571)) % 0.53/0.65 [70]~P2(x703)+~P2(x702)+~P2(x701)+E(f8(f8(x701,x702),x703),f8(x701,f8(x702,x703))) % 0.53/0.65 [71]~P2(x713)+~P2(x712)+~P2(x711)+E(f7(f7(x711,x712),x713),f7(x711,f7(x712,x713))) % 0.53/0.65 [73]~P2(x733)+~P2(x732)+~P2(x731)+E(f8(f7(x731,x732),f7(x731,x733)),f7(x731,f8(x732,x733))) % 0.53/0.65 [74]~P2(x742)+~P2(x743)+~P2(x741)+E(f8(f7(x741,x742),f7(x743,x742)),f7(f8(x741,x743),x742)) % 0.53/0.65 [62]~P2(x622)+~P2(x621)+~P4(x622,x621)+~P4(x621,x622)+E(x621,x622) % 0.53/0.65 [55]~P3(x552)+~P3(x551)+~E(f3(x551),f3(x552))+~E(f3(x552),a1)+E(f2(x551,x552),a10) % 0.53/0.65 [68]~P2(x682)+~P2(x681)+~P4(a10,x682)+~P4(a10,x681)+P4(a10,f8(x681,x682)) % 0.53/0.65 [69]~P2(x692)+~P2(x691)+~P4(a10,x692)+~P4(a10,x691)+P4(a10,f7(x691,x692)) % 0.53/0.65 [58]~P3(x581)+~P3(x582)+~E(f3(x582),f3(x581))+E(f3(x581),a1)+E(f3(f13(x582)),f3(f13(x581))) % 0.53/0.65 [78]~P3(x781)+~P3(x782)+~E(f3(x782),f3(x781))+E(f3(x781),a1)+E(f8(f2(f13(x782),f13(x781)),f7(f9(x782,f3(x782)),f9(x781,f3(x781)))),f2(x782,x781)) % 0.53/0.65 [60]~P1(x603)+~P3(x601)+~E(x602,f13(x601))+E(f9(x602,x603),f9(x601,x603))+E(f3(x601),a1) % 0.53/0.65 [79]~P2(x793)+~P2(x792)+~P2(x794)+~P2(x791)+E(f8(f8(f7(x791,x792),f7(x791,x793)),f8(f7(x794,x792),f7(x794,x793))),f7(f8(x791,x794),f8(x792,x793))) % 0.53/0.65 [72]~P2(x722)+~P2(x721)+E(x721,x722)+~E(f7(x721,x721),f7(x722,x722))+~P4(a10,x722)+~P4(a10,x721) % 0.53/0.65 [65]~P3(x651)+~P3(x652)+E(x651,f13(x652))+E(f3(x652),a1)+P1(f5(x652,x651))+~E(f12(f3(x651)),f3(x652)) % 0.53/0.65 [77]~P3(x772)+~P3(x771)+E(x771,f13(x772))+E(f3(x772),a1)+~E(f12(f3(x771)),f3(x772))+~E(f9(x771,f5(x772,x771)),f9(x772,f5(x772,x771))) % 0.53/0.65 [66]~P2(x662)+~P2(x661)+~P4(x663,x662)+~P4(x661,x663)+P4(x661,x662)+~P2(x663) % 0.53/0.65 [75]~P2(x754)+~P2(x752)+~P2(x753)+~P2(x751)+~P4(x752,x754)+~P4(x751,x753)+P4(f8(x751,x752),f8(x753,x754)) % 0.53/0.65 [76]~P2(x764)+~P2(x762)+~P2(x763)+~P2(x761)+~P4(x762,x764)+~P4(x761,x763)+~P4(a10,x762)+P4(f7(x761,x762),f7(x763,x764)) % 0.53/0.65 %EqnAxiom % 0.53/0.65 [1]E(x11,x11) % 0.53/0.65 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.65 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.53/0.65 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.53/0.65 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 0.53/0.65 [7]~E(x71,x72)+E(f12(x71),f12(x72)) % 0.53/0.65 [8]~E(x81,x82)+E(f9(x81,x83),f9(x82,x83)) % 0.53/0.65 [9]~E(x91,x92)+E(f9(x93,x91),f9(x93,x92)) % 0.53/0.65 [10]~E(x101,x102)+E(f3(x101),f3(x102)) % 0.53/0.65 [11]~E(x111,x112)+E(f7(x111,x113),f7(x112,x113)) % 0.53/0.65 [12]~E(x121,x122)+E(f7(x123,x121),f7(x123,x122)) % 0.53/0.65 [13]~E(x131,x132)+E(f8(x131,x133),f8(x132,x133)) % 0.53/0.65 [14]~E(x141,x142)+E(f8(x143,x141),f8(x143,x142)) % 0.53/0.65 [15]~E(x151,x152)+E(f13(x151),f13(x152)) % 0.53/0.65 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 0.53/0.65 [17]~E(x171,x172)+E(f5(x171,x173),f5(x172,x173)) % 0.53/0.65 [18]~E(x181,x182)+E(f5(x183,x181),f5(x183,x182)) % 0.53/0.65 [19]~P1(x191)+P1(x192)+~E(x191,x192) % 0.53/0.65 [20]~P2(x201)+P2(x202)+~E(x201,x202) % 0.53/0.65 [21]~P3(x211)+P3(x212)+~E(x211,x212) % 0.53/0.65 [22]P4(x222,x223)+~E(x221,x222)+~P4(x221,x223) % 0.53/0.65 [23]P4(x233,x232)+~E(x231,x232)+~P4(x233,x231) % 0.53/0.65 [24]P5(x242,x243)+~E(x241,x242)+~P5(x241,x243) % 0.53/0.65 [25]P5(x253,x252)+~E(x251,x252)+~P5(x253,x251) % 0.53/0.65 % 0.53/0.65 %------------------------------------------- % 0.53/0.65 cnf(90,plain, % 0.53/0.65 (P4(a10,a10)), % 0.53/0.65 inference(scs_inference,[],[29,27,28,67,50])). % 0.53/0.65 cnf(95,plain, % 0.53/0.65 (~E(a10,f2(a11,a11))), % 0.53/0.65 inference(scs_inference,[],[29,27,28,67,50,76,22,23])). % 0.53/0.65 cnf(99,plain, % 0.53/0.65 (E(f6(a10),a10)), % 0.53/0.65 inference(scs_inference,[],[27,30])). % 0.53/0.65 cnf(100,plain, % 0.53/0.65 (E(f3(a11),a1)), % 0.53/0.65 inference(scs_inference,[],[29,49])). % 0.53/0.65 cnf(121,plain, % 0.53/0.65 (E(f2(a11,a11),a10)), % 0.53/0.65 inference(scs_inference,[],[100,90,27,99,28,2,20,22,23,21,19,55])). % 0.53/0.65 cnf(124,plain, % 0.53/0.65 ($false), % 0.53/0.65 inference(scs_inference,[],[95,121,2]), % 0.53/0.65 ['proof']). % 0.53/0.65 % SZS output end Proof % 0.53/0.65 % Total time :0.010000s %------------------------------------------------------------------------------