%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : RNG047+2 : 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 : n029.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 14:00:51 EDT 2024 % Result : Theorem 12.92s 13.03s % Output : CNFRefutation 12.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : RNG047+2 : TPTP v8.2.0. Released v4.0.0. % 0.10/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n029.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Tue Jun 18 14:35:39 EDT 2024 % 0.11/0.33 % CPUTime : % 0.17/0.58 start to proof:theBenchmark % 12.92/13.02 %------------------------------------------- % 12.92/13.02 % File :CSE---1.7 % 12.92/13.02 % Problem :theBenchmark % 12.92/13.02 % Transform :cnf % 12.92/13.02 % Format :tptp:raw % 12.92/13.02 % Command :java -jar mcs_scs.jar %d %s % 12.92/13.02 % 12.92/13.02 % Result :Theorem 12.360000s % 12.92/13.02 % Output :CNFRefutation 12.360000s % 12.92/13.02 %------------------------------------------- % 12.92/13.02 %------------------------------------------------------------------------------ % 12.92/13.02 % File : RNG047+2 : TPTP v8.2.0. Released v4.0.0. % 12.92/13.02 % Domain : Ring Theory % 12.92/13.02 % Problem : Cauchy-Bouniakowsky-Schwarz inequality 03, 01 expansion % 12.92/13.03 % Version : Especial. % 12.92/13.03 % English : % 12.92/13.03 % 12.92/13.03 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 12.92/13.03 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 12.92/13.03 % Source : [Pas08] % 12.92/13.03 % Names : cauchy_03.01 [Pas08] % 12.92/13.03 % 12.92/13.03 % Status : Theorem % 12.92/13.03 % Rating : 0.19 v8.2.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.07 v7.3.0, 0.10 v7.1.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.44 v5.2.0, 0.30 v5.1.0, 0.43 v5.0.0, 0.50 v4.1.0, 0.52 v4.0.1, 0.87 v4.0.0 % 12.92/13.03 % Syntax : Number of formulae : 35 ( 2 unt; 1 def) % 12.92/13.03 % Number of atoms : 141 ( 37 equ) % 12.92/13.03 % Maximal formula atoms : 9 ( 4 avg) % 12.92/13.03 % Number of connectives : 110 ( 4 ~; 1 |; 59 &) % 12.92/13.03 % ( 1 <=>; 45 =>; 0 <=; 0 <~>) % 12.92/13.03 % Maximal formula depth : 10 ( 5 avg) % 12.92/13.03 % Maximal term depth : 4 ( 1 avg) % 12.92/13.03 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 12.92/13.03 % Number of functors : 11 ( 11 usr; 4 con; 0-2 aty) % 12.92/13.03 % Number of variables : 62 ( 61 !; 1 ?) % 12.92/13.03 % SPC : FOF_THM_RFO_SEQ % 12.92/13.03 % 12.92/13.03 % Comments : Problem generated by the SAD system [VLP07] % 12.92/13.03 %------------------------------------------------------------------------------ % 12.92/13.03 fof(mNatSort,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aNaturalNumber0(W0) % 12.92/13.03 => $true ) ). % 12.92/13.03 % 12.92/13.03 fof(mZeroNat,axiom, % 12.92/13.03 aNaturalNumber0(sz00) ). % 12.92/13.03 % 12.92/13.03 fof(mSuccNat,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aNaturalNumber0(W0) % 12.92/13.03 => ( aNaturalNumber0(szszuzczcdt0(W0)) % 12.92/13.03 & szszuzczcdt0(W0) != sz00 ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mNatExtr,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( ( aNaturalNumber0(W0) % 12.92/13.03 & W0 != sz00 ) % 12.92/13.03 => ? [W1] : % 12.92/13.03 ( aNaturalNumber0(W1) % 12.92/13.03 & W0 = szszuzczcdt0(W1) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mSuccEqu,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aNaturalNumber0(W0) % 12.92/13.03 & aNaturalNumber0(W1) ) % 12.92/13.03 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 12.92/13.03 => W0 = W1 ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mIHOrd,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aNaturalNumber0(W0) % 12.92/13.03 & aNaturalNumber0(W1) ) % 12.92/13.03 => ( iLess0(W0,W1) % 12.92/13.03 => $true ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mIH,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aNaturalNumber0(W0) % 12.92/13.03 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mScSort,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aScalar0(W0) % 12.92/13.03 => $true ) ). % 12.92/13.03 % 12.92/13.03 fof(mSZeroSc,axiom, % 12.92/13.03 aScalar0(sz0z00) ). % 12.92/13.03 % 12.92/13.03 fof(mSumSc,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => aScalar0(sdtpldt0(W0,W1)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mMulSc,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => aScalar0(sdtasdt0(W0,W1)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mNegSc,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aScalar0(W0) % 12.92/13.03 => aScalar0(smndt0(W0)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mScZero,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aScalar0(W0) % 12.92/13.03 => ( sdtpldt0(W0,sz0z00) = W0 % 12.92/13.03 & sdtpldt0(sz0z00,W0) = W0 % 12.92/13.03 & sdtasdt0(W0,sz0z00) = sz0z00 % 12.92/13.03 & sdtasdt0(sz0z00,W0) = sz0z00 % 12.92/13.03 & sdtpldt0(W0,smndt0(W0)) = sz0z00 % 12.92/13.03 & sdtpldt0(smndt0(W0),W0) = sz0z00 % 12.92/13.03 & smndt0(smndt0(W0)) = W0 % 12.92/13.03 & smndt0(sz0z00) = sz0z00 ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mArith,axiom, % 12.92/13.03 ! [W0,W1,W2] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) ) % 12.92/13.03 => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) % 12.92/13.03 & sdtpldt0(W0,W1) = sdtpldt0(W1,W0) % 12.92/13.03 & sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) % 12.92/13.03 & sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mDistr,axiom, % 12.92/13.03 ! [W0,W1,W2] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) ) % 12.92/13.03 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 12.92/13.03 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mDistr2,axiom, % 12.92/13.03 ! [W0,W1,W2,W3] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) % 12.92/13.03 & aScalar0(W3) ) % 12.92/13.03 => sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ). % 12.92/13.03 % 12.92/13.03 fof(mMNeg,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) % 12.92/13.03 & sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mMDNeg,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLess,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( sdtlseqdt0(W0,W1) % 12.92/13.03 => $true ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLERef,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aScalar0(W0) % 12.92/13.03 => sdtlseqdt0(W0,W0) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLEASm,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( ( sdtlseqdt0(W0,W1) % 12.92/13.03 & sdtlseqdt0(W1,W0) ) % 12.92/13.03 => W0 = W1 ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLETrn,axiom, % 12.92/13.03 ! [W0,W1,W2] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) ) % 12.92/13.03 => ( ( sdtlseqdt0(W0,W1) % 12.92/13.03 & sdtlseqdt0(W1,W2) ) % 12.92/13.03 => sdtlseqdt0(W0,W2) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLEMon,axiom, % 12.92/13.03 ! [W0,W1,W2,W3] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) % 12.92/13.03 & aScalar0(W3) ) % 12.92/13.03 => ( ( sdtlseqdt0(W0,W1) % 12.92/13.03 & sdtlseqdt0(W2,W3) ) % 12.92/13.03 => sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLEMonM,axiom, % 12.92/13.03 ! [W0,W1,W2,W3] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) % 12.92/13.03 & aScalar0(W2) % 12.92/13.03 & aScalar0(W3) ) % 12.92/13.03 => ( ( sdtlseqdt0(W0,W1) % 12.92/13.03 & sdtlseqdt0(sz0z00,W2) % 12.92/13.03 & sdtlseqdt0(W2,W3) ) % 12.92/13.03 => sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mLETot,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( sdtlseqdt0(W0,W1) % 12.92/13.03 | sdtlseqdt0(W1,W0) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mPosMon,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( ( sdtlseqdt0(sz0z00,W0) % 12.92/13.03 & sdtlseqdt0(sz0z00,W1) ) % 12.92/13.03 => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) % 12.92/13.03 & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mSqPos,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aScalar0(W0) % 12.92/13.03 => sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mSqrt,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aScalar0(W0) % 12.92/13.03 & aScalar0(W1) ) % 12.92/13.03 => ( ( sdtlseqdt0(sz0z00,W0) % 12.92/13.03 & sdtlseqdt0(sz0z00,W1) % 12.92/13.03 & sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) % 12.92/13.03 => W0 = W1 ) ) ). % 12.92/13.03 % 12.92/13.03 fof(mVcSort,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aVector0(W0) % 12.92/13.03 => $true ) ). % 12.92/13.03 % 12.92/13.03 fof(mDimNat,axiom, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aVector0(W0) % 12.92/13.03 => aNaturalNumber0(aDimensionOf0(W0)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mElmSc,axiom, % 12.92/13.03 ! [W0,W1] : % 12.92/13.03 ( ( aVector0(W0) % 12.92/13.03 & aNaturalNumber0(W1) ) % 12.92/13.03 => aScalar0(sdtlbdtrb0(W0,W1)) ) ). % 12.92/13.03 % 12.92/13.03 fof(mDefInit,definition, % 12.92/13.03 ! [W0] : % 12.92/13.03 ( aVector0(W0) % 12.92/13.03 => ( aDimensionOf0(W0) != sz00 % 12.92/13.03 => ! [W1] : % 12.92/13.03 ( W1 = sziznziztdt0(W0) % 12.92/13.03 <=> ( aVector0(W1) % 12.92/13.03 & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) % 12.92/13.03 & ! [W2] : % 12.92/13.03 ( aNaturalNumber0(W2) % 12.92/13.03 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ). % 12.92/13.03 % 12.92/13.03 fof(m__1329,hypothesis, % 12.92/13.03 ( aVector0(xs) % 12.92/13.03 & aVector0(xt) ) ). % 12.92/13.03 % 12.92/13.03 fof(m__1329_01,hypothesis, % 12.92/13.03 ( aDimensionOf0(xs) = aDimensionOf0(xt) % 12.92/13.03 & aDimensionOf0(xt) != sz00 ) ). % 12.92/13.03 % 12.92/13.03 fof(m__,conjecture, % 12.92/13.03 ( ( aVector0(sziznziztdt0(xs)) % 12.92/13.03 & szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) % 12.92/13.03 & ! [W0] : % 12.92/13.03 ( aNaturalNumber0(W0) % 12.92/13.03 => sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) % 12.92/13.03 => ( ( aVector0(sziznziztdt0(xt)) % 12.92/13.03 & szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) % 12.92/13.03 & ! [W0] : % 12.92/13.03 ( aNaturalNumber0(W0) % 12.92/13.03 => sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) % 12.92/13.03 => aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ) ). % 12.92/13.03 % 12.92/13.03 %------------------------------------------------------------------------------ % 12.92/13.03 %------------------------------------------- % 12.92/13.03 % Proof found % 12.92/13.03 % SZS status Theorem for theBenchmark % 12.92/13.03 % SZS output start Proof % 12.92/13.03 %ClaNum:80(EqnAxiom:23) % 12.92/13.03 %VarNum:266(SingletonVarNum:87) % 12.92/13.03 %MaxLitNum:8 % 12.92/13.03 %MaxfuncDepth:3 % 12.92/13.03 %SharedTerms:25 % 12.92/13.03 %goalClause: 29 30 31 32 34 54 55 % 12.92/13.03 %singleGoalClaCount:5 % 12.92/13.03 [24]P1(a1) % 12.92/13.03 [25]P2(a9) % 12.92/13.03 [26]P3(a10) % 12.92/13.03 [27]P3(a13) % 12.92/13.03 [28]E(f2(a13),f2(a10)) % 12.92/13.03 [29]P3(f11(a10)) % 12.92/13.03 [30]P3(f11(a13)) % 12.92/13.03 [33]~E(f2(a13),a1) % 12.92/13.03 [34]~E(f2(f11(a13)),f2(f11(a10))) % 12.92/13.03 [31]E(f12(f2(f11(a10))),f2(a10)) % 12.92/13.03 [32]E(f12(f2(f11(a13))),f2(a13)) % 12.92/13.03 [47]~P2(x471)+P4(x471,x471) % 12.92/13.03 [35]~P2(x351)+E(f3(a9),a9) % 12.92/13.03 [36]~P1(x361)+~E(f12(x361),a1) % 12.92/13.03 [37]~P1(x371)+P1(f12(x371)) % 12.92/13.03 [38]~P3(x381)+P1(f2(x381)) % 12.92/13.03 [39]~P2(x391)+P2(f3(x391)) % 12.92/13.03 [42]~P2(x421)+E(f5(x421,a9),a9) % 12.92/13.03 [43]~P2(x431)+E(f5(a9,x431),a9) % 12.92/13.03 [45]~P2(x451)+E(f7(x451,a9),x451) % 12.92/13.03 [46]~P2(x461)+E(f7(a9,x461),x461) % 12.92/13.03 [51]~P1(x511)+P5(x511,f12(x511)) % 12.92/13.03 [60]~P2(x601)+P4(a9,f5(x601,x601)) % 12.92/13.03 [40]~P2(x401)+E(f3(f3(x401)),x401) % 12.92/13.03 [49]~P2(x491)+E(f7(x491,f3(x491)),a9) % 12.92/13.03 [50]~P2(x501)+E(f7(f3(x501),x501),a9) % 12.92/13.03 [54]~P1(x541)+E(f8(f11(a10),x541),f8(a10,x541)) % 12.92/13.03 [55]~P1(x551)+E(f8(f11(a13),x551),f8(a13,x551)) % 12.92/13.04 [41]~P1(x411)+E(x411,a1)+P1(f4(x411)) % 12.92/13.04 [44]~P1(x441)+E(x441,a1)+E(f12(f4(x441)),x441) % 12.92/13.04 [57]~P2(x572)+~P2(x571)+P2(f7(x571,x572)) % 12.92/13.04 [58]~P2(x582)+~P2(x581)+P2(f5(x581,x582)) % 12.92/13.04 [59]~P1(x592)+~P3(x591)+P2(f8(x591,x592)) % 12.92/13.04 [63]~P2(x632)+~P2(x631)+E(f5(f3(x631),f3(x632)),f5(x631,x632)) % 12.92/13.04 [66]~P2(x662)+~P2(x661)+E(f3(f5(x661,x662)),f5(x661,f3(x662))) % 12.92/13.04 [67]~P2(x672)+~P2(x671)+E(f3(f5(x671,x672)),f5(f3(x671),x672)) % 12.92/13.04 [56]P4(x562,x561)+~P2(x561)+~P2(x562)+P4(x561,x562) % 12.92/13.04 [48]~P3(x481)+P3(x482)+~E(x482,f11(x481))+E(f2(x481),a1) % 12.92/13.04 [52]~P1(x522)+~P1(x521)+E(x521,x522)+~E(f12(x521),f12(x522)) % 12.92/13.04 [53]~P3(x531)+~E(x532,f11(x531))+E(f2(x531),a1)+E(f12(f2(x532)),f2(x531)) % 12.92/13.04 [61]~P2(x612)+~P2(x611)+~P2(x613)+E(f7(x611,x612),f7(x612,x611)) % 12.92/13.04 [62]~P2(x622)+~P2(x621)+~P2(x623)+E(f5(x621,x622),f5(x622,x621)) % 12.92/13.04 [72]~P2(x723)+~P2(x722)+~P2(x721)+E(f7(f7(x721,x722),x723),f7(x721,f7(x722,x723))) % 12.92/13.04 [73]~P2(x733)+~P2(x732)+~P2(x731)+E(f5(f5(x731,x732),x733),f5(x731,f5(x732,x733))) % 12.92/13.04 [75]~P2(x753)+~P2(x752)+~P2(x751)+E(f7(f5(x751,x752),f5(x751,x753)),f5(x751,f7(x752,x753))) % 12.92/13.04 [76]~P2(x762)+~P2(x763)+~P2(x761)+E(f7(f5(x761,x762),f5(x763,x762)),f5(f7(x761,x763),x762)) % 12.92/13.04 [65]~P2(x652)+~P2(x651)+~P4(x652,x651)+~P4(x651,x652)+E(x651,x652) % 12.92/13.04 [70]~P2(x702)+~P2(x701)+~P4(a9,x702)+~P4(a9,x701)+P4(a9,f7(x701,x702)) % 12.92/13.04 [71]~P2(x712)+~P2(x711)+~P4(a9,x712)+~P4(a9,x711)+P4(a9,f5(x711,x712)) % 12.92/13.04 [64]~P1(x643)+~P3(x641)+~E(x642,f11(x641))+E(f8(x642,x643),f8(x641,x643))+E(f2(x641),a1) % 12.92/13.04 [80]~P2(x803)+~P2(x802)+~P2(x804)+~P2(x801)+E(f7(f7(f5(x801,x802),f5(x801,x803)),f7(f5(x804,x802),f5(x804,x803))),f5(f7(x801,x804),f7(x802,x803))) % 12.92/13.04 [74]~P2(x742)+~P2(x741)+E(x741,x742)+~E(f5(x741,x741),f5(x742,x742))+~P4(a9,x742)+~P4(a9,x741) % 12.92/13.04 [68]~P3(x681)+~P3(x682)+E(x681,f11(x682))+E(f2(x682),a1)+P1(f6(x682,x681))+~E(f12(f2(x681)),f2(x682)) % 12.92/13.04 [79]~P3(x792)+~P3(x791)+E(x791,f11(x792))+E(f2(x792),a1)+~E(f12(f2(x791)),f2(x792))+~E(f8(x791,f6(x792,x791)),f8(x792,f6(x792,x791))) % 12.92/13.04 [69]~P2(x692)+~P2(x691)+~P4(x693,x692)+~P4(x691,x693)+P4(x691,x692)+~P2(x693) % 12.92/13.04 [77]~P2(x774)+~P2(x772)+~P2(x773)+~P2(x771)+~P4(x772,x774)+~P4(x771,x773)+P4(f7(x771,x772),f7(x773,x774)) % 12.92/13.04 [78]~P2(x784)+~P2(x782)+~P2(x783)+~P2(x781)+~P4(x782,x784)+~P4(x781,x783)+~P4(a9,x782)+P4(f5(x781,x782),f5(x783,x784)) % 12.92/13.04 %EqnAxiom % 12.92/13.04 [1]E(x11,x11) % 12.92/13.04 [2]E(x22,x21)+~E(x21,x22) % 12.92/13.04 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 12.92/13.04 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 12.92/13.04 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53)) % 12.92/13.04 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62)) % 12.92/13.04 [7]~E(x71,x72)+E(f11(x71),f11(x72)) % 12.92/13.04 [8]~E(x81,x82)+E(f3(x81),f3(x82)) % 12.92/13.04 [9]~E(x91,x92)+E(f12(x91),f12(x92)) % 12.92/13.04 [10]~E(x101,x102)+E(f7(x101,x103),f7(x102,x103)) % 12.92/13.04 [11]~E(x111,x112)+E(f7(x113,x111),f7(x113,x112)) % 12.92/13.04 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123)) % 12.92/13.04 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132)) % 12.92/13.04 [14]~E(x141,x142)+E(f8(x141,x143),f8(x142,x143)) % 12.92/13.04 [15]~E(x151,x152)+E(f8(x153,x151),f8(x153,x152)) % 12.92/13.04 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 12.92/13.04 [17]~P1(x171)+P1(x172)+~E(x171,x172) % 12.92/13.04 [18]~P2(x181)+P2(x182)+~E(x181,x182) % 12.92/13.04 [19]~P3(x191)+P3(x192)+~E(x191,x192) % 12.92/13.04 [20]P4(x202,x203)+~E(x201,x202)+~P4(x201,x203) % 12.92/13.04 [21]P4(x213,x212)+~E(x211,x212)+~P4(x213,x211) % 12.92/13.04 [22]P5(x222,x223)+~E(x221,x222)+~P5(x221,x223) % 12.92/13.04 [23]P5(x233,x232)+~E(x231,x232)+~P5(x233,x231) % 12.92/13.04 % 12.92/13.04 %------------------------------------------- % 12.92/13.04 cnf(84,plain, % 12.92/13.04 (~P1(x841)+~P3(x842)+E(f8(f11(x842),x841),f8(x842,x841))+E(f2(x842),a1)), % 12.92/13.04 inference(equality_inference,[],[64])). % 12.92/13.04 cnf(86,plain, % 12.92/13.04 (E(f2(a10),f12(f2(f11(a10))))), % 12.92/13.04 inference(scs_inference,[],[31,2])). % 12.92/13.04 cnf(89,plain, % 12.92/13.04 (E(f12(f2(f11(a13))),f2(a10))), % 12.92/13.04 inference(scs_inference,[],[34,31,32,28,2,4,7,3])). % 12.92/13.04 cnf(92,plain, % 12.92/13.04 (P4(a9,a9)), % 12.92/13.04 inference(scs_inference,[],[34,31,32,24,25,27,28,33,2,4,7,3,84,56])). % 12.92/13.04 cnf(110,plain, % 12.92/13.04 (E(f12(f2(f11(a10))),f12(f2(f11(a13))))), % 12.92/13.04 inference(scs_inference,[],[31,89,2,3])). % 12.92/13.04 cnf(116,plain, % 12.92/13.04 (E(f12(f2(f11(a13))),f12(f2(f11(a10))))), % 12.92/13.04 inference(scs_inference,[],[110,2])). % 12.92/13.04 cnf(117,plain, % 12.92/13.04 (E(f12(f2(f11(a10))),f2(a13))), % 12.92/13.04 inference(scs_inference,[],[32,110,2,3])). % 12.92/13.04 cnf(129,plain, % 12.92/13.04 (~P1(f2(f11(a10)))+~P1(f2(f11(a13)))), % 12.92/13.04 inference(scs_inference,[],[34,31,86,116,117,92,2,3,20,17,19,21,18,52])). % 12.92/13.04 cnf(1040,plain, % 12.92/13.04 (~P1(f2(f11(a13)))), % 12.92/13.04 inference(scs_inference,[],[29,129,38])). % 12.92/13.04 cnf(1041,plain, % 12.92/13.04 ($false), % 12.92/13.04 inference(scs_inference,[],[30,1040,38]), % 12.92/13.04 ['proof']). % 12.92/13.04 % SZS output end Proof % 12.92/13.04 % Total time :12.360000s %------------------------------------------------------------------------------