%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM559+3 : 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 : 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 12:25:02 EDT 2024 % Result : Theorem 0.59s 0.67s % Output : CNFRefutation 0.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM559+3 : 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 : n020.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 : Sat Jun 22 22:09:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.59/0.65 %------------------------------------------- % 0.59/0.65 % File :CSE---1.7 % 0.59/0.65 % Problem :theBenchmark % 0.59/0.65 % Transform :cnf % 0.59/0.65 % Format :tptp:raw % 0.59/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.59/0.65 % 0.59/0.65 % Result :Theorem 0.010000s % 0.59/0.65 % Output :CNFRefutation 0.010000s % 0.59/0.65 %------------------------------------------- % 0.59/0.65 %------------------------------------------------------------------------------ % 0.59/0.65 % File : NUM559+3 : TPTP v8.2.0. Released v4.0.0. % 0.59/0.65 % Domain : Number Theory % 0.59/0.65 % Problem : Ramsey's Infinite Theorem 12_06, 02 expansion % 0.59/0.65 % Version : Especial. % 0.59/0.65 % English : % 0.59/0.65 % 0.59/0.65 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.59/0.65 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.59/0.65 % Source : [Pas08] % 0.59/0.65 % Names : ramsey_12_06.02 [Pas08] % 0.59/0.65 % 0.59/0.65 % Status : ContradictoryAxioms % 0.59/0.65 % Rating : 0.08 v8.2.0, 0.06 v7.5.0, 0.00 v7.4.0, 0.29 v7.3.0, 0.00 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.10 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.74 v4.0.0 % 0.59/0.65 % Syntax : Number of formulae : 70 ( 8 unt; 8 def) % 0.59/0.65 % Number of atoms : 290 ( 46 equ) % 0.59/0.65 % Maximal formula atoms : 43 ( 4 avg) % 0.59/0.65 % Number of connectives : 242 ( 22 ~; 8 |; 96 &) % 0.59/0.65 % ( 17 <=>; 99 =>; 0 <=; 0 <~>) % 0.59/0.65 % Maximal formula depth : 17 ( 5 avg) % 0.59/0.65 % Maximal term depth : 4 ( 1 avg) % 0.59/0.65 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 0.59/0.65 % Number of functors : 17 ( 17 usr; 9 con; 0-2 aty) % 0.59/0.65 % Number of variables : 118 ( 113 !; 5 ?) % 0.59/0.65 % SPC : FOF_CAX_RFO_SEQ % 0.59/0.65 % 0.59/0.65 % Comments : Problem generated by the SAD system [VLP07] % 0.59/0.65 %------------------------------------------------------------------------------ % 0.59/0.65 fof(mSetSort,axiom, % 0.59/0.65 ! [W0] : % 0.59/0.65 ( aSet0(W0) % 0.59/0.65 => $true ) ). % 0.59/0.65 % 0.59/0.65 fof(mElmSort,axiom, % 0.59/0.65 ! [W0] : % 0.59/0.65 ( aElement0(W0) % 0.59/0.65 => $true ) ). % 0.59/0.65 % 0.59/0.65 fof(mEOfElem,axiom, % 0.59/0.65 ! [W0] : % 0.59/0.65 ( aSet0(W0) % 0.59/0.65 => ! [W1] : % 0.59/0.65 ( aElementOf0(W1,W0) % 0.59/0.65 => aElement0(W1) ) ) ). % 0.59/0.65 % 0.59/0.65 fof(mFinRel,axiom, % 0.59/0.65 ! [W0] : % 0.59/0.65 ( aSet0(W0) % 0.59/0.65 => ( isFinite0(W0) % 0.59/0.65 => $true ) ) ). % 0.59/0.65 % 0.59/0.65 fof(mDefEmp,definition, % 0.59/0.65 ! [W0] : % 0.59/0.65 ( W0 = slcrc0 % 0.59/0.65 <=> ( aSet0(W0) % 0.59/0.65 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 0.59/0.65 % 0.59/0.65 fof(mEmpFin,axiom, % 0.59/0.65 isFinite0(slcrc0) ). % 0.59/0.66 % 0.59/0.66 fof(mCntRel,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => ( isCountable0(W0) % 0.59/0.66 => $true ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCountNFin,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & isCountable0(W0) ) % 0.59/0.66 => ~ isFinite0(W0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCountNFin_01,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & isCountable0(W0) ) % 0.59/0.66 => W0 != slcrc0 ) ). % 0.59/0.66 % 0.59/0.66 fof(mDefSub,definition, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( aSubsetOf0(W1,W0) % 0.59/0.66 <=> ( aSet0(W1) % 0.59/0.66 & ! [W2] : % 0.59/0.66 ( aElementOf0(W2,W1) % 0.59/0.66 => aElementOf0(W2,W0) ) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSubFSet,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & isFinite0(W0) ) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( aSubsetOf0(W1,W0) % 0.59/0.66 => isFinite0(W1) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSubRefl,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => aSubsetOf0(W0,W0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSubASymm,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & aSet0(W1) ) % 0.59/0.66 => ( ( aSubsetOf0(W0,W1) % 0.59/0.66 & aSubsetOf0(W1,W0) ) % 0.59/0.66 => W0 = W1 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSubTrans,axiom, % 0.59/0.66 ! [W0,W1,W2] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & aSet0(W1) % 0.59/0.66 & aSet0(W2) ) % 0.59/0.66 => ( ( aSubsetOf0(W0,W1) % 0.59/0.66 & aSubsetOf0(W1,W2) ) % 0.59/0.66 => aSubsetOf0(W0,W2) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mDefCons,definition, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & aElement0(W1) ) % 0.59/0.66 => ! [W2] : % 0.59/0.66 ( W2 = sdtpldt0(W0,W1) % 0.59/0.66 <=> ( aSet0(W2) % 0.59/0.66 & ! [W3] : % 0.59/0.66 ( aElementOf0(W3,W2) % 0.59/0.66 <=> ( aElement0(W3) % 0.59/0.66 & ( aElementOf0(W3,W0) % 0.59/0.66 | W3 = W1 ) ) ) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mDefDiff,definition, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & aElement0(W1) ) % 0.59/0.66 => ! [W2] : % 0.59/0.66 ( W2 = sdtmndt0(W0,W1) % 0.59/0.66 <=> ( aSet0(W2) % 0.59/0.66 & ! [W3] : % 0.59/0.66 ( aElementOf0(W3,W2) % 0.59/0.66 <=> ( aElement0(W3) % 0.59/0.66 & aElementOf0(W3,W0) % 0.59/0.66 & W3 != W1 ) ) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mConsDiff,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( aElementOf0(W1,W0) % 0.59/0.66 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mDiffCons,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElement0(W0) % 0.59/0.66 & aSet0(W1) ) % 0.59/0.66 => ( ~ aElementOf0(W0,W1) % 0.59/0.66 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCConsSet,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElement0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( ( aSet0(W1) % 0.59/0.66 & isCountable0(W1) ) % 0.59/0.66 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCDiffSet,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElement0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( ( aSet0(W1) % 0.59/0.66 & isCountable0(W1) ) % 0.59/0.66 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mFConsSet,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElement0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( ( aSet0(W1) % 0.59/0.66 & isFinite0(W1) ) % 0.59/0.66 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mFDiffSet,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElement0(W0) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( ( aSet0(W1) % 0.59/0.66 & isFinite0(W1) ) % 0.59/0.66 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mNATSet,axiom, % 0.59/0.66 ( aSet0(szNzAzT0) % 0.59/0.66 & isCountable0(szNzAzT0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mZeroNum,axiom, % 0.59/0.66 aElementOf0(sz00,szNzAzT0) ). % 0.59/0.66 % 0.59/0.66 fof(mSuccNum,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 0.59/0.66 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSuccEquSucc,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.59/0.66 => W0 = W1 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mNatExtra,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => ( W0 = sz00 % 0.59/0.66 | ? [W1] : % 0.59/0.66 ( aElementOf0(W1,szNzAzT0) % 0.59/0.66 & W0 = szszuzczcdt0(W1) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mNatNSucc,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => W0 != szszuzczcdt0(W0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessRel,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( sdtlseqdt0(W0,W1) % 0.59/0.66 => $true ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mZeroLess,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => sdtlseqdt0(sz00,W0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mNoScLessZr,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 0.59/0.66 % 0.59/0.66 fof(mSuccLess,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( sdtlseqdt0(W0,W1) % 0.59/0.66 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessSucc,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessRefl,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => sdtlseqdt0(W0,W0) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessASymm,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( ( sdtlseqdt0(W0,W1) % 0.59/0.66 & sdtlseqdt0(W1,W0) ) % 0.59/0.66 => W0 = W1 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessTrans,axiom, % 0.59/0.66 ! [W0,W1,W2] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) % 0.59/0.66 & aElementOf0(W2,szNzAzT0) ) % 0.59/0.66 => ( ( sdtlseqdt0(W0,W1) % 0.59/0.66 & sdtlseqdt0(W1,W2) ) % 0.59/0.66 => sdtlseqdt0(W0,W2) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mLessTotal,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( sdtlseqdt0(W0,W1) % 0.59/0.66 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mIHSort,axiom, % 0.59/0.66 ! [W0,W1] : % 0.59/0.66 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.66 => ( iLess0(W0,W1) % 0.59/0.66 => $true ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mIH,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aElementOf0(W0,szNzAzT0) % 0.59/0.66 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCardS,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => aElement0(sbrdtbr0(W0)) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCardNum,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 0.59/0.66 <=> isFinite0(W0) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCardEmpty,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( aSet0(W0) % 0.59/0.66 => ( sbrdtbr0(W0) = sz00 % 0.59/0.66 <=> W0 = slcrc0 ) ) ). % 0.59/0.66 % 0.59/0.66 fof(mCardCons,axiom, % 0.59/0.66 ! [W0] : % 0.59/0.66 ( ( aSet0(W0) % 0.59/0.66 & isFinite0(W0) ) % 0.59/0.66 => ! [W1] : % 0.59/0.66 ( aElement0(W1) % 0.59/0.66 => ( ~ aElementOf0(W1,W0) % 0.59/0.66 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mCardDiff,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( aSet0(W0) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( ( isFinite0(W0) % 0.59/0.67 & aElementOf0(W1,W0) ) % 0.59/0.67 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mCardSub,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( aSet0(W0) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( ( isFinite0(W0) % 0.59/0.67 & aSubsetOf0(W1,W0) ) % 0.59/0.67 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mCardSubEx,axiom, % 0.59/0.67 ! [W0,W1] : % 0.59/0.67 ( ( aSet0(W0) % 0.59/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.67 => ( ( isFinite0(W0) % 0.59/0.67 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 0.59/0.67 => ? [W2] : % 0.59/0.67 ( aSubsetOf0(W2,W0) % 0.59/0.67 & sbrdtbr0(W2) = W1 ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mDefMin,definition, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.67 & W0 != slcrc0 ) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( W1 = szmzizndt0(W0) % 0.59/0.67 <=> ( aElementOf0(W1,W0) % 0.59/0.67 & ! [W2] : % 0.59/0.67 ( aElementOf0(W2,W0) % 0.59/0.67 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mDefMax,definition, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.67 & isFinite0(W0) % 0.59/0.67 & W0 != slcrc0 ) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( W1 = szmzazxdt0(W0) % 0.59/0.67 <=> ( aElementOf0(W1,W0) % 0.59/0.67 & ! [W2] : % 0.59/0.67 ( aElementOf0(W2,W0) % 0.59/0.67 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mMinMin,axiom, % 0.59/0.67 ! [W0,W1] : % 0.59/0.67 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.67 & aSubsetOf0(W1,szNzAzT0) % 0.59/0.67 & W0 != slcrc0 % 0.59/0.67 & W1 != slcrc0 ) % 0.59/0.67 => ( ( aElementOf0(szmzizndt0(W0),W1) % 0.59/0.67 & aElementOf0(szmzizndt0(W1),W0) ) % 0.59/0.67 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mDefSeg,definition, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( aElementOf0(W0,szNzAzT0) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( W1 = slbdtrb0(W0) % 0.59/0.67 <=> ( aSet0(W1) % 0.59/0.67 & ! [W2] : % 0.59/0.67 ( aElementOf0(W2,W1) % 0.59/0.67 <=> ( aElementOf0(W2,szNzAzT0) % 0.59/0.67 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSegFin,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( aElementOf0(W0,szNzAzT0) % 0.59/0.67 => isFinite0(slbdtrb0(W0)) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSegZero,axiom, % 0.59/0.67 slbdtrb0(sz00) = slcrc0 ). % 0.59/0.67 % 0.59/0.67 fof(mSegSucc,axiom, % 0.59/0.67 ! [W0,W1] : % 0.59/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.67 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 0.59/0.67 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 0.59/0.67 | W0 = W1 ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSegLess,axiom, % 0.59/0.67 ! [W0,W1] : % 0.59/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.67 => ( sdtlseqdt0(W0,W1) % 0.59/0.67 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mFinSubSeg,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.67 & isFinite0(W0) ) % 0.59/0.67 => ? [W1] : % 0.59/0.67 ( aElementOf0(W1,szNzAzT0) % 0.59/0.67 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mCardSeg,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( aElementOf0(W0,szNzAzT0) % 0.59/0.67 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 0.59/0.67 % 0.59/0.67 fof(mDefSel,definition, % 0.59/0.67 ! [W0,W1] : % 0.59/0.67 ( ( aSet0(W0) % 0.59/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.67 => ! [W2] : % 0.59/0.67 ( W2 = slbdtsldtrb0(W0,W1) % 0.59/0.67 <=> ( aSet0(W2) % 0.59/0.67 & ! [W3] : % 0.59/0.67 ( aElementOf0(W3,W2) % 0.59/0.67 <=> ( aSubsetOf0(W3,W0) % 0.59/0.67 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSelFSet,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSet0(W0) % 0.59/0.67 & isFinite0(W0) ) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( aElementOf0(W1,szNzAzT0) % 0.59/0.67 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSelNSet,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSet0(W0) % 0.59/0.67 & ~ isFinite0(W0) ) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( aElementOf0(W1,szNzAzT0) % 0.59/0.67 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 0.59/0.67 % 0.59/0.67 fof(mSelCSet,axiom, % 0.59/0.67 ! [W0] : % 0.59/0.67 ( ( aSet0(W0) % 0.59/0.67 & isCountable0(W0) ) % 0.59/0.67 => ! [W1] : % 0.59/0.67 ( ( aElementOf0(W1,szNzAzT0) % 0.59/0.67 & W1 != sz00 ) % 0.59/0.67 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2202,hypothesis, % 0.59/0.67 aElementOf0(xk,szNzAzT0) ). % 0.59/0.67 % 0.59/0.67 fof(m__2202_02,hypothesis, % 0.59/0.67 ( aSet0(xS) % 0.59/0.67 & aSet0(xT) % 0.59/0.67 & xk != sz00 ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2227,hypothesis, % 0.59/0.67 ( aSet0(slbdtsldtrb0(xS,xk)) % 0.59/0.67 & ! [W0] : % 0.59/0.67 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.59/0.67 => ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xS) ) % 0.59/0.67 & aSubsetOf0(W0,xS) % 0.59/0.67 & sbrdtbr0(W0) = xk ) ) % 0.59/0.67 & ( ( ( ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xS) ) ) % 0.59/0.67 | aSubsetOf0(W0,xS) ) % 0.59/0.67 & sbrdtbr0(W0) = xk ) % 0.59/0.67 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.59/0.67 & aSet0(slbdtsldtrb0(xT,xk)) % 0.59/0.67 & ! [W0] : % 0.59/0.67 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk)) % 0.59/0.67 => ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xT) ) % 0.59/0.67 & aSubsetOf0(W0,xT) % 0.59/0.67 & sbrdtbr0(W0) = xk ) ) % 0.59/0.67 & ( ( ( ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xT) ) ) % 0.59/0.67 | aSubsetOf0(W0,xT) ) % 0.59/0.67 & sbrdtbr0(W0) = xk ) % 0.59/0.67 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) % 0.59/0.67 & ! [W0] : % 0.59/0.67 ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.59/0.67 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) % 0.59/0.67 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) % 0.59/0.67 & ~ ( ! [W0] : % 0.59/0.67 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.59/0.67 => ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xS) ) % 0.59/0.67 & aSubsetOf0(W0,xS) % 0.59/0.67 & sbrdtbr0(W0) = xk ) ) % 0.59/0.67 & ( ( ( ( aSet0(W0) % 0.59/0.67 & ! [W1] : % 0.59/0.67 ( aElementOf0(W1,W0) % 0.59/0.67 => aElementOf0(W1,xS) ) ) % 0.59/0.67 | aSubsetOf0(W0,xS) ) % 0.59/0.67 & sbrdtbr0(W0) = xk ) % 0.59/0.67 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.59/0.67 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.59/0.67 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2256,hypothesis, % 0.59/0.67 aElementOf0(xx,xS) ). % 0.59/0.67 % 0.59/0.67 fof(m__2270,hypothesis, % 0.59/0.67 ( aSet0(xQ) % 0.59/0.67 & ! [W0] : % 0.59/0.67 ( aElementOf0(W0,xQ) % 0.59/0.67 => aElementOf0(W0,xS) ) % 0.59/0.67 & aSubsetOf0(xQ,xS) % 0.59/0.67 & sbrdtbr0(xQ) = xk % 0.59/0.67 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2291,hypothesis, % 0.59/0.67 ( aSet0(xQ) % 0.59/0.67 & isFinite0(xQ) % 0.59/0.67 & sbrdtbr0(xQ) = xk ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2304,hypothesis, % 0.59/0.67 ( aElement0(xy) % 0.59/0.67 & aElementOf0(xy,xQ) ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2323,hypothesis, % 0.59/0.67 ~ aElementOf0(xx,xQ) ). % 0.59/0.67 % 0.59/0.67 fof(m__2338,hypothesis, % 0.59/0.67 ~ ~ aElementOf0(xx,xQ) ). % 0.59/0.67 % 0.59/0.67 fof(m__,conjecture, % 0.59/0.67 aElementOf0(xx,xT) ). % 0.59/0.67 % 0.59/0.67 %------------------------------------------------------------------------------ % 0.59/0.67 %------------------------------------------- % 0.59/0.67 % Proof found % 0.59/0.67 % SZS status Theorem for theBenchmark % 0.59/0.67 % SZS output start Proof % 0.59/0.67 %ClaNum:200(EqnAxiom:51) % 0.59/0.67 %VarNum:771(SingletonVarNum:238) % 0.59/0.67 %MaxLitNum:8 % 0.59/0.67 %MaxfuncDepth:3 % 0.59/0.67 %SharedTerms:39 % 0.59/0.67 %goalClause: 77 % 0.59/0.67 %singleGoalClaCount:1 % 0.59/0.67 [55]P1(a24) % 0.59/0.67 [56]P1(a29) % 0.59/0.67 [57]P1(a30) % 0.59/0.67 [59]P1(a1) % 0.59/0.67 [60]P2(a31) % 0.59/0.67 [61]P4(a22) % 0.59/0.67 [62]P4(a1) % 0.59/0.67 [63]P5(a24) % 0.59/0.67 [64]P3(a18,a24) % 0.59/0.67 [65]P3(a28,a24) % 0.59/0.67 [66]P3(a32,a29) % 0.59/0.67 [67]P3(a32,a1) % 0.59/0.67 [68]P3(a31,a1) % 0.59/0.67 [69]P6(a1,a29) % 0.59/0.67 [75]~E(a18,a28) % 0.59/0.67 [77]~P3(a32,a30) % 0.59/0.67 [78]~P3(a32,a1) % 0.59/0.67 [53]E(f2(a1),a28) % 0.59/0.67 [54]E(f19(a18),a22) % 0.59/0.67 [70]P1(f23(a29,a28)) % 0.59/0.67 [71]P1(f23(a30,a28)) % 0.59/0.67 [72]P3(a1,f23(a29,a28)) % 0.59/0.67 [73]P3(a3,f23(a29,a28)) % 0.59/0.67 [74]P6(f23(a29,a28),f23(a30,a28)) % 0.59/0.67 [76]~E(f23(a29,a28),a22) % 0.59/0.67 [79]P1(x791)+~E(x791,a22) % 0.59/0.67 [85]~P1(x851)+P6(x851,x851) % 0.59/0.67 [92]~P3(x921,a1)+P3(x921,a29) % 0.59/0.67 [93]~P3(x931,a24)+P8(a18,x931) % 0.59/0.67 [99]P8(x991,x991)+~P3(x991,a24) % 0.59/0.67 [83]~P1(x831)+P2(f2(x831)) % 0.59/0.67 [87]~P3(x871,a24)+~E(f25(x871),a18) % 0.59/0.67 [88]~P3(x881,a24)+~E(f25(x881),x881) % 0.59/0.67 [90]~P3(x901,a24)+P4(f19(x901)) % 0.59/0.67 [100]~P3(x1001,a24)+P3(f25(x1001),a24) % 0.59/0.67 [101]~P3(x1011,a24)+P8(x1011,f25(x1011)) % 0.59/0.67 [102]~P3(x1021,a24)+P7(x1021,f25(x1021)) % 0.59/0.67 [110]~P3(x1101,a24)+~P8(f25(x1101),a18) % 0.59/0.67 [120]~P3(x1201,f23(a29,a28))+E(f2(x1201),a28) % 0.59/0.67 [121]~P3(x1211,f23(a30,a28))+E(f2(x1211),a28) % 0.59/0.67 [123]P1(x1231)+~P3(x1231,f23(a29,a28)) % 0.59/0.67 [124]P1(x1241)+~P3(x1241,f23(a30,a28)) % 0.59/0.67 [139]P6(x1391,a29)+~P3(x1391,f23(a29,a28)) % 0.59/0.67 [140]P6(x1401,a30)+~P3(x1401,f23(a30,a28)) % 0.59/0.67 [163]~P3(x1631,f23(a29,a28))+P3(x1631,f23(a30,a28)) % 0.59/0.67 [91]~P3(x911,a24)+E(f2(f19(x911)),x911) % 0.59/0.67 [86]~P3(x862,x861)+~E(x861,a22) % 0.59/0.67 [82]~P1(x821)+~P5(x821)+~E(x821,a22) % 0.59/0.67 [84]~P4(x841)+~P5(x841)+~P1(x841) % 0.59/0.67 [80]~P1(x801)+~E(x801,a22)+E(f2(x801),a18) % 0.59/0.67 [81]~P1(x811)+E(x811,a22)+~E(f2(x811),a18) % 0.59/0.67 [89]~P1(x891)+P3(f9(x891),x891)+E(x891,a22) % 0.59/0.67 [96]~P1(x961)+~P4(x961)+P3(f2(x961),a24) % 0.59/0.67 [103]~P3(x1031,a24)+E(x1031,a18)+P3(f10(x1031),a24) % 0.59/0.67 [104]~P1(x1041)+P4(x1041)+~P3(f2(x1041),a24) % 0.59/0.67 [109]~P4(x1091)+~P6(x1091,a24)+P3(f4(x1091),a24) % 0.59/0.67 [127]~P6(x1271,a29)+P3(x1271,f23(a29,a28))+~E(f2(x1271),a28) % 0.59/0.67 [128]~P6(x1281,a30)+P3(x1281,f23(a30,a28))+~E(f2(x1281),a28) % 0.59/0.67 [94]~P3(x941,a24)+E(x941,a18)+E(f25(f10(x941)),x941) % 0.59/0.67 [125]~P4(x1251)+~P6(x1251,a24)+P6(x1251,f19(f4(x1251))) % 0.59/0.67 [97]~P6(x971,x972)+P1(x971)+~P1(x972) % 0.59/0.67 [98]~P3(x981,x982)+P2(x981)+~P1(x982) % 0.59/0.67 [95]P1(x951)+~P3(x952,a24)+~E(x951,f19(x952)) % 0.59/0.67 [167]~P3(x1671,x1672)+P3(x1671,a29)+~P3(x1672,f23(a29,a28)) % 0.59/0.67 [168]~P3(x1681,x1682)+P3(x1681,a30)+~P3(x1682,f23(a30,a28)) % 0.59/0.67 [148]~P1(x1481)+~P3(x1482,x1481)+E(f20(f21(x1481,x1482),x1482),x1481) % 0.59/0.67 [144]~P1(x1441)+P3(f5(x1441),x1441)+P3(x1441,f23(a29,a28))+~E(f2(x1441),a28) % 0.59/0.67 [145]~P1(x1451)+P3(f7(x1451),x1451)+P3(x1451,f23(a30,a28))+~E(f2(x1451),a28) % 0.59/0.67 [146]~P1(x1461)+P3(f8(x1461),x1461)+P3(x1461,f23(a29,a28))+~E(f2(x1461),a28) % 0.59/0.67 [156]~P1(x1561)+P3(x1561,f23(a29,a28))+~E(f2(x1561),a28)+~P3(f5(x1561),a29) % 0.59/0.67 [157]~P1(x1571)+P3(x1571,f23(a29,a28))+~E(f2(x1571),a28)+~P3(f8(x1571),a29) % 0.59/0.67 [158]~P1(x1581)+P3(x1581,f23(a30,a28))+~E(f2(x1581),a28)+~P3(f7(x1581),a30) % 0.59/0.67 [105]~P4(x1052)+~P6(x1051,x1052)+P4(x1051)+~P1(x1052) % 0.59/0.67 [108]P3(x1082,x1081)+~E(x1082,f26(x1081))+~P6(x1081,a24)+E(x1081,a22) % 0.59/0.67 [112]~P1(x1121)+~P2(x1122)+~P4(x1121)+P4(f20(x1121,x1122)) % 0.59/0.67 [113]~P1(x1131)+~P2(x1132)+~P4(x1131)+P4(f21(x1131,x1132)) % 0.59/0.67 [114]~P1(x1141)+~P2(x1142)+~P5(x1141)+P5(f20(x1141,x1142)) % 0.59/0.67 [115]~P1(x1151)+~P2(x1152)+~P5(x1151)+P5(f21(x1151,x1152)) % 0.59/0.67 [116]~P1(x1161)+P4(x1161)+~P3(x1162,a24)+~E(f23(x1161,x1162),a22) % 0.59/0.67 [118]E(x1181,x1182)+~E(f25(x1181),f25(x1182))+~P3(x1182,a24)+~P3(x1181,a24) % 0.59/0.67 [131]~P1(x1312)+~P4(x1312)+~P6(x1311,x1312)+P8(f2(x1311),f2(x1312)) % 0.59/0.67 [134]~P1(x1341)+~P4(x1341)+~P3(x1342,a24)+P4(f23(x1341,x1342)) % 0.59/0.67 [143]~P1(x1431)+~P1(x1432)+P6(x1431,x1432)+P3(f11(x1432,x1431),x1431) % 0.59/0.67 [152]P8(x1521,x1522)+P8(f25(x1522),x1521)+~P3(x1522,a24)+~P3(x1521,a24) % 0.59/0.67 [169]~P8(x1691,x1692)+~P3(x1692,a24)+~P3(x1691,a24)+P6(f19(x1691),f19(x1692)) % 0.59/0.67 [170]~P8(x1701,x1702)+~P3(x1702,a24)+~P3(x1701,a24)+P8(f25(x1701),f25(x1702)) % 0.59/0.67 [172]~P1(x1721)+~P1(x1722)+P6(x1721,x1722)+~P3(f11(x1722,x1721),x1722) % 0.59/0.67 [174]P8(x1741,x1742)+~P3(x1742,a24)+~P3(x1741,a24)+~P6(f19(x1741),f19(x1742)) % 0.59/0.67 [175]P8(x1751,x1752)+~P3(x1752,a24)+~P3(x1751,a24)+~P8(f25(x1751),f25(x1752)) % 0.59/0.67 [147]P3(x1472,x1471)+~P1(x1471)+~P2(x1472)+E(f21(f20(x1471,x1472),x1472),x1471) % 0.59/0.67 [154]~E(x1541,x1542)+~P3(x1542,a24)+~P3(x1541,a24)+P3(x1541,f19(f25(x1542))) % 0.59/0.67 [180]~P3(x1802,a24)+~P3(x1801,a24)+~P3(x1801,f19(x1802))+P3(x1801,f19(f25(x1802))) % 0.59/0.67 [179]~P1(x1791)+~P4(x1791)+~P3(x1792,x1791)+E(f25(f2(f21(x1791,x1792))),f2(x1791)) % 0.59/0.67 [141]~P1(x1412)+~P6(x1413,x1412)+P3(x1411,x1412)+~P3(x1411,x1413) % 0.59/0.67 [106]~P1(x1062)+~P2(x1063)+P1(x1061)+~E(x1061,f20(x1062,x1063)) % 0.59/0.67 [107]~P1(x1072)+~P2(x1073)+P1(x1071)+~E(x1071,f21(x1072,x1073)) % 0.59/0.67 [117]~P1(x1172)+P1(x1171)+~P3(x1173,a24)+~E(x1171,f23(x1172,x1173)) % 0.59/0.67 [132]~P3(x1321,x1322)+~P3(x1323,a24)+P3(x1321,a24)+~E(x1322,f19(x1323)) % 0.59/0.67 [149]~P3(x1491,x1493)+~P3(x1492,a24)+P8(f25(x1491),x1492)+~E(x1493,f19(x1492)) % 0.59/0.67 [129]~P1(x1292)+~P1(x1291)+~P6(x1292,x1291)+~P6(x1291,x1292)+E(x1291,x1292) % 0.59/0.67 [164]~P8(x1642,x1641)+~P8(x1641,x1642)+E(x1641,x1642)+~P3(x1642,a24)+~P3(x1641,a24) % 0.59/0.67 [111]~P4(x1111)+P3(x1112,x1111)+~E(x1112,f27(x1111))+~P6(x1111,a24)+E(x1111,a22) % 0.59/0.67 [137]~P1(x1372)+~P5(x1372)+~P3(x1371,a24)+E(x1371,a18)+P5(f23(x1372,x1371)) % 0.59/0.67 [171]~P3(x1712,x1711)+P3(f14(x1711,x1712),x1711)+~P6(x1711,a24)+E(x1711,a22)+E(x1712,f26(x1711)) % 0.59/0.67 [181]~P1(x1811)+~P4(x1811)+~P3(x1812,a24)+~P8(x1812,f2(x1811))+P6(f15(x1811,x1812),x1811) % 0.59/0.67 [182]~P1(x1821)+P3(f17(x1822,x1821),x1821)+~P3(x1822,a24)+E(x1821,f19(x1822))+P3(f17(x1822,x1821),a24) % 0.59/0.67 [183]~P3(x1832,x1831)+~P6(x1831,a24)+~P8(x1832,f14(x1831,x1832))+E(x1831,a22)+E(x1832,f26(x1831)) % 0.59/0.67 [153]P3(x1532,x1531)+~P1(x1531)+~P2(x1532)+~P4(x1531)+E(f2(f20(x1531,x1532)),f25(f2(x1531))) % 0.59/0.67 [178]~P1(x1781)+~P4(x1781)+~P3(x1782,a24)+~P8(x1782,f2(x1781))+E(f2(f15(x1781,x1782)),x1782) % 0.59/0.67 [184]E(x1841,x1842)+P3(x1841,f19(x1842))+~P3(x1842,a24)+~P3(x1841,a24)+~P3(x1841,f19(f25(x1842))) % 0.59/0.67 [188]~P1(x1881)+P3(f17(x1882,x1881),x1881)+~P3(x1882,a24)+E(x1881,f19(x1882))+P8(f25(f17(x1882,x1881)),x1882) % 0.59/0.67 [142]~P3(x1423,x1421)+P8(x1422,x1423)+~E(x1422,f26(x1421))+~P6(x1421,a24)+E(x1421,a22) % 0.59/0.67 [173]P3(x1731,x1732)+~P3(x1733,a24)+~P3(x1731,a24)+~P8(f25(x1731),x1733)+~E(x1732,f19(x1733)) % 0.59/0.67 [133]~P1(x1334)+~P2(x1332)+~P3(x1331,x1333)+~E(x1331,x1332)+~E(x1333,f21(x1334,x1332)) % 0.59/0.67 [135]~P1(x1353)+~P2(x1354)+~P3(x1351,x1352)+P2(x1351)+~E(x1352,f20(x1353,x1354)) % 0.59/0.67 [136]~P1(x1363)+~P2(x1364)+~P3(x1361,x1362)+P2(x1361)+~E(x1362,f21(x1363,x1364)) % 0.59/0.67 [151]~P1(x1512)+~P2(x1514)+~P3(x1511,x1513)+P3(x1511,x1512)+~E(x1513,f21(x1512,x1514)) % 0.59/0.67 [159]~P1(x1594)+~P3(x1591,x1593)+~P3(x1592,a24)+E(f2(x1591),x1592)+~E(x1593,f23(x1594,x1592)) % 0.59/0.67 [165]~P1(x1652)+~P3(x1651,x1653)+P6(x1651,x1652)+~P3(x1654,a24)+~E(x1653,f23(x1652,x1654)) % 0.59/0.67 [177]~P4(x1771)+~P3(x1772,x1771)+P3(f16(x1771,x1772),x1771)+~P6(x1771,a24)+E(x1771,a22)+E(x1772,f27(x1771)) % 0.59/0.67 [186]~P4(x1861)+~P3(x1862,x1861)+~P6(x1861,a24)+~P8(f16(x1861,x1862),x1862)+E(x1861,a22)+E(x1862,f27(x1861)) % 0.59/0.67 [192]~P1(x1921)+~P3(x1922,a24)+~P3(f17(x1922,x1921),x1921)+E(x1921,f19(x1922))+~P3(f17(x1922,x1921),a24)+~P8(f25(f17(x1922,x1921)),x1922) % 0.59/0.67 [160]~P1(x1602)+~P1(x1601)+~P6(x1603,x1602)+~P6(x1601,x1603)+P6(x1601,x1602)+~P1(x1603) % 0.59/0.67 [187]~P8(x1871,x1873)+P8(x1871,x1872)+~P8(x1873,x1872)+~P3(x1872,a24)+~P3(x1873,a24)+~P3(x1871,a24) % 0.59/0.67 [150]~P4(x1501)+~P3(x1502,x1501)+P8(x1502,x1503)+~E(x1503,f27(x1501))+~P6(x1501,a24)+E(x1501,a22) % 0.59/0.67 [189]~P1(x1891)+~P1(x1892)+~P2(x1893)+P3(f12(x1892,x1893,x1891),x1891)+~E(f12(x1892,x1893,x1891),x1893)+E(x1891,f21(x1892,x1893)) % 0.59/0.67 [190]~P1(x1901)+~P1(x1902)+~P2(x1903)+P3(f13(x1902,x1903,x1901),x1901)+E(x1901,f20(x1902,x1903))+P2(f13(x1902,x1903,x1901)) % 0.59/0.67 [191]~P1(x1911)+~P1(x1912)+~P2(x1913)+P3(f12(x1912,x1913,x1911),x1911)+E(x1911,f21(x1912,x1913))+P2(f12(x1912,x1913,x1911)) % 0.59/0.67 [193]~P1(x1931)+~P1(x1932)+~P2(x1933)+P3(f12(x1932,x1933,x1931),x1931)+P3(f12(x1932,x1933,x1931),x1932)+E(x1931,f21(x1932,x1933)) % 0.59/0.67 [195]~P1(x1951)+~P1(x1952)+P3(f6(x1952,x1953,x1951),x1951)+P6(f6(x1952,x1953,x1951),x1952)+~P3(x1953,a24)+E(x1951,f23(x1952,x1953)) % 0.59/0.67 [194]~P1(x1941)+~P1(x1942)+P3(f6(x1942,x1943,x1941),x1941)+~P3(x1943,a24)+E(x1941,f23(x1942,x1943))+E(f2(f6(x1942,x1943,x1941)),x1943) % 0.59/0.67 [130]~P1(x1304)+~P2(x1303)+~P2(x1301)+P3(x1301,x1302)+~E(x1301,x1303)+~E(x1302,f20(x1304,x1303)) % 0.59/0.67 [155]~P1(x1553)+~P2(x1552)+~P3(x1551,x1554)+E(x1551,x1552)+P3(x1551,x1553)+~E(x1554,f20(x1553,x1552)) % 0.59/0.67 [161]~P1(x1613)+~P2(x1614)+~P2(x1611)+~P3(x1611,x1613)+P3(x1611,x1612)+~E(x1612,f20(x1613,x1614)) % 0.59/0.67 [176]~P1(x1764)+~P6(x1761,x1764)+P3(x1761,x1762)+~P3(x1763,a24)+~E(x1762,f23(x1764,x1763))+~E(f2(x1761),x1763) % 0.59/0.67 [185]E(f26(x1852),f26(x1851))+~P6(x1851,a24)+~P6(x1852,a24)+~P3(f26(x1851),x1852)+~P3(f26(x1852),x1851)+E(x1851,a22)+E(x1852,a22) % 0.59/0.67 [196]~P1(x1961)+~P1(x1962)+~P2(x1963)+E(f13(x1962,x1963,x1961),x1963)+P3(f13(x1962,x1963,x1961),x1961)+P3(f13(x1962,x1963,x1961),x1962)+E(x1961,f20(x1962,x1963)) % 0.59/0.67 [197]~P1(x1971)+~P1(x1972)+~P2(x1973)+~E(f13(x1972,x1973,x1971),x1973)+~P3(f13(x1972,x1973,x1971),x1971)+E(x1971,f20(x1972,x1973))+~P2(f13(x1972,x1973,x1971)) % 0.59/0.67 [198]~P1(x1981)+~P1(x1982)+~P2(x1983)+~P3(f13(x1982,x1983,x1981),x1981)+~P3(f13(x1982,x1983,x1981),x1982)+E(x1981,f20(x1982,x1983))+~P2(f13(x1982,x1983,x1981)) % 0.59/0.67 [199]~P1(x1991)+~P1(x1992)+~P3(x1993,a24)+~P3(f6(x1992,x1993,x1991),x1991)+~P6(f6(x1992,x1993,x1991),x1992)+E(x1991,f23(x1992,x1993))+~E(f2(f6(x1992,x1993,x1991)),x1993) % 0.59/0.67 [162]~P1(x1624)+~P2(x1622)+~P2(x1621)+~P3(x1621,x1624)+E(x1621,x1622)+P3(x1621,x1623)+~E(x1623,f21(x1624,x1622)) % 0.59/0.67 [200]~P1(x2001)+~P1(x2002)+~P2(x2003)+E(f12(x2002,x2003,x2001),x2003)+~P3(f12(x2002,x2003,x2001),x2001)+~P3(f12(x2002,x2003,x2001),x2002)+E(x2001,f21(x2002,x2003))+~P2(f12(x2002,x2003,x2001)) % 0.59/0.67 %EqnAxiom % 0.59/0.67 [1]E(x11,x11) % 0.59/0.67 [2]E(x22,x21)+~E(x21,x22) % 0.59/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.59/0.67 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.59/0.67 [5]~E(x51,x52)+E(f12(x51,x53,x54),f12(x52,x53,x54)) % 0.59/0.67 [6]~E(x61,x62)+E(f12(x63,x61,x64),f12(x63,x62,x64)) % 0.59/0.67 [7]~E(x71,x72)+E(f12(x73,x74,x71),f12(x73,x74,x72)) % 0.59/0.67 [8]~E(x81,x82)+E(f19(x81),f19(x82)) % 0.59/0.67 [9]~E(x91,x92)+E(f23(x91,x93),f23(x92,x93)) % 0.59/0.67 [10]~E(x101,x102)+E(f23(x103,x101),f23(x103,x102)) % 0.59/0.67 [11]~E(x111,x112)+E(f26(x111),f26(x112)) % 0.59/0.67 [12]~E(x121,x122)+E(f17(x121,x123),f17(x122,x123)) % 0.59/0.67 [13]~E(x131,x132)+E(f17(x133,x131),f17(x133,x132)) % 0.59/0.67 [14]~E(x141,x142)+E(f8(x141),f8(x142)) % 0.59/0.67 [15]~E(x151,x152)+E(f14(x151,x153),f14(x152,x153)) % 0.59/0.67 [16]~E(x161,x162)+E(f14(x163,x161),f14(x163,x162)) % 0.59/0.67 [17]~E(x171,x172)+E(f21(x171,x173),f21(x172,x173)) % 0.59/0.67 [18]~E(x181,x182)+E(f21(x183,x181),f21(x183,x182)) % 0.59/0.67 [19]~E(x191,x192)+E(f15(x191,x193),f15(x192,x193)) % 0.59/0.67 [20]~E(x201,x202)+E(f15(x203,x201),f15(x203,x202)) % 0.59/0.67 [21]~E(x211,x212)+E(f25(x211),f25(x212)) % 0.59/0.67 [22]~E(x221,x222)+E(f6(x221,x223,x224),f6(x222,x223,x224)) % 0.59/0.67 [23]~E(x231,x232)+E(f6(x233,x231,x234),f6(x233,x232,x234)) % 0.59/0.67 [24]~E(x241,x242)+E(f6(x243,x244,x241),f6(x243,x244,x242)) % 0.59/0.67 [25]~E(x251,x252)+E(f13(x251,x253,x254),f13(x252,x253,x254)) % 0.59/0.67 [26]~E(x261,x262)+E(f13(x263,x261,x264),f13(x263,x262,x264)) % 0.59/0.67 [27]~E(x271,x272)+E(f13(x273,x274,x271),f13(x273,x274,x272)) % 0.59/0.67 [28]~E(x281,x282)+E(f20(x281,x283),f20(x282,x283)) % 0.59/0.67 [29]~E(x291,x292)+E(f20(x293,x291),f20(x293,x292)) % 0.59/0.67 [30]~E(x301,x302)+E(f27(x301),f27(x302)) % 0.59/0.67 [31]~E(x311,x312)+E(f9(x311),f9(x312)) % 0.59/0.67 [32]~E(x321,x322)+E(f16(x321,x323),f16(x322,x323)) % 0.59/0.67 [33]~E(x331,x332)+E(f16(x333,x331),f16(x333,x332)) % 0.59/0.67 [34]~E(x341,x342)+E(f5(x341),f5(x342)) % 0.59/0.67 [35]~E(x351,x352)+E(f11(x351,x353),f11(x352,x353)) % 0.59/0.67 [36]~E(x361,x362)+E(f11(x363,x361),f11(x363,x362)) % 0.59/0.67 [37]~E(x371,x372)+E(f10(x371),f10(x372)) % 0.59/0.67 [38]~E(x381,x382)+E(f7(x381),f7(x382)) % 0.59/0.67 [39]~E(x391,x392)+E(f4(x391),f4(x392)) % 0.59/0.67 [40]~P1(x401)+P1(x402)+~E(x401,x402) % 0.59/0.68 [41]P3(x412,x413)+~E(x411,x412)+~P3(x411,x413) % 0.59/0.68 [42]P3(x423,x422)+~E(x421,x422)+~P3(x423,x421) % 0.59/0.68 [43]~P4(x431)+P4(x432)+~E(x431,x432) % 0.59/0.68 [44]~P2(x441)+P2(x442)+~E(x441,x442) % 0.59/0.68 [45]P8(x452,x453)+~E(x451,x452)+~P8(x451,x453) % 0.59/0.68 [46]P8(x463,x462)+~E(x461,x462)+~P8(x463,x461) % 0.59/0.68 [47]~P5(x471)+P5(x472)+~E(x471,x472) % 0.59/0.68 [48]P6(x482,x483)+~E(x481,x482)+~P6(x481,x483) % 0.59/0.68 [49]P6(x493,x492)+~E(x491,x492)+~P6(x493,x491) % 0.59/0.68 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503) % 0.59/0.68 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511) % 0.59/0.68 % 0.59/0.68 %------------------------------------------- % 0.59/0.68 cnf(226,plain, % 0.59/0.68 ($false), % 0.59/0.68 inference(scs_inference,[],[67,78]), % 0.59/0.68 ['proof']). % 0.59/0.68 % SZS output end Proof % 0.59/0.68 % Total time :0.010000s %------------------------------------------------------------------------------