%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM545+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 : 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 12:24:56 EDT 2024 % Result : Theorem 5.66s 5.77s % Output : CNFRefutation 5.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : NUM545+2 : TPTP v8.2.0. Released v4.0.0. % 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n026.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 % 0.12/0.34 % DateTime : Sun Jun 23 03:53:54 EDT 2024 % 0.12/0.35 % CPUTime : % 0.55/0.59 start to proof:theBenchmark % 5.66/5.75 %------------------------------------------- % 5.66/5.75 % File :CSE---1.7 % 5.66/5.75 % Problem :theBenchmark % 5.66/5.75 % Transform :cnf % 5.66/5.75 % Format :tptp:raw % 5.66/5.75 % Command :java -jar mcs_scs.jar %d %s % 5.66/5.75 % 5.66/5.75 % Result :Theorem 5.100000s % 5.66/5.75 % Output :CNFRefutation 5.100000s % 5.66/5.75 %------------------------------------------- % 5.66/5.75 %------------------------------------------------------------------------------ % 5.66/5.75 % File : NUM545+2 : TPTP v8.2.0. Released v4.0.0. % 5.66/5.75 % Domain : Number Theory % 5.66/5.75 % Problem : Ramsey's Infinite Theorem 11_02, 01 expansion % 5.66/5.75 % Version : Especial. % 5.66/5.75 % English : % 5.66/5.75 % 5.66/5.75 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 5.66/5.75 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 5.66/5.75 % Source : [Pas08] % 5.66/5.75 % Names : ramsey_11_02.01 [Pas08] % 5.66/5.75 % 5.66/5.75 % Status : Theorem % 5.66/5.75 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.07 v7.3.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.12 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0, 0.48 v5.2.0, 0.35 v5.1.0, 0.43 v5.0.0, 0.54 v4.1.0, 0.61 v4.0.1, 0.74 v4.0.0 % 5.66/5.75 % Syntax : Number of formulae : 57 ( 3 unt; 7 def) % 5.66/5.75 % Number of atoms : 227 ( 32 equ) % 5.66/5.75 % Maximal formula atoms : 12 ( 3 avg) % 5.66/5.75 % Number of connectives : 185 ( 15 ~; 5 |; 67 &) % 5.66/5.75 % ( 17 <=>; 81 =>; 0 <=; 0 <~>) % 5.66/5.75 % Maximal formula depth : 12 ( 5 avg) % 5.66/5.75 % Maximal term depth : 4 ( 1 avg) % 5.66/5.75 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 5.66/5.75 % Number of functors : 11 ( 11 usr; 4 con; 0-2 aty) % 5.66/5.75 % Number of variables : 101 ( 96 !; 5 ?) % 5.66/5.75 % SPC : FOF_THM_RFO_SEQ % 5.66/5.75 % 5.66/5.75 % Comments : Problem generated by the SAD system [VLP07] % 5.66/5.75 %------------------------------------------------------------------------------ % 5.66/5.75 fof(mSetSort,axiom, % 5.66/5.75 ! [W0] : % 5.66/5.75 ( aSet0(W0) % 5.66/5.75 => $true ) ). % 5.66/5.75 % 5.66/5.75 fof(mElmSort,axiom, % 5.66/5.75 ! [W0] : % 5.66/5.75 ( aElement0(W0) % 5.66/5.75 => $true ) ). % 5.66/5.75 % 5.66/5.75 fof(mEOfElem,axiom, % 5.66/5.75 ! [W0] : % 5.66/5.75 ( aSet0(W0) % 5.66/5.75 => ! [W1] : % 5.66/5.75 ( aElementOf0(W1,W0) % 5.66/5.75 => aElement0(W1) ) ) ). % 5.66/5.75 % 5.66/5.75 fof(mFinRel,axiom, % 5.66/5.75 ! [W0] : % 5.66/5.75 ( aSet0(W0) % 5.66/5.75 => ( isFinite0(W0) % 5.66/5.75 => $true ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mDefEmp,definition, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( W0 = slcrc0 % 5.66/5.76 <=> ( aSet0(W0) % 5.66/5.76 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mEmpFin,axiom, % 5.66/5.76 isFinite0(slcrc0) ). % 5.66/5.76 % 5.66/5.76 fof(mCntRel,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aSet0(W0) % 5.66/5.76 => ( isCountable0(W0) % 5.66/5.76 => $true ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mCountNFin,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & isCountable0(W0) ) % 5.66/5.76 => ~ isFinite0(W0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mCountNFin_01,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & isCountable0(W0) ) % 5.66/5.76 => W0 != slcrc0 ) ). % 5.66/5.76 % 5.66/5.76 fof(mDefSub,definition, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aSet0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( aSubsetOf0(W1,W0) % 5.66/5.76 <=> ( aSet0(W1) % 5.66/5.76 & ! [W2] : % 5.66/5.76 ( aElementOf0(W2,W1) % 5.66/5.76 => aElementOf0(W2,W0) ) ) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSubFSet,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & isFinite0(W0) ) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( aSubsetOf0(W1,W0) % 5.66/5.76 => isFinite0(W1) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSubRefl,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aSet0(W0) % 5.66/5.76 => aSubsetOf0(W0,W0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSubASymm,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & aSet0(W1) ) % 5.66/5.76 => ( ( aSubsetOf0(W0,W1) % 5.66/5.76 & aSubsetOf0(W1,W0) ) % 5.66/5.76 => W0 = W1 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSubTrans,axiom, % 5.66/5.76 ! [W0,W1,W2] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & aSet0(W1) % 5.66/5.76 & aSet0(W2) ) % 5.66/5.76 => ( ( aSubsetOf0(W0,W1) % 5.66/5.76 & aSubsetOf0(W1,W2) ) % 5.66/5.76 => aSubsetOf0(W0,W2) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mDefCons,definition, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & aElement0(W1) ) % 5.66/5.76 => ! [W2] : % 5.66/5.76 ( W2 = sdtpldt0(W0,W1) % 5.66/5.76 <=> ( aSet0(W2) % 5.66/5.76 & ! [W3] : % 5.66/5.76 ( aElementOf0(W3,W2) % 5.66/5.76 <=> ( aElement0(W3) % 5.66/5.76 & ( aElementOf0(W3,W0) % 5.66/5.76 | W3 = W1 ) ) ) ) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mDefDiff,definition, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aSet0(W0) % 5.66/5.76 & aElement0(W1) ) % 5.66/5.76 => ! [W2] : % 5.66/5.76 ( W2 = sdtmndt0(W0,W1) % 5.66/5.76 <=> ( aSet0(W2) % 5.66/5.76 & ! [W3] : % 5.66/5.76 ( aElementOf0(W3,W2) % 5.66/5.76 <=> ( aElement0(W3) % 5.66/5.76 & aElementOf0(W3,W0) % 5.66/5.76 & W3 != W1 ) ) ) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mConsDiff,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aSet0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( aElementOf0(W1,W0) % 5.66/5.76 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mDiffCons,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElement0(W0) % 5.66/5.76 & aSet0(W1) ) % 5.66/5.76 => ( ~ aElementOf0(W0,W1) % 5.66/5.76 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mCConsSet,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElement0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( ( aSet0(W1) % 5.66/5.76 & isCountable0(W1) ) % 5.66/5.76 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mCDiffSet,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElement0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( ( aSet0(W1) % 5.66/5.76 & isCountable0(W1) ) % 5.66/5.76 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mFConsSet,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElement0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( ( aSet0(W1) % 5.66/5.76 & isFinite0(W1) ) % 5.66/5.76 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mFDiffSet,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElement0(W0) % 5.66/5.76 => ! [W1] : % 5.66/5.76 ( ( aSet0(W1) % 5.66/5.76 & isFinite0(W1) ) % 5.66/5.76 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mNATSet,axiom, % 5.66/5.76 ( aSet0(szNzAzT0) % 5.66/5.76 & isCountable0(szNzAzT0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mZeroNum,axiom, % 5.66/5.76 aElementOf0(sz00,szNzAzT0) ). % 5.66/5.76 % 5.66/5.76 fof(mSuccNum,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 5.66/5.76 & szszuzczcdt0(W0) != sz00 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSuccEquSucc,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 5.66/5.76 => W0 = W1 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mNatExtra,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => ( W0 = sz00 % 5.66/5.76 | ? [W1] : % 5.66/5.76 ( aElementOf0(W1,szNzAzT0) % 5.66/5.76 & W0 = szszuzczcdt0(W1) ) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mNatNSucc,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => W0 != szszuzczcdt0(W0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessRel,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( sdtlseqdt0(W0,W1) % 5.66/5.76 => $true ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mZeroLess,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => sdtlseqdt0(sz00,W0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mNoScLessZr,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 5.66/5.76 % 5.66/5.76 fof(mSuccLess,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( sdtlseqdt0(W0,W1) % 5.66/5.76 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessSucc,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessRefl,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => sdtlseqdt0(W0,W0) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessASymm,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( ( sdtlseqdt0(W0,W1) % 5.66/5.76 & sdtlseqdt0(W1,W0) ) % 5.66/5.76 => W0 = W1 ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessTrans,axiom, % 5.66/5.76 ! [W0,W1,W2] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) % 5.66/5.76 & aElementOf0(W2,szNzAzT0) ) % 5.66/5.76 => ( ( sdtlseqdt0(W0,W1) % 5.66/5.76 & sdtlseqdt0(W1,W2) ) % 5.66/5.76 => sdtlseqdt0(W0,W2) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mLessTotal,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( sdtlseqdt0(W0,W1) % 5.66/5.76 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mIHSort,axiom, % 5.66/5.76 ! [W0,W1] : % 5.66/5.76 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.76 => ( iLess0(W0,W1) % 5.66/5.76 => $true ) ) ). % 5.66/5.76 % 5.66/5.76 fof(mIH,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aElementOf0(W0,szNzAzT0) % 5.66/5.76 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 5.66/5.76 % 5.66/5.76 fof(mCardS,axiom, % 5.66/5.76 ! [W0] : % 5.66/5.76 ( aSet0(W0) % 5.66/5.76 => aElement0(sbrdtbr0(W0)) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardNum,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aSet0(W0) % 5.66/5.77 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 5.66/5.77 <=> isFinite0(W0) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardEmpty,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aSet0(W0) % 5.66/5.77 => ( sbrdtbr0(W0) = sz00 % 5.66/5.77 <=> W0 = slcrc0 ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardCons,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( ( aSet0(W0) % 5.66/5.77 & isFinite0(W0) ) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( aElement0(W1) % 5.66/5.77 => ( ~ aElementOf0(W1,W0) % 5.66/5.77 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardDiff,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aSet0(W0) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( ( isFinite0(W0) % 5.66/5.77 & aElementOf0(W1,W0) ) % 5.66/5.77 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardSub,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aSet0(W0) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( ( isFinite0(W0) % 5.66/5.77 & aSubsetOf0(W1,W0) ) % 5.66/5.77 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mCardSubEx,axiom, % 5.66/5.77 ! [W0,W1] : % 5.66/5.77 ( ( aSet0(W0) % 5.66/5.77 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.77 => ( ( isFinite0(W0) % 5.66/5.77 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 5.66/5.77 => ? [W2] : % 5.66/5.77 ( aSubsetOf0(W2,W0) % 5.66/5.77 & sbrdtbr0(W2) = W1 ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mDefMin,definition, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( ( aSubsetOf0(W0,szNzAzT0) % 5.66/5.77 & W0 != slcrc0 ) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( W1 = szmzizndt0(W0) % 5.66/5.77 <=> ( aElementOf0(W1,W0) % 5.66/5.77 & ! [W2] : % 5.66/5.77 ( aElementOf0(W2,W0) % 5.66/5.77 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mDefMax,definition, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( ( aSubsetOf0(W0,szNzAzT0) % 5.66/5.77 & isFinite0(W0) % 5.66/5.77 & W0 != slcrc0 ) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( W1 = szmzazxdt0(W0) % 5.66/5.77 <=> ( aElementOf0(W1,W0) % 5.66/5.77 & ! [W2] : % 5.66/5.77 ( aElementOf0(W2,W0) % 5.66/5.77 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mMinMin,axiom, % 5.66/5.77 ! [W0,W1] : % 5.66/5.77 ( ( aSubsetOf0(W0,szNzAzT0) % 5.66/5.77 & aSubsetOf0(W1,szNzAzT0) % 5.66/5.77 & W0 != slcrc0 % 5.66/5.77 & W1 != slcrc0 ) % 5.66/5.77 => ( ( aElementOf0(szmzizndt0(W0),W1) % 5.66/5.77 & aElementOf0(szmzizndt0(W1),W0) ) % 5.66/5.77 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mDefSeg,definition, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 => ! [W1] : % 5.66/5.77 ( W1 = slbdtrb0(W0) % 5.66/5.77 <=> ( aSet0(W1) % 5.66/5.77 & ! [W2] : % 5.66/5.77 ( aElementOf0(W2,W1) % 5.66/5.77 <=> ( aElementOf0(W2,szNzAzT0) % 5.66/5.77 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mSegFin,axiom, % 5.66/5.77 ! [W0] : % 5.66/5.77 ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 => isFinite0(slbdtrb0(W0)) ) ). % 5.66/5.77 % 5.66/5.77 fof(mSegZero,axiom, % 5.66/5.77 slbdtrb0(sz00) = slcrc0 ). % 5.66/5.77 % 5.66/5.77 fof(mSegSucc,axiom, % 5.66/5.77 ! [W0,W1] : % 5.66/5.77 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.77 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 5.66/5.77 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 5.66/5.77 | W0 = W1 ) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(mSegLess,axiom, % 5.66/5.77 ! [W0,W1] : % 5.66/5.77 ( ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 & aElementOf0(W1,szNzAzT0) ) % 5.66/5.77 => ( sdtlseqdt0(W0,W1) % 5.66/5.77 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(m__1986,hypothesis, % 5.66/5.77 ( aSet0(xS) % 5.66/5.77 & ! [W0] : % 5.66/5.77 ( aElementOf0(W0,xS) % 5.66/5.77 => aElementOf0(W0,szNzAzT0) ) % 5.66/5.77 & aSubsetOf0(xS,szNzAzT0) % 5.66/5.77 & isFinite0(xS) ) ). % 5.66/5.77 % 5.66/5.77 fof(m__2035,hypothesis, % 5.66/5.77 ( ~ ( ~ ? [W0] : aElementOf0(W0,xS) % 5.66/5.77 & xS = slcrc0 ) % 5.66/5.77 => ( aElementOf0(szmzazxdt0(xS),xS) % 5.66/5.77 & ! [W0] : % 5.66/5.77 ( aElementOf0(W0,xS) % 5.66/5.77 => sdtlseqdt0(W0,szmzazxdt0(xS)) ) % 5.66/5.77 & aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) % 5.66/5.77 & ! [W0] : % 5.66/5.77 ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) % 5.66/5.77 <=> ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 & sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS))) ) ) % 5.66/5.77 & ! [W0] : % 5.66/5.77 ( aElementOf0(W0,xS) % 5.66/5.77 => aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) % 5.66/5.77 & aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ) ). % 5.66/5.77 % 5.66/5.77 fof(m__,conjecture, % 5.66/5.77 ? [W0] : % 5.66/5.77 ( aElementOf0(W0,szNzAzT0) % 5.66/5.77 & ( ( aSet0(slbdtrb0(W0)) % 5.66/5.77 & ! [W1] : % 5.66/5.77 ( aElementOf0(W1,slbdtrb0(W0)) % 5.66/5.77 <=> ( aElementOf0(W1,szNzAzT0) % 5.66/5.77 & sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ) % 5.66/5.77 => ( ! [W1] : % 5.66/5.77 ( aElementOf0(W1,xS) % 5.66/5.77 => aElementOf0(W1,slbdtrb0(W0)) ) % 5.66/5.77 | aSubsetOf0(xS,slbdtrb0(W0)) ) ) ) ). % 5.66/5.77 % 5.66/5.77 %------------------------------------------------------------------------------ % 5.66/5.77 %------------------------------------------- % 5.66/5.77 % Proof found % 5.66/5.77 % SZS status Theorem for theBenchmark % 5.66/5.77 % SZS output start Proof % 5.66/5.77 %ClaNum:161(EqnAxiom:43) % 5.66/5.77 %VarNum:659(SingletonVarNum:212) % 5.66/5.77 %MaxLitNum:8 % 5.66/5.77 %MaxfuncDepth:3 % 5.66/5.77 %SharedTerms:20 % 5.66/5.77 %goalClause: 64 78 88 99 105 115 132 % 5.66/5.77 [45]P1(a17) % 5.66/5.77 [46]P1(a18) % 5.66/5.77 [47]P4(a16) % 5.66/5.77 [48]P4(a18) % 5.66/5.77 [49]P5(a17) % 5.66/5.77 [50]P2(a1,a17) % 5.66/5.77 [51]P6(a18,a17) % 5.66/5.77 [44]E(f2(a1),a16) % 5.66/5.77 [55]E(a18,a16)+P2(f19(a18),a18) % 5.66/5.77 [74]E(a18,a16)+P1(f2(f20(f19(a18)))) % 5.66/5.77 [86]E(a18,a16)+P6(a18,f2(f20(f19(a18)))) % 5.66/5.77 [52]P1(x521)+~E(x521,a16) % 5.66/5.77 [59]~P1(x591)+P6(x591,x591) % 5.66/5.77 [66]~P2(x661,a18)+P2(x661,a17) % 5.66/5.77 [67]~P2(x671,a17)+P8(a1,x671) % 5.66/5.77 [73]P8(x731,x731)+~P2(x731,a17) % 5.66/5.77 [57]~P1(x571)+P3(f3(x571)) % 5.66/5.77 [61]~P2(x611,a17)+~E(f20(x611),a1) % 5.66/5.77 [62]~P2(x621,a17)+~E(f20(x621),x621) % 5.66/5.77 [64]~P2(x641,a17)+P1(f2(x641)) % 5.66/5.77 [65]~P2(x651,a17)+P4(f2(x651)) % 5.66/5.77 [75]~P2(x751,a18)+P2(f19(a18),a18) % 5.66/5.77 [77]~P2(x771,a17)+P2(f20(x771),a17) % 5.66/5.77 [78]~P2(x781,a17)+P2(f5(x781),a18) % 5.66/5.77 [79]~P2(x791,a17)+P8(x791,f20(x791)) % 5.66/5.77 [80]~P2(x801,a17)+P7(x801,f20(x801)) % 5.66/5.77 [88]~P2(x881,a17)+~P6(a18,f2(x881)) % 5.66/5.77 [89]~P2(x891,a17)+~P8(f20(x891),a1) % 5.66/5.77 [99]~P2(f5(x991),f2(x991))+~P2(x991,a17) % 5.66/5.77 [95]~P2(x951,a18)+P1(f2(f20(f19(a18)))) % 5.66/5.77 [101]~P2(x1011,a18)+P6(a18,f2(f20(f19(a18)))) % 5.66/5.77 [60]~P2(x602,x601)+~E(x601,a16) % 5.66/5.77 [56]~P1(x561)+~P5(x561)+~E(x561,a16) % 5.66/5.77 [58]~P4(x581)+~P5(x581)+~P1(x581) % 5.66/5.77 [53]~P1(x531)+~E(x531,a16)+E(f3(x531),a1) % 5.66/5.77 [54]~P1(x541)+E(x541,a16)+~E(f3(x541),a1) % 5.66/5.77 [63]~P1(x631)+P2(f4(x631),x631)+E(x631,a16) % 5.66/5.77 [70]~P1(x701)+~P4(x701)+P2(f3(x701),a17) % 5.66/5.77 [81]~P2(x811,a17)+E(x811,a1)+P2(f6(x811),a17) % 5.66/5.77 [82]~P1(x821)+P4(x821)+~P2(f3(x821),a17) % 5.66/5.77 [68]~P2(x681,a17)+E(x681,a1)+E(f20(f6(x681)),x681) % 5.66/5.77 [124]E(a18,a16)+P2(x1241,a17)+~P2(x1241,f2(f20(f19(a18)))) % 5.66/5.77 [140]E(a18,a16)+P8(f20(x1401),f20(f19(a18)))+~P2(x1401,f2(f20(f19(a18)))) % 5.66/5.77 [71]~P6(x711,x712)+P1(x711)+~P1(x712) % 5.66/5.77 [72]~P2(x721,x722)+P3(x721)+~P1(x722) % 5.66/5.77 [69]P1(x691)+~P2(x692,a17)+~E(x691,f2(x692)) % 5.66/5.77 [97]~P2(x971,a18)+~P2(x972,a18)+P8(x971,f19(a18)) % 5.66/5.77 [105]~P2(x1051,f2(x1052))+P2(x1051,a17)+~P2(x1052,a17) % 5.66/5.77 [115]~P2(x1152,a17)+~P2(x1151,f2(x1152))+P8(f20(x1151),x1152) % 5.66/5.77 [113]~P1(x1131)+~P2(x1132,x1131)+E(f14(f15(x1131,x1132),x1132),x1131) % 5.66/5.77 [126]~P2(x1261,a18)+~P2(x1262,a18)+P2(x1261,f2(f20(f19(a18)))) % 5.66/5.77 [139]P2(x1391,a17)+~P2(x1392,a18)+~P2(x1391,f2(f20(f19(a18)))) % 5.66/5.77 [150]~P2(x1502,a18)+P8(f20(x1501),f20(f19(a18)))+~P2(x1501,f2(f20(f19(a18)))) % 5.66/5.77 [147]E(a18,a16)+~P2(x1471,a17)+~P8(f20(x1471),f20(f19(a18)))+P2(x1471,f2(f20(f19(a18)))) % 5.66/5.77 [83]~P4(x832)+~P6(x831,x832)+P4(x831)+~P1(x832) % 5.66/5.77 [87]P2(x872,x871)+~E(x872,f21(x871))+~P6(x871,a17)+E(x871,a16) % 5.66/5.77 [91]~P1(x911)+~P3(x912)+~P4(x911)+P4(f14(x911,x912)) % 5.66/5.77 [92]~P1(x921)+~P3(x922)+~P4(x921)+P4(f15(x921,x922)) % 5.66/5.77 [93]~P1(x931)+~P3(x932)+~P5(x931)+P5(f14(x931,x932)) % 5.66/5.77 [94]~P1(x941)+~P3(x942)+~P5(x941)+P5(f15(x941,x942)) % 5.66/5.77 [96]E(x961,x962)+~E(f20(x961),f20(x962))+~P2(x962,a17)+~P2(x961,a17) % 5.66/5.77 [102]~P1(x1022)+~P4(x1022)+~P6(x1021,x1022)+P8(f3(x1021),f3(x1022)) % 5.66/5.77 [111]~P1(x1111)+~P1(x1112)+P6(x1111,x1112)+P2(f7(x1112,x1111),x1111) % 5.66/5.77 [118]P8(x1181,x1182)+P8(f20(x1182),x1181)+~P2(x1182,a17)+~P2(x1181,a17) % 5.66/5.77 [128]~P8(x1281,x1282)+~P2(x1282,a17)+~P2(x1281,a17)+P6(f2(x1281),f2(x1282)) % 5.66/5.77 [129]~P8(x1291,x1292)+~P2(x1292,a17)+~P2(x1291,a17)+P8(f20(x1291),f20(x1292)) % 5.66/5.77 [131]~P1(x1311)+~P1(x1312)+P6(x1311,x1312)+~P2(f7(x1312,x1311),x1312) % 5.66/5.77 [132]~P2(x1322,a17)+~P2(x1321,a17)+~P8(f20(x1321),x1322)+P2(x1321,f2(x1322)) % 5.66/5.77 [134]P8(x1341,x1342)+~P2(x1342,a17)+~P2(x1341,a17)+~P6(f2(x1341),f2(x1342)) % 5.66/5.77 [135]P8(x1351,x1352)+~P2(x1352,a17)+~P2(x1351,a17)+~P8(f20(x1351),f20(x1352)) % 5.66/5.77 [112]P2(x1122,x1121)+~P1(x1121)+~P3(x1122)+E(f15(f14(x1121,x1122),x1122),x1121) % 5.66/5.77 [120]~E(x1201,x1202)+~P2(x1202,a17)+~P2(x1201,a17)+P2(x1201,f2(f20(x1202))) % 5.66/5.77 [141]~P2(x1412,a17)+~P2(x1411,a17)+~P2(x1411,f2(x1412))+P2(x1411,f2(f20(x1412))) % 5.66/5.77 [138]~P1(x1381)+~P4(x1381)+~P2(x1382,x1381)+E(f20(f3(f15(x1381,x1382))),f3(x1381)) % 5.66/5.77 [151]~P2(x1511,a17)+~P2(x1512,a18)+~P8(f20(x1511),f20(f19(a18)))+P2(x1511,f2(f20(f19(a18)))) % 5.66/5.77 [109]~P1(x1092)+~P6(x1093,x1092)+P2(x1091,x1092)+~P2(x1091,x1093) % 5.66/5.77 [84]~P1(x842)+~P3(x843)+P1(x841)+~E(x841,f14(x842,x843)) % 5.66/5.77 [85]~P1(x852)+~P3(x853)+P1(x851)+~E(x851,f15(x852,x853)) % 5.66/5.77 [103]~P2(x1031,x1032)+~P2(x1033,a17)+P2(x1031,a17)+~E(x1032,f2(x1033)) % 5.66/5.77 [114]~P2(x1141,x1143)+~P2(x1142,a17)+P8(f20(x1141),x1142)+~E(x1143,f2(x1142)) % 5.66/5.77 [98]~P1(x982)+~P1(x981)+~P6(x982,x981)+~P6(x981,x982)+E(x981,x982) % 5.66/5.77 [127]~P8(x1272,x1271)+~P8(x1271,x1272)+E(x1271,x1272)+~P2(x1272,a17)+~P2(x1271,a17) % 5.66/5.77 [90]~P4(x901)+P2(x902,x901)+~E(x902,f19(x901))+~P6(x901,a17)+E(x901,a16) % 5.66/5.77 [130]~P2(x1302,x1301)+P2(f10(x1301,x1302),x1301)+~P6(x1301,a17)+E(x1301,a16)+E(x1302,f21(x1301)) % 5.66/5.77 [142]~P1(x1421)+~P4(x1421)+~P2(x1422,a17)+~P8(x1422,f3(x1421))+P6(f11(x1421,x1422),x1421) % 5.66/5.77 [143]~P1(x1431)+P2(f13(x1432,x1431),x1431)+~P2(x1432,a17)+E(x1431,f2(x1432))+P2(f13(x1432,x1431),a17) % 5.66/5.77 [144]~P2(x1442,x1441)+~P6(x1441,a17)+~P8(x1442,f10(x1441,x1442))+E(x1441,a16)+E(x1442,f21(x1441)) % 5.66/5.77 [119]P2(x1192,x1191)+~P1(x1191)+~P3(x1192)+~P4(x1191)+E(f3(f14(x1191,x1192)),f20(f3(x1191))) % 5.66/5.77 [137]~P1(x1371)+~P4(x1371)+~P2(x1372,a17)+~P8(x1372,f3(x1371))+E(f3(f11(x1371,x1372)),x1372) % 5.66/5.77 [145]E(x1451,x1452)+P2(x1451,f2(x1452))+~P2(x1452,a17)+~P2(x1451,a17)+~P2(x1451,f2(f20(x1452))) % 5.66/5.77 [152]~P1(x1521)+P2(f13(x1522,x1521),x1521)+~P2(x1522,a17)+E(x1521,f2(x1522))+P8(f20(f13(x1522,x1521)),x1522) % 5.66/5.77 [110]~P2(x1103,x1101)+P8(x1102,x1103)+~E(x1102,f21(x1101))+~P6(x1101,a17)+E(x1101,a16) % 5.66/5.77 [133]P2(x1331,x1332)+~P2(x1333,a17)+~P2(x1331,a17)+~P8(f20(x1331),x1333)+~E(x1332,f2(x1333)) % 5.66/5.77 [104]~P1(x1044)+~P3(x1042)+~P2(x1041,x1043)+~E(x1041,x1042)+~E(x1043,f15(x1044,x1042)) % 5.66/5.77 [106]~P1(x1063)+~P3(x1064)+~P2(x1061,x1062)+P3(x1061)+~E(x1062,f14(x1063,x1064)) % 5.66/5.77 [107]~P1(x1073)+~P3(x1074)+~P2(x1071,x1072)+P3(x1071)+~E(x1072,f15(x1073,x1074)) % 5.66/5.77 [117]~P1(x1172)+~P3(x1174)+~P2(x1171,x1173)+P2(x1171,x1172)+~E(x1173,f15(x1172,x1174)) % 5.66/5.77 [136]~P4(x1361)+~P2(x1362,x1361)+P2(f12(x1361,x1362),x1361)+~P6(x1361,a17)+E(x1361,a16)+E(x1362,f19(x1361)) % 5.66/5.77 [148]~P4(x1481)+~P2(x1482,x1481)+~P6(x1481,a17)+~P8(f12(x1481,x1482),x1482)+E(x1481,a16)+E(x1482,f19(x1481)) % 5.66/5.77 [156]~P1(x1561)+~P2(x1562,a17)+~P2(f13(x1562,x1561),x1561)+E(x1561,f2(x1562))+~P2(f13(x1562,x1561),a17)+~P8(f20(f13(x1562,x1561)),x1562) % 5.66/5.77 [122]~P1(x1222)+~P1(x1221)+~P6(x1223,x1222)+~P6(x1221,x1223)+P6(x1221,x1222)+~P1(x1223) % 5.66/5.77 [149]~P8(x1491,x1493)+P8(x1491,x1492)+~P8(x1493,x1492)+~P2(x1492,a17)+~P2(x1493,a17)+~P2(x1491,a17) % 5.66/5.77 [116]~P4(x1161)+~P2(x1162,x1161)+P8(x1162,x1163)+~E(x1163,f19(x1161))+~P6(x1161,a17)+E(x1161,a16) % 5.66/5.77 [153]~P1(x1531)+~P1(x1532)+~P3(x1533)+P2(f8(x1532,x1533,x1531),x1531)+~E(f8(x1532,x1533,x1531),x1533)+E(x1531,f15(x1532,x1533)) % 5.66/5.77 [154]~P1(x1541)+~P1(x1542)+~P3(x1543)+P2(f9(x1542,x1543,x1541),x1541)+E(x1541,f14(x1542,x1543))+P3(f9(x1542,x1543,x1541)) % 5.66/5.77 [155]~P1(x1551)+~P1(x1552)+~P3(x1553)+P2(f8(x1552,x1553,x1551),x1551)+E(x1551,f15(x1552,x1553))+P3(f8(x1552,x1553,x1551)) % 5.66/5.77 [157]~P1(x1571)+~P1(x1572)+~P3(x1573)+P2(f8(x1572,x1573,x1571),x1571)+P2(f8(x1572,x1573,x1571),x1572)+E(x1571,f15(x1572,x1573)) % 5.66/5.77 [100]~P1(x1004)+~P3(x1003)+~P3(x1001)+P2(x1001,x1002)+~E(x1001,x1003)+~E(x1002,f14(x1004,x1003)) % 5.66/5.77 [121]~P1(x1213)+~P3(x1212)+~P2(x1211,x1214)+E(x1211,x1212)+P2(x1211,x1213)+~E(x1214,f14(x1213,x1212)) % 5.66/5.77 [123]~P1(x1233)+~P3(x1234)+~P3(x1231)+~P2(x1231,x1233)+P2(x1231,x1232)+~E(x1232,f14(x1233,x1234)) % 5.66/5.77 [146]E(f21(x1462),f21(x1461))+~P6(x1461,a17)+~P6(x1462,a17)+~P2(f21(x1461),x1462)+~P2(f21(x1462),x1461)+E(x1461,a16)+E(x1462,a16) % 5.66/5.77 [158]~P1(x1581)+~P1(x1582)+~P3(x1583)+E(f9(x1582,x1583,x1581),x1583)+P2(f9(x1582,x1583,x1581),x1581)+P2(f9(x1582,x1583,x1581),x1582)+E(x1581,f14(x1582,x1583)) % 5.66/5.77 [159]~P1(x1591)+~P1(x1592)+~P3(x1593)+~E(f9(x1592,x1593,x1591),x1593)+~P2(f9(x1592,x1593,x1591),x1591)+E(x1591,f14(x1592,x1593))+~P3(f9(x1592,x1593,x1591)) % 5.66/5.77 [160]~P1(x1601)+~P1(x1602)+~P3(x1603)+~P2(f9(x1602,x1603,x1601),x1601)+~P2(f9(x1602,x1603,x1601),x1602)+E(x1601,f14(x1602,x1603))+~P3(f9(x1602,x1603,x1601)) % 5.66/5.77 [125]~P1(x1254)+~P3(x1252)+~P3(x1251)+~P2(x1251,x1254)+E(x1251,x1252)+P2(x1251,x1253)+~E(x1253,f15(x1254,x1252)) % 5.66/5.77 [161]~P1(x1611)+~P1(x1612)+~P3(x1613)+E(f8(x1612,x1613,x1611),x1613)+~P2(f8(x1612,x1613,x1611),x1611)+~P2(f8(x1612,x1613,x1611),x1612)+E(x1611,f15(x1612,x1613))+~P3(f8(x1612,x1613,x1611)) % 5.66/5.77 %EqnAxiom % 5.66/5.77 [1]E(x11,x11) % 5.66/5.77 [2]E(x22,x21)+~E(x21,x22) % 5.66/5.77 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 5.66/5.77 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 5.66/5.77 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 5.66/5.77 [6]~E(x61,x62)+E(f13(x61,x63),f13(x62,x63)) % 5.66/5.77 [7]~E(x71,x72)+E(f13(x73,x71),f13(x73,x72)) % 5.66/5.77 [8]~E(x81,x82)+E(f19(x81),f19(x82)) % 5.66/5.77 [9]~E(x91,x92)+E(f20(x91),f20(x92)) % 5.66/5.77 [10]~E(x101,x102)+E(f8(x101,x103,x104),f8(x102,x103,x104)) % 5.66/5.77 [11]~E(x111,x112)+E(f8(x113,x111,x114),f8(x113,x112,x114)) % 5.66/5.77 [12]~E(x121,x122)+E(f8(x123,x124,x121),f8(x123,x124,x122)) % 5.66/5.77 [13]~E(x131,x132)+E(f15(x131,x133),f15(x132,x133)) % 5.66/5.77 [14]~E(x141,x142)+E(f15(x143,x141),f15(x143,x142)) % 5.66/5.77 [15]~E(x151,x152)+E(f4(x151),f4(x152)) % 5.66/5.77 [16]~E(x161,x162)+E(f14(x161,x163),f14(x162,x163)) % 5.66/5.77 [17]~E(x171,x172)+E(f14(x173,x171),f14(x173,x172)) % 5.66/5.77 [18]~E(x181,x182)+E(f9(x181,x183,x184),f9(x182,x183,x184)) % 5.66/5.77 [19]~E(x191,x192)+E(f9(x193,x191,x194),f9(x193,x192,x194)) % 5.66/5.77 [20]~E(x201,x202)+E(f9(x203,x204,x201),f9(x203,x204,x202)) % 5.66/5.77 [21]~E(x211,x212)+E(f6(x211),f6(x212)) % 5.66/5.77 [22]~E(x221,x222)+E(f21(x221),f21(x222)) % 5.66/5.77 [23]~E(x231,x232)+E(f7(x231,x233),f7(x232,x233)) % 5.66/5.77 [24]~E(x241,x242)+E(f7(x243,x241),f7(x243,x242)) % 5.66/5.77 [25]~E(x251,x252)+E(f12(x251,x253),f12(x252,x253)) % 5.66/5.77 [26]~E(x261,x262)+E(f12(x263,x261),f12(x263,x262)) % 5.66/5.77 [27]~E(x271,x272)+E(f10(x271,x273),f10(x272,x273)) % 5.66/5.77 [28]~E(x281,x282)+E(f10(x283,x281),f10(x283,x282)) % 5.66/5.77 [29]~E(x291,x292)+E(f5(x291),f5(x292)) % 5.66/5.77 [30]~E(x301,x302)+E(f11(x301,x303),f11(x302,x303)) % 5.66/5.77 [31]~E(x311,x312)+E(f11(x313,x311),f11(x313,x312)) % 5.66/5.77 [32]~P1(x321)+P1(x322)+~E(x321,x322) % 5.66/5.77 [33]P2(x332,x333)+~E(x331,x332)+~P2(x331,x333) % 5.66/5.77 [34]P2(x343,x342)+~E(x341,x342)+~P2(x343,x341) % 5.66/5.77 [35]~P4(x351)+P4(x352)+~E(x351,x352) % 5.66/5.77 [36]~P3(x361)+P3(x362)+~E(x361,x362) % 5.66/5.77 [37]~P5(x371)+P5(x372)+~E(x371,x372) % 5.66/5.77 [38]P6(x382,x383)+~E(x381,x382)+~P6(x381,x383) % 5.66/5.77 [39]P6(x393,x392)+~E(x391,x392)+~P6(x393,x391) % 5.66/5.77 [40]P8(x402,x403)+~E(x401,x402)+~P8(x401,x403) % 5.66/5.77 [41]P8(x413,x412)+~E(x411,x412)+~P8(x413,x411) % 5.66/5.77 [42]P7(x422,x423)+~E(x421,x422)+~P7(x421,x423) % 5.66/5.77 [43]P7(x433,x432)+~E(x431,x432)+~P7(x433,x431) % 5.66/5.77 % 5.66/5.77 %------------------------------------------- % 5.66/5.77 cnf(162,plain, % 5.66/5.77 (P1(a16)), % 5.66/5.77 inference(equality_inference,[],[52])). % 5.66/5.77 cnf(163,plain, % 5.66/5.77 (~P1(a16)+E(f3(a16),a1)), % 5.66/5.77 inference(equality_inference,[],[53])). % 5.66/5.77 cnf(165,plain, % 5.66/5.77 (~P2(x1651,a16)), % 5.66/5.77 inference(equality_inference,[],[60])). % 5.66/5.77 cnf(169,plain, % 5.66/5.77 (P2(f21(x1691),x1691)+~P6(x1691,a17)+E(x1691,a16)), % 5.66/5.77 inference(equality_inference,[],[87])). % 5.66/5.77 cnf(175,plain, % 5.66/5.77 (~P2(x1751,x1752)+P8(f21(x1752),x1751)+~P6(x1752,a17)+E(x1752,a16)), % 5.66/5.77 inference(equality_inference,[],[110])). % 5.66/5.77 cnf(178,plain, % 5.66/5.77 (P2(x1781,x1782)+~P1(x1782)+~P3(x1783)+~P2(x1781,f15(x1782,x1783))), % 5.66/5.77 inference(equality_inference,[],[117])). % 5.66/5.77 cnf(179,plain, % 5.66/5.77 (~P2(x1791,a17)+~P2(x1791,a17)+P2(x1791,f2(f20(x1791)))), % 5.66/5.77 inference(equality_inference,[],[120])). % 5.66/5.77 cnf(184,plain, % 5.66/5.77 (E(f3(a16),a1)), % 5.66/5.77 inference(scs_inference,[],[162,163])). % 5.66/5.77 cnf(188,plain, % 5.66/5.77 (P1(f2(a1))), % 5.66/5.77 inference(scs_inference,[],[44,50,99,52])). % 5.66/5.78 cnf(190,plain, % 5.66/5.78 (~P2(x1901,f2(a1))), % 5.66/5.78 inference(scs_inference,[],[44,50,99,52,60])). % 5.66/5.78 cnf(192,plain, % 5.66/5.78 (P8(a1,a1)), % 5.66/5.78 inference(scs_inference,[],[44,50,99,52,60,73])). % 5.66/5.78 cnf(194,plain, % 5.66/5.78 (E(a16,f2(a1))), % 5.66/5.78 inference(scs_inference,[],[44,50,99,52,60,73,2])). % 5.66/5.78 cnf(197,plain, % 5.66/5.78 (P2(a1,f2(f20(a1)))), % 5.66/5.78 inference(scs_inference,[],[44,50,99,52,60,73,2,56,179])). % 5.66/5.78 cnf(199,plain, % 5.66/5.78 (~E(a17,a16)), % 5.66/5.78 inference(scs_inference,[],[44,50,165,99,52,60,73,2,56,179,34])). % 5.66/5.78 cnf(200,plain, % 5.66/5.78 (~P2(x2001,a16)), % 5.66/5.78 inference(rename_variables,[],[165])). % 5.66/5.78 cnf(201,plain, % 5.66/5.78 (~P4(a17)), % 5.66/5.78 inference(scs_inference,[],[44,50,165,45,49,99,52,60,73,2,56,179,34,58])). % 5.66/5.78 cnf(208,plain, % 5.66/5.78 (P6(f2(a1),f2(a1))), % 5.66/5.78 inference(scs_inference,[],[44,50,165,200,45,47,49,162,99,52,60,73,2,56,179,34,58,3,35,111,128])). % 5.66/5.78 cnf(212,plain, % 5.66/5.78 (~P6(a17,a16)), % 5.66/5.78 inference(scs_inference,[],[44,50,165,200,45,47,49,162,99,52,60,73,2,56,179,34,58,3,35,111,128,129,98])). % 5.66/5.78 cnf(217,plain, % 5.66/5.78 (P6(f2(a1),a16)), % 5.66/5.78 inference(scs_inference,[],[44,50,165,200,45,47,49,51,162,99,52,60,73,2,56,179,34,58,3,35,111,128,129,98,169,38,39])). % 5.66/5.78 cnf(218,plain, % 5.66/5.78 (P2(x2181,a17)+~E(a1,x2181)), % 5.66/5.78 inference(scs_inference,[],[44,50,165,200,45,47,49,51,162,99,52,60,73,2,56,179,34,58,3,35,111,128,129,98,169,38,39,33])). % 5.66/5.78 cnf(222,plain, % 5.66/5.78 (E(a1,f3(a16))), % 5.66/5.78 inference(scs_inference,[],[184,2])). % 5.66/5.78 cnf(223,plain, % 5.66/5.78 (P6(a16,f2(a1))), % 5.66/5.78 inference(scs_inference,[],[44,208,184,2,38])). % 5.66/5.78 cnf(225,plain, % 5.66/5.78 (P2(f3(a16),a17)), % 5.66/5.78 inference(scs_inference,[],[44,50,192,208,184,2,38,41,33])). % 5.66/5.78 cnf(226,plain, % 5.66/5.78 (~E(f2(f20(a1)),f2(a1))), % 5.66/5.78 inference(scs_inference,[],[44,50,190,197,192,208,184,2,38,41,33,34])). % 5.66/5.78 cnf(227,plain, % 5.66/5.78 (~P2(x2271,f2(a1))), % 5.66/5.78 inference(rename_variables,[],[190])). % 5.66/5.78 cnf(228,plain, % 5.66/5.78 (P8(f3(a16),a1)), % 5.66/5.78 inference(scs_inference,[],[44,50,190,197,192,208,184,2,38,41,33,34,40])). % 5.66/5.78 cnf(233,plain, % 5.66/5.78 (~P8(f20(f3(a16)),a1)), % 5.66/5.78 inference(scs_inference,[],[44,50,190,227,197,192,188,208,184,194,165,2,38,41,33,34,40,39,109,133])). % 5.66/5.78 cnf(236,plain, % 5.66/5.78 (P6(f11(a16,a1),a16)), % 5.66/5.78 inference(scs_inference,[],[44,50,190,227,197,192,188,208,184,194,165,47,162,2,38,41,33,34,40,39,109,133,142])). % 5.66/5.78 cnf(239,plain, % 5.66/5.78 (P8(f3(a16),f3(a16))), % 5.66/5.78 inference(scs_inference,[],[44,50,190,227,197,192,188,208,184,194,165,47,162,2,38,41,33,34,40,39,109,133,142,4,73])). % 5.66/5.78 cnf(243,plain, % 5.66/5.78 (P2(f3(a16),f2(f20(f3(a16))))), % 5.66/5.78 inference(scs_inference,[],[44,50,190,227,197,192,188,208,184,194,165,47,162,2,38,41,33,34,40,39,109,133,142,4,73,99,179])). % 5.66/5.78 cnf(257,plain, % 5.66/5.78 (~P2(x2571,f2(a1))), % 5.66/5.78 inference(rename_variables,[],[190])). % 5.66/5.78 cnf(263,plain, % 5.66/5.78 (P6(f2(a1),a18)), % 5.66/5.78 inference(scs_inference,[],[243,226,233,190,257,194,217,201,212,228,236,48,46,188,184,33,38,34,40,3,39,83,111])). % 5.66/5.78 cnf(272,plain, % 5.66/5.78 (P6(a16,a18)), % 5.66/5.78 inference(scs_inference,[],[225,243,226,233,190,257,194,217,201,223,212,239,228,236,48,46,188,47,162,184,33,38,34,40,3,39,83,111,129,128,142,122])). % 5.66/5.78 cnf(280,plain, % 5.66/5.78 (P2(f3(a16),f2(f20(a1)))), % 5.66/5.78 inference(scs_inference,[],[197,222,33])). % 5.66/5.78 cnf(354,plain, % 5.66/5.78 (~P6(f2(f20(a1)),a16)), % 5.66/5.78 inference(scs_inference,[],[280,165,162,109])). % 5.66/5.78 cnf(363,plain, % 5.66/5.78 (P3(f3(f2(a1)))), % 5.66/5.78 inference(scs_inference,[],[44,57,52])). % 5.66/5.78 cnf(368,plain, % 5.66/5.78 (~P2(x3681,f2(a1))), % 5.66/5.78 inference(rename_variables,[],[190])). % 5.66/5.78 cnf(374,plain, % 5.66/5.78 (E(f15(f2(a1),f3(f2(a1))),f2(a1))), % 5.66/5.78 inference(scs_inference,[],[280,190,368,363,354,217,188,38,178,109,157,2])). % 5.66/5.78 cnf(378,plain, % 5.66/5.78 (E(a16,f15(f2(a1),f3(f2(a1))))), % 5.66/5.78 inference(scs_inference,[],[50,280,190,368,363,354,194,217,188,38,178,109,157,2,4,69,3])). % 5.66/5.78 cnf(445,plain, % 5.66/5.78 (P2(f21(a17),a17)), % 5.66/5.78 inference(scs_inference,[],[45,199,59,169])). % 5.66/5.78 cnf(460,plain, % 5.66/5.78 (P2(x4601,a17)+~E(f21(a17),x4601)), % 5.66/5.78 inference(scs_inference,[],[190,226,445,374,73,99,179,34,3,129,128,4,33])). % 5.66/5.78 cnf(1088,plain, % 5.66/5.78 (~E(a18,f15(f2(a1),f3(f2(a1))))+~P2(x10881,a18)), % 5.66/5.78 inference(scs_inference,[],[190,188,363,75,117])). % 5.66/5.78 cnf(1128,plain, % 5.66/5.78 (P2(f5(f3(a16)),a18)), % 5.66/5.78 inference(scs_inference,[],[222,78,218])). % 5.66/5.78 cnf(1129,plain, % 5.66/5.78 (P2(f19(a18),a18)), % 5.66/5.78 inference(scs_inference,[],[1128,75])). % 5.66/5.78 cnf(1130,plain, % 5.66/5.78 (P1(f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1128,95])). % 5.66/5.78 cnf(1131,plain, % 5.66/5.78 (~P2(x11311,a18)+P8(x11311,f19(a18))), % 5.66/5.78 inference(scs_inference,[],[1128,97])). % 5.66/5.78 cnf(1132,plain, % 5.66/5.78 (P6(a18,f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1128,101])). % 5.66/5.78 cnf(1133,plain, % 5.66/5.78 (~P2(x11331,a18)+P2(x11331,f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1128,126])). % 5.66/5.78 cnf(1137,plain, % 5.66/5.78 (~E(a18,f15(f2(a1),f3(f2(a1))))), % 5.66/5.78 inference(scs_inference,[],[1128,1088])). % 5.66/5.78 cnf(1140,plain, % 5.66/5.78 (P2(f5(f3(a16)),f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1128,1131,1133])). % 5.66/5.78 cnf(1144,plain, % 5.66/5.78 (~P6(a18,f2(a1))), % 5.66/5.78 inference(scs_inference,[],[1128,190,263,188,46,1131,1133,34,98])). % 5.66/5.78 cnf(1159,plain, % 5.66/5.78 (P2(f19(a18),f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1129,1131,1133])). % 5.66/5.78 cnf(1166,plain, % 5.66/5.78 (~E(a18,a16)), % 5.66/5.78 inference(scs_inference,[],[1137,1132,378,1129,1131,1133,88,66,460,3])). % 5.66/5.78 cnf(1180,plain, % 5.66/5.78 (~P2(f19(a18),a17)), % 5.66/5.78 inference(scs_inference,[],[50,1128,190,1140,1137,1132,363,378,188,162,51,272,45,46,1129,1144,1130,1131,1133,88,66,460,3,33,169,34,178,175,98,122,77])). % 5.66/5.78 cnf(1207,plain, % 5.66/5.78 (P2(x12071,a17)+~P2(x12071,f2(f20(f19(a18))))), % 5.66/5.78 inference(scs_inference,[],[1166,124])). % 5.66/5.78 cnf(1213,plain, % 5.66/5.78 ($false), % 5.66/5.78 inference(scs_inference,[],[1159,1180,1207]), % 5.66/5.78 ['proof']). % 5.66/5.78 % SZS output end Proof % 5.66/5.78 % Total time :5.100000s %------------------------------------------------------------------------------