%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM613+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 : n027.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 12:25:24 EDT 2024 % Result : Theorem 0.83s 0.82s % Output : CNFRefutation 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : NUM613+1 : TPTP v8.2.0. Released v4.0.0. % 0.09/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Jun 23 00:13:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.50/0.61 start to proof:theBenchmark % 0.59/0.78 %------------------------------------------- % 0.59/0.78 % File :CSE---1.7 % 0.59/0.78 % Problem :theBenchmark % 0.59/0.78 % Transform :cnf % 0.59/0.78 % Format :tptp:raw % 0.59/0.78 % Command :java -jar mcs_scs.jar %d %s % 0.59/0.78 % 0.59/0.78 % Result :Theorem 0.060000s % 0.59/0.78 % Output :CNFRefutation 0.060000s % 0.59/0.78 %------------------------------------------- % 0.59/0.79 %------------------------------------------------------------------------------ % 0.59/0.79 % File : NUM613+1 : TPTP v8.2.0. Released v4.0.0. % 0.59/0.79 % Domain : Number Theory % 0.59/0.79 % Problem : Ramsey's Infinite Theorem 15_02_23_07_02, 00 expansion % 0.59/0.79 % Version : Especial. % 0.59/0.79 % English : % 0.59/0.79 % 0.59/0.79 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.59/0.79 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.59/0.79 % Source : [Pas08] % 0.59/0.79 % Names : ramsey_15_02_23_07_02.00 [Pas08] % 0.59/0.79 % 0.59/0.79 % Status : Theorem % 0.59/0.79 % Rating : 0.25 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.21 v7.1.0, 0.26 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.40 v6.0.0, 0.26 v5.5.0, 0.41 v5.4.0, 0.50 v5.3.0, 0.56 v5.2.0, 0.40 v5.1.0, 0.48 v5.0.0, 0.54 v4.1.0, 0.61 v4.0.1, 0.83 v4.0.0 % 0.59/0.79 % Syntax : Number of formulae : 110 ( 17 unt; 11 def) % 0.59/0.79 % Number of atoms : 402 ( 74 equ) % 0.59/0.79 % Maximal formula atoms : 12 ( 3 avg) % 0.59/0.79 % Number of connectives : 317 ( 25 ~; 4 |; 131 &) % 0.59/0.79 % ( 22 <=>; 135 =>; 0 <=; 0 <~>) % 0.59/0.79 % Maximal formula depth : 15 ( 5 avg) % 0.59/0.79 % Maximal term depth : 5 ( 1 avg) % 0.59/0.79 % Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty) % 0.59/0.79 % Number of functors : 30 ( 30 usr; 16 con; 0-2 aty) % 0.59/0.79 % Number of variables : 171 ( 159 !; 12 ?) % 0.59/0.79 % SPC : FOF_THM_RFO_SEQ % 0.59/0.79 % 0.59/0.79 % Comments : Problem generated by the SAD system [VLP07] % 0.59/0.79 %------------------------------------------------------------------------------ % 0.59/0.79 fof(mSetSort,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => $true ) ). % 0.59/0.79 % 0.59/0.79 fof(mElmSort,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aElement0(W0) % 0.59/0.79 => $true ) ). % 0.59/0.79 % 0.59/0.79 fof(mEOfElem,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => ! [W1] : % 0.59/0.79 ( aElementOf0(W1,W0) % 0.59/0.79 => aElement0(W1) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mFinRel,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => ( isFinite0(W0) % 0.59/0.79 => $true ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mDefEmp,definition, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( W0 = slcrc0 % 0.59/0.79 <=> ( aSet0(W0) % 0.59/0.79 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mEmpFin,axiom, % 0.59/0.79 isFinite0(slcrc0) ). % 0.59/0.79 % 0.59/0.79 fof(mCntRel,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => ( isCountable0(W0) % 0.59/0.79 => $true ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mCountNFin,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & isCountable0(W0) ) % 0.59/0.79 => ~ isFinite0(W0) ) ). % 0.59/0.79 % 0.59/0.79 fof(mCountNFin_01,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & isCountable0(W0) ) % 0.59/0.79 => W0 != slcrc0 ) ). % 0.59/0.79 % 0.59/0.79 fof(mDefSub,definition, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => ! [W1] : % 0.59/0.79 ( aSubsetOf0(W1,W0) % 0.59/0.79 <=> ( aSet0(W1) % 0.59/0.79 & ! [W2] : % 0.59/0.79 ( aElementOf0(W2,W1) % 0.59/0.79 => aElementOf0(W2,W0) ) ) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mSubFSet,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & isFinite0(W0) ) % 0.59/0.79 => ! [W1] : % 0.59/0.79 ( aSubsetOf0(W1,W0) % 0.59/0.79 => isFinite0(W1) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mSubRefl,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => aSubsetOf0(W0,W0) ) ). % 0.59/0.79 % 0.59/0.79 fof(mSubASymm,axiom, % 0.59/0.79 ! [W0,W1] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & aSet0(W1) ) % 0.59/0.79 => ( ( aSubsetOf0(W0,W1) % 0.59/0.79 & aSubsetOf0(W1,W0) ) % 0.59/0.79 => W0 = W1 ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mSubTrans,axiom, % 0.59/0.79 ! [W0,W1,W2] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & aSet0(W1) % 0.59/0.79 & aSet0(W2) ) % 0.59/0.79 => ( ( aSubsetOf0(W0,W1) % 0.59/0.79 & aSubsetOf0(W1,W2) ) % 0.59/0.79 => aSubsetOf0(W0,W2) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mDefCons,definition, % 0.59/0.79 ! [W0,W1] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & aElement0(W1) ) % 0.59/0.79 => ! [W2] : % 0.59/0.79 ( W2 = sdtpldt0(W0,W1) % 0.59/0.79 <=> ( aSet0(W2) % 0.59/0.79 & ! [W3] : % 0.59/0.79 ( aElementOf0(W3,W2) % 0.59/0.79 <=> ( aElement0(W3) % 0.59/0.79 & ( aElementOf0(W3,W0) % 0.59/0.79 | W3 = W1 ) ) ) ) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mDefDiff,definition, % 0.59/0.79 ! [W0,W1] : % 0.59/0.79 ( ( aSet0(W0) % 0.59/0.79 & aElement0(W1) ) % 0.59/0.79 => ! [W2] : % 0.59/0.79 ( W2 = sdtmndt0(W0,W1) % 0.59/0.79 <=> ( aSet0(W2) % 0.59/0.79 & ! [W3] : % 0.59/0.79 ( aElementOf0(W3,W2) % 0.59/0.79 <=> ( aElement0(W3) % 0.59/0.79 & aElementOf0(W3,W0) % 0.59/0.79 & W3 != W1 ) ) ) ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mConsDiff,axiom, % 0.59/0.79 ! [W0] : % 0.59/0.79 ( aSet0(W0) % 0.59/0.79 => ! [W1] : % 0.59/0.79 ( aElementOf0(W1,W0) % 0.59/0.79 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 0.59/0.79 % 0.59/0.79 fof(mDiffCons,axiom, % 0.59/0.79 ! [W0,W1] : % 0.59/0.80 ( ( aElement0(W0) % 0.59/0.80 & aSet0(W1) ) % 0.59/0.80 => ( ~ aElementOf0(W0,W1) % 0.59/0.80 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCConsSet,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElement0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( aSet0(W1) % 0.59/0.80 & isCountable0(W1) ) % 0.59/0.80 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCDiffSet,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElement0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( aSet0(W1) % 0.59/0.80 & isCountable0(W1) ) % 0.59/0.80 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mFConsSet,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElement0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( aSet0(W1) % 0.59/0.80 & isFinite0(W1) ) % 0.59/0.80 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mFDiffSet,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElement0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( aSet0(W1) % 0.59/0.80 & isFinite0(W1) ) % 0.59/0.80 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mNATSet,axiom, % 0.59/0.80 ( aSet0(szNzAzT0) % 0.59/0.80 & isCountable0(szNzAzT0) ) ). % 0.59/0.80 % 0.59/0.80 fof(mZeroNum,axiom, % 0.59/0.80 aElementOf0(sz00,szNzAzT0) ). % 0.59/0.80 % 0.59/0.80 fof(mSuccNum,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 0.59/0.80 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mSuccEquSucc,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.59/0.80 => W0 = W1 ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mNatExtra,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => ( W0 = sz00 % 0.59/0.80 | ? [W1] : % 0.59/0.80 ( aElementOf0(W1,szNzAzT0) % 0.59/0.80 & W0 = szszuzczcdt0(W1) ) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mNatNSucc,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => W0 != szszuzczcdt0(W0) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessRel,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( sdtlseqdt0(W0,W1) % 0.59/0.80 => $true ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mZeroLess,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => sdtlseqdt0(sz00,W0) ) ). % 0.59/0.80 % 0.59/0.80 fof(mNoScLessZr,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 0.59/0.80 % 0.59/0.80 fof(mSuccLess,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( sdtlseqdt0(W0,W1) % 0.59/0.80 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessSucc,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessRefl,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => sdtlseqdt0(W0,W0) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessASymm,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( ( sdtlseqdt0(W0,W1) % 0.59/0.80 & sdtlseqdt0(W1,W0) ) % 0.59/0.80 => W0 = W1 ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessTrans,axiom, % 0.59/0.80 ! [W0,W1,W2] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) % 0.59/0.80 & aElementOf0(W2,szNzAzT0) ) % 0.59/0.80 => ( ( sdtlseqdt0(W0,W1) % 0.59/0.80 & sdtlseqdt0(W1,W2) ) % 0.59/0.80 => sdtlseqdt0(W0,W2) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mLessTotal,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( sdtlseqdt0(W0,W1) % 0.59/0.80 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mIHSort,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( iLess0(W0,W1) % 0.59/0.80 => $true ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mIH,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aElementOf0(W0,szNzAzT0) % 0.59/0.80 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardS,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aSet0(W0) % 0.59/0.80 => aElement0(sbrdtbr0(W0)) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardNum,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aSet0(W0) % 0.59/0.80 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 0.59/0.80 <=> isFinite0(W0) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardEmpty,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aSet0(W0) % 0.59/0.80 => ( sbrdtbr0(W0) = sz00 % 0.59/0.80 <=> W0 = slcrc0 ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardCons,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( ( aSet0(W0) % 0.59/0.80 & isFinite0(W0) ) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( aElement0(W1) % 0.59/0.80 => ( ~ aElementOf0(W1,W0) % 0.59/0.80 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardDiff,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aSet0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( isFinite0(W0) % 0.59/0.80 & aElementOf0(W1,W0) ) % 0.59/0.80 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardSub,axiom, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( aSet0(W0) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( ( isFinite0(W0) % 0.59/0.80 & aSubsetOf0(W1,W0) ) % 0.59/0.80 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mCardSubEx,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.80 ( ( aSet0(W0) % 0.59/0.80 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.80 => ( ( isFinite0(W0) % 0.59/0.80 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 0.59/0.80 => ? [W2] : % 0.59/0.80 ( aSubsetOf0(W2,W0) % 0.59/0.80 & sbrdtbr0(W2) = W1 ) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mDefMin,definition, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.80 & W0 != slcrc0 ) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( W1 = szmzizndt0(W0) % 0.59/0.80 <=> ( aElementOf0(W1,W0) % 0.59/0.80 & ! [W2] : % 0.59/0.80 ( aElementOf0(W2,W0) % 0.59/0.80 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mDefMax,definition, % 0.59/0.80 ! [W0] : % 0.59/0.80 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.80 & isFinite0(W0) % 0.59/0.80 & W0 != slcrc0 ) % 0.59/0.80 => ! [W1] : % 0.59/0.80 ( W1 = szmzazxdt0(W0) % 0.59/0.80 <=> ( aElementOf0(W1,W0) % 0.59/0.80 & ! [W2] : % 0.59/0.80 ( aElementOf0(W2,W0) % 0.59/0.80 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 0.59/0.80 % 0.59/0.80 fof(mMinMin,axiom, % 0.59/0.80 ! [W0,W1] : % 0.59/0.81 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.81 & aSubsetOf0(W1,szNzAzT0) % 0.59/0.81 & W0 != slcrc0 % 0.59/0.81 & W1 != slcrc0 ) % 0.59/0.81 => ( ( aElementOf0(szmzizndt0(W0),W1) % 0.59/0.81 & aElementOf0(szmzizndt0(W1),W0) ) % 0.59/0.81 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mDefSeg,definition, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( W1 = slbdtrb0(W0) % 0.59/0.81 <=> ( aSet0(W1) % 0.59/0.81 & ! [W2] : % 0.59/0.81 ( aElementOf0(W2,W1) % 0.59/0.81 <=> ( aElementOf0(W2,szNzAzT0) % 0.59/0.81 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSegFin,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 => isFinite0(slbdtrb0(W0)) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSegZero,axiom, % 0.59/0.81 slbdtrb0(sz00) = slcrc0 ). % 0.59/0.81 % 0.59/0.81 fof(mSegSucc,axiom, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.81 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 0.59/0.81 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 0.59/0.81 | W0 = W1 ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSegLess,axiom, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.81 => ( sdtlseqdt0(W0,W1) % 0.59/0.81 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mFinSubSeg,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( ( aSubsetOf0(W0,szNzAzT0) % 0.59/0.81 & isFinite0(W0) ) % 0.59/0.81 => ? [W1] : % 0.59/0.81 ( aElementOf0(W1,szNzAzT0) % 0.59/0.81 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mCardSeg,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 0.59/0.81 % 0.59/0.81 fof(mDefSel,definition, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aSet0(W0) % 0.59/0.81 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.81 => ! [W2] : % 0.59/0.81 ( W2 = slbdtsldtrb0(W0,W1) % 0.59/0.81 <=> ( aSet0(W2) % 0.59/0.81 & ! [W3] : % 0.59/0.81 ( aElementOf0(W3,W2) % 0.59/0.81 <=> ( aSubsetOf0(W3,W0) % 0.59/0.81 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSelFSet,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( ( aSet0(W0) % 0.59/0.81 & isFinite0(W0) ) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aElementOf0(W1,szNzAzT0) % 0.59/0.81 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSelNSet,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( ( aSet0(W0) % 0.59/0.81 & ~ isFinite0(W0) ) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aElementOf0(W1,szNzAzT0) % 0.59/0.81 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSelCSet,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( ( aSet0(W0) % 0.59/0.81 & isCountable0(W0) ) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( ( aElementOf0(W1,szNzAzT0) % 0.59/0.81 & W1 != sz00 ) % 0.59/0.81 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSelSub,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aElementOf0(W0,szNzAzT0) % 0.59/0.81 => ! [W1,W2] : % 0.59/0.81 ( ( aSet0(W1) % 0.59/0.81 & aSet0(W2) % 0.59/0.81 & W0 != sz00 ) % 0.59/0.81 => ( ( aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0)) % 0.59/0.81 & slbdtsldtrb0(W1,W0) != slcrc0 ) % 0.59/0.81 => aSubsetOf0(W1,W2) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mSelExtra,axiom, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aSet0(W0) % 0.59/0.81 & aElementOf0(W1,szNzAzT0) ) % 0.59/0.81 => ! [W2] : % 0.59/0.81 ( ( aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) % 0.59/0.81 & isFinite0(W2) ) % 0.59/0.81 => ? [W3] : % 0.59/0.81 ( aSubsetOf0(W3,W0) % 0.59/0.81 & isFinite0(W3) % 0.59/0.81 & aSubsetOf0(W2,slbdtsldtrb0(W3,W1)) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mFunSort,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => $true ) ). % 0.59/0.81 % 0.59/0.81 fof(mDomSet,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => aSet0(szDzozmdt0(W0)) ) ). % 0.59/0.81 % 0.59/0.81 fof(mImgElm,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aElementOf0(W1,szDzozmdt0(W0)) % 0.59/0.81 => aElement0(sdtlpdtrp0(W0,W1)) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mDefPtt,definition, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aFunction0(W0) % 0.59/0.81 & aElement0(W1) ) % 0.59/0.81 => ! [W2] : % 0.59/0.81 ( W2 = sdtlbdtrb0(W0,W1) % 0.59/0.81 <=> ( aSet0(W2) % 0.59/0.81 & ! [W3] : % 0.59/0.81 ( aElementOf0(W3,W2) % 0.59/0.81 <=> ( aElementOf0(W3,szDzozmdt0(W0)) % 0.59/0.81 & sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mPttSet,axiom, % 0.59/0.81 ! [W0,W1] : % 0.59/0.81 ( ( aFunction0(W0) % 0.59/0.81 & aElement0(W1) ) % 0.59/0.81 => aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ). % 0.59/0.81 % 0.59/0.81 fof(mDefSImg,definition, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.59/0.81 => ! [W2] : % 0.59/0.81 ( W2 = sdtlcdtrc0(W0,W1) % 0.59/0.81 <=> ( aSet0(W2) % 0.59/0.81 & ! [W3] : % 0.59/0.81 ( aElementOf0(W3,W2) % 0.59/0.81 <=> ? [W4] : % 0.59/0.81 ( aElementOf0(W4,W1) % 0.59/0.81 & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mImgRng,axiom, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aElementOf0(W1,szDzozmdt0(W0)) % 0.59/0.81 => aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ). % 0.59/0.81 % 0.59/0.81 fof(mDefRst,definition, % 0.59/0.81 ! [W0] : % 0.59/0.81 ( aFunction0(W0) % 0.59/0.81 => ! [W1] : % 0.59/0.81 ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.59/0.81 => ! [W2] : % 0.59/0.81 ( W2 = sdtexdt0(W0,W1) % 0.59/0.81 <=> ( aFunction0(W2) % 0.59/0.81 & szDzozmdt0(W2) = W1 % 0.59/0.81 & ! [W3] : % 0.59/0.81 ( aElementOf0(W3,W1) % 0.83/0.81 => sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3) ) ) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(mImgCount,axiom, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aFunction0(W0) % 0.83/0.81 => ! [W1] : % 0.83/0.81 ( ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.83/0.81 & isCountable0(W1) ) % 0.83/0.81 => ( ! [W2,W3] : % 0.83/0.81 ( ( aElementOf0(W2,szDzozmdt0(W0)) % 0.83/0.81 & aElementOf0(W3,szDzozmdt0(W0)) % 0.83/0.81 & W2 != W3 ) % 0.83/0.81 => sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) % 0.83/0.81 => isCountable0(sdtlcdtrc0(W0,W1)) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(mDirichlet,axiom, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aFunction0(W0) % 0.83/0.81 => ( ( isCountable0(szDzozmdt0(W0)) % 0.83/0.81 & isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) % 0.83/0.81 => ( aElement0(szDzizrdt0(W0)) % 0.83/0.81 & isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3291,hypothesis, % 0.83/0.81 ( aSet0(xT) % 0.83/0.81 & isFinite0(xT) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3418,hypothesis, % 0.83/0.81 aElementOf0(xK,szNzAzT0) ). % 0.83/0.81 % 0.83/0.81 fof(m__3435,hypothesis, % 0.83/0.81 ( aSubsetOf0(xS,szNzAzT0) % 0.83/0.81 & isCountable0(xS) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3453,hypothesis, % 0.83/0.81 ( aFunction0(xc) % 0.83/0.81 & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) % 0.83/0.81 & aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3398,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ! [W1] : % 0.83/0.81 ( ( aSubsetOf0(W1,szNzAzT0) % 0.83/0.81 & isCountable0(W1) ) % 0.83/0.81 => ! [W2] : % 0.83/0.81 ( ( aFunction0(W2) % 0.83/0.81 & szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) % 0.83/0.81 & aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) % 0.83/0.81 => ( iLess0(W0,xK) % 0.83/0.81 => ? [W3] : % 0.83/0.81 ( aElementOf0(W3,xT) % 0.83/0.81 & ? [W4] : % 0.83/0.81 ( aSubsetOf0(W4,W1) % 0.83/0.81 & isCountable0(W4) % 0.83/0.81 & ! [W5] : % 0.83/0.81 ( aElementOf0(W5,slbdtsldtrb0(W4,W0)) % 0.83/0.81 => sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3462,hypothesis, % 0.83/0.81 xK != sz00 ). % 0.83/0.81 % 0.83/0.81 fof(m__3520,hypothesis, % 0.83/0.81 xK != sz00 ). % 0.83/0.81 % 0.83/0.81 fof(m__3533,hypothesis, % 0.83/0.81 ( aElementOf0(xk,szNzAzT0) % 0.83/0.81 & szszuzczcdt0(xk) = xK ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3623,hypothesis, % 0.83/0.81 ( aFunction0(xN) % 0.83/0.81 & szDzozmdt0(xN) = szNzAzT0 % 0.83/0.81 & sdtlpdtrp0(xN,sz00) = xS % 0.83/0.81 & ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) % 0.83/0.81 & isCountable0(sdtlpdtrp0(xN,W0)) ) % 0.83/0.81 => ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.83/0.81 & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3671,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) % 0.83/0.81 & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3754,hypothesis, % 0.83/0.81 ! [W0,W1] : % 0.83/0.81 ( ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 & aElementOf0(W1,szNzAzT0) ) % 0.83/0.81 => ( sdtlseqdt0(W1,W0) % 0.83/0.81 => aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3821,hypothesis, % 0.83/0.81 ! [W0,W1] : % 0.83/0.81 ( ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 & aElementOf0(W1,szNzAzT0) % 0.83/0.81 & W0 != W1 ) % 0.83/0.81 => szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__3965,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ! [W1] : % 0.83/0.81 ( ( aSet0(W1) % 0.83/0.81 & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) % 0.83/0.81 => aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4151,hypothesis, % 0.83/0.81 ( aFunction0(xC) % 0.83/0.81 & szDzozmdt0(xC) = szNzAzT0 % 0.83/0.81 & ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ( aFunction0(sdtlpdtrp0(xC,W0)) % 0.83/0.81 & szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) % 0.83/0.81 & ! [W1] : % 0.83/0.81 ( ( aSet0(W1) % 0.83/0.81 & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) % 0.83/0.81 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4182,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4331,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ! [W1] : % 0.83/0.81 ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.83/0.81 & isCountable0(W1) ) % 0.83/0.81 => ! [W2] : % 0.83/0.81 ( ( aSet0(W2) % 0.83/0.81 & aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) % 0.83/0.81 => aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4411,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ? [W1] : % 0.83/0.81 ( aElementOf0(W1,xT) % 0.83/0.81 & ? [W2] : % 0.83/0.81 ( aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.83/0.81 & isCountable0(W2) % 0.83/0.81 & ! [W3] : % 0.83/0.81 ( ( aSet0(W3) % 0.83/0.81 & aElementOf0(W3,slbdtsldtrb0(W2,xk)) ) % 0.83/0.81 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 ) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4618,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ? [W1] : % 0.83/0.81 ( aElementOf0(W1,xT) % 0.83/0.81 & ! [W2] : % 0.83/0.81 ( ( aSet0(W2) % 0.83/0.81 & aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) % 0.83/0.81 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4660,hypothesis, % 0.83/0.81 ( aFunction0(xe) % 0.83/0.81 & szDzozmdt0(xe) = szNzAzT0 % 0.83/0.81 & ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4730,hypothesis, % 0.83/0.81 ( aFunction0(xd) % 0.83/0.81 & szDzozmdt0(xd) = szNzAzT0 % 0.83/0.81 & ! [W0] : % 0.83/0.81 ( aElementOf0(W0,szNzAzT0) % 0.83/0.81 => ! [W1] : % 0.83/0.81 ( ( aSet0(W1) % 0.83/0.81 & aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) % 0.83/0.81 => sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4758,hypothesis, % 0.83/0.81 aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ). % 0.83/0.81 % 0.83/0.81 fof(m__4854,hypothesis, % 0.83/0.81 ( aElementOf0(szDzizrdt0(xd),xT) % 0.83/0.81 & isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4891,hypothesis, % 0.83/0.81 ( aSet0(xO) % 0.83/0.81 & xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4908,hypothesis, % 0.83/0.81 ( aSet0(xO) % 0.83/0.81 & isCountable0(xO) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4982,hypothesis, % 0.83/0.81 ! [W0] : % 0.83/0.81 ( aElementOf0(W0,xO) % 0.83/0.81 => ? [W1] : % 0.83/0.81 ( aElementOf0(W1,szNzAzT0) % 0.83/0.81 & aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) % 0.83/0.81 & sdtlpdtrp0(xe,W1) = W0 ) ) ). % 0.83/0.81 % 0.83/0.81 fof(m__4998,hypothesis, % 0.83/0.81 aSubsetOf0(xO,xS) ). % 0.83/0.81 % 0.83/0.81 fof(m__5078,hypothesis, % 0.83/0.81 aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ). % 0.83/0.81 % 0.83/0.81 fof(m__5093,hypothesis, % 0.83/0.81 ( aSubsetOf0(xQ,xO) % 0.83/0.81 & xQ != slcrc0 ) ). % 0.83/0.81 % 0.83/0.81 fof(m__5106,hypothesis, % 0.83/0.81 aSubsetOf0(xQ,szNzAzT0) ). % 0.83/0.81 % 0.83/0.81 fof(m__5116,hypothesis, % 0.83/0.81 aElementOf0(xQ,szDzozmdt0(xc)) ). % 0.83/0.81 % 0.83/0.81 fof(m__5147,hypothesis, % 0.83/0.82 xp = szmzizndt0(xQ) ). % 0.83/0.82 % 0.83/0.82 fof(m__5164,hypothesis, % 0.83/0.82 ( aSet0(xP) % 0.83/0.82 & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ). % 0.83/0.82 % 0.83/0.82 fof(m__5173,hypothesis, % 0.83/0.82 aElementOf0(xp,xQ) ). % 0.83/0.82 % 0.83/0.82 fof(m__5182,hypothesis, % 0.83/0.82 aElementOf0(xp,xO) ). % 0.83/0.82 % 0.83/0.82 fof(m__5195,hypothesis, % 0.83/0.82 aSubsetOf0(xP,xQ) ). % 0.83/0.82 % 0.83/0.82 fof(m__5208,hypothesis, % 0.83/0.82 aSubsetOf0(xP,xO) ). % 0.83/0.82 % 0.83/0.82 fof(m__5255,hypothesis, % 0.83/0.82 ( sbrdtbr0(xQ) = szszuzczcdt0(xk) % 0.83/0.82 & szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) % 0.83/0.82 & aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ). % 0.83/0.82 % 0.83/0.82 fof(m__,conjecture, % 0.83/0.82 sbrdtbr0(xP) = xk ). % 0.83/0.82 % 0.83/0.82 %------------------------------------------------------------------------------ % 0.83/0.82 %------------------------------------------- % 0.83/0.82 % Proof found % 0.83/0.82 % SZS status Theorem for theBenchmark % 0.83/0.82 % SZS output start Proof % 0.83/0.82 %ClaNum:301(EqnAxiom:92) % 0.83/0.82 %VarNum:1229(SingletonVarNum:358) % 0.83/0.82 %MaxLitNum:9 % 0.83/0.82 %MaxfuncDepth:4 % 0.83/0.82 %SharedTerms:84 % 0.83/0.82 %goalClause: 142 % 0.83/0.82 %singleGoalClaCount:1 % 0.83/0.82 [100]P1(a41) % 0.83/0.82 [101]P1(a53) % 0.83/0.82 [103]P1(a47) % 0.83/0.82 [104]P1(a48) % 0.83/0.82 [105]P5(a37) % 0.83/0.82 [106]P5(a53) % 0.83/0.82 [107]P6(a41) % 0.83/0.82 [108]P6(a54) % 0.83/0.82 [109]P6(a47) % 0.83/0.82 [110]P2(a55) % 0.83/0.82 [111]P2(a46) % 0.83/0.82 [112]P2(a45) % 0.83/0.82 [113]P2(a51) % 0.83/0.82 [114]P2(a52) % 0.83/0.82 [118]P3(a3,a41) % 0.83/0.82 [119]P3(a44,a41) % 0.83/0.82 [120]P3(a50,a41) % 0.83/0.82 [121]P3(a49,a47) % 0.83/0.82 [122]P3(a49,a1) % 0.83/0.82 [123]P7(a54,a41) % 0.83/0.82 [124]P7(a47,a54) % 0.83/0.82 [125]P7(a1,a41) % 0.83/0.82 [126]P7(a1,a47) % 0.83/0.82 [127]P7(a48,a47) % 0.83/0.82 [128]P7(a48,a1) % 0.83/0.82 [140]~E(a3,a44) % 0.83/0.82 [141]~E(a37,a1) % 0.83/0.82 [93]E(f2(a1),a49) % 0.83/0.82 [94]E(f43(a50),a44) % 0.83/0.82 [95]E(f4(a3),a37) % 0.83/0.82 [96]E(f39(a46),a41) % 0.83/0.82 [97]E(f39(a45),a41) % 0.83/0.82 [98]E(f39(a51),a41) % 0.83/0.82 [99]E(f39(a52),a41) % 0.83/0.82 [115]E(f5(a1),f43(a50)) % 0.83/0.82 [117]E(f31(a46,a3),a54) % 0.83/0.82 [129]E(f38(a54,a44),f39(a55)) % 0.83/0.82 [131]P3(a1,f39(a55)) % 0.83/0.82 [132]P3(f5(a48),a41) % 0.83/0.82 [133]P3(f40(a52),a53) % 0.83/0.82 [134]P3(a1,f38(a47,a44)) % 0.83/0.82 [142]~E(f5(a48),a50) % 0.83/0.82 [116]E(f43(f5(a48)),f5(a1)) % 0.83/0.82 [130]E(f35(a1,f2(a1)),a48) % 0.83/0.82 [135]P6(f32(a52,f40(a52))) % 0.83/0.82 [137]P7(f34(a55,f39(a55)),a53) % 0.83/0.82 [138]P7(f34(a52,f39(a52)),a53) % 0.83/0.82 [136]E(f34(a51,f32(a52,f40(a52))),a47) % 0.83/0.82 [143]P1(x1431)+~E(x1431,a37) % 0.83/0.82 [150]~P1(x1501)+P7(x1501,x1501) % 0.83/0.82 [158]~P3(x1581,a41)+P9(a3,x1581) % 0.83/0.82 [164]P9(x1641,x1641)+~P3(x1641,a41) % 0.83/0.82 [147]~P2(x1471)+P1(f39(x1471)) % 0.83/0.82 [148]~P1(x1481)+P4(f5(x1481)) % 0.83/0.82 [152]~P3(x1521,a41)+~E(f43(x1521),a3) % 0.83/0.82 [153]~P3(x1531,a41)+~E(f43(x1531),x1531) % 0.83/0.82 [155]~P3(x1551,a41)+P5(f4(x1551)) % 0.83/0.82 [156]~P3(x1561,a41)+P6(f17(x1561)) % 0.83/0.82 [165]~P3(x1651,a41)+P3(f43(x1651),a41) % 0.83/0.82 [166]~P3(x1661,a41)+P3(f18(x1661),a53) % 0.83/0.82 [167]~P3(x1671,a41)+P3(f22(x1671),a53) % 0.83/0.82 [168]~P3(x1681,a47)+P3(f23(x1681),a41) % 0.83/0.82 [170]~P3(x1701,a41)+P9(x1701,f43(x1701)) % 0.83/0.82 [171]~P3(x1711,a41)+P8(x1711,f43(x1711)) % 0.83/0.82 [180]~P3(x1801,a41)+P6(f31(a46,x1801)) % 0.83/0.82 [181]~P3(x1811,a41)+P2(f31(a45,x1811)) % 0.83/0.82 [182]~P3(x1821,a41)+~P9(f43(x1821),a3) % 0.83/0.82 [190]~P3(x1901,a41)+P7(f31(a46,x1901),a41) % 0.83/0.82 [157]~P3(x1571,a41)+E(f5(f4(x1571)),x1571) % 0.83/0.82 [169]~P3(x1691,a47)+E(f31(a51,f23(x1691)),x1691) % 0.83/0.82 [192]~P3(x1921,a41)+E(f2(f31(a46,x1921)),f31(a51,x1921)) % 0.83/0.82 [210]~P3(x2101,a47)+P3(f23(x2101),f32(a52,f40(a52))) % 0.83/0.82 [265]~P3(x2651,a41)+P7(f34(f31(a45,x2651),f39(f31(a45,x2651))),a53) % 0.83/0.82 [267]~P3(x2671,a41)+P7(f17(x2671),f35(f31(a46,x2671),f2(f31(a46,x2671)))) % 0.83/0.82 [269]~P3(x2691,a41)+E(f38(f35(f31(a46,x2691),f2(f31(a46,x2691))),a50),f39(f31(a45,x2691))) % 0.83/0.82 [151]~P3(x1512,x1511)+~E(x1511,a37) % 0.83/0.82 [146]~P1(x1461)+~P6(x1461)+~E(x1461,a37) % 0.83/0.82 [149]~P5(x1491)+~P6(x1491)+~P1(x1491) % 0.83/0.82 [144]~P1(x1441)+~E(x1441,a37)+E(f5(x1441),a3) % 0.83/0.82 [145]~P1(x1451)+E(x1451,a37)+~E(f5(x1451),a3) % 0.83/0.82 [154]~P1(x1541)+P3(f6(x1541),x1541)+E(x1541,a37) % 0.83/0.82 [161]~P1(x1611)+~P5(x1611)+P3(f5(x1611),a41) % 0.83/0.82 [172]~P3(x1721,a41)+E(x1721,a3)+P3(f21(x1721),a41) % 0.83/0.82 [173]~P1(x1731)+P5(x1731)+~P3(f5(x1731),a41) % 0.83/0.82 [179]~P5(x1791)+~P7(x1791,a41)+P3(f7(x1791),a41) % 0.83/0.82 [159]~P3(x1591,a41)+E(x1591,a3)+E(f43(f21(x1591)),x1591) % 0.83/0.82 [193]~P5(x1931)+~P7(x1931,a41)+P7(x1931,f4(f7(x1931))) % 0.83/0.82 [162]~P7(x1621,x1622)+P1(x1621)+~P1(x1622) % 0.83/0.82 [163]~P3(x1631,x1632)+P4(x1631)+~P1(x1632) % 0.83/0.82 [160]P1(x1601)+~P3(x1602,a41)+~E(x1601,f4(x1602)) % 0.83/0.82 [194]~P4(x1942)+~P2(x1941)+P7(f32(x1941,x1942),f39(x1941)) % 0.83/0.82 [211]~P2(x2111)+~P3(x2112,f39(x2111))+P4(f31(x2111,x2112)) % 0.83/0.82 [213]~P1(x2131)+~P3(x2132,x2131)+E(f36(f35(x2131,x2132),x2132),x2131) % 0.83/0.82 [249]~P2(x2491)+~P3(x2492,f39(x2491))+P3(f31(x2491,x2492),f34(x2491,f39(x2491))) % 0.83/0.82 [239]~P2(x2391)+~P6(f39(x2391))+P4(f40(x2391))+~P5(f34(x2391,f39(x2391))) % 0.83/0.82 [258]~P2(x2581)+~P6(f39(x2581))+~P5(f34(x2581,f39(x2581)))+P6(f32(x2581,f40(x2581))) % 0.83/0.82 [262]~P3(x2621,a41)+~P7(f31(a46,x2621),a41)+~P6(f31(a46,x2621))+P6(f31(a46,f43(x2621))) % 0.83/0.82 [286]~P3(x2861,a41)+~P7(f31(a46,x2861),a41)+~P6(f31(a46,x2861))+P7(f31(a46,f43(x2861)),f35(f31(a46,x2861),f2(f31(a46,x2861)))) % 0.83/0.82 [174]~P5(x1742)+~P7(x1741,x1742)+P5(x1741)+~P1(x1742) % 0.83/0.82 [178]P3(x1782,x1781)+~E(x1782,f2(x1781))+~P7(x1781,a41)+E(x1781,a37) % 0.83/0.82 [184]~P1(x1841)+~P4(x1842)+~P5(x1841)+P5(f36(x1841,x1842)) % 0.83/0.82 [185]~P1(x1851)+~P4(x1852)+~P5(x1851)+P5(f35(x1851,x1852)) % 0.83/0.82 [186]~P1(x1861)+~P4(x1862)+~P6(x1861)+P6(f36(x1861,x1862)) % 0.83/0.82 [187]~P1(x1871)+~P4(x1872)+~P6(x1871)+P6(f35(x1871,x1872)) % 0.83/0.82 [188]~P1(x1881)+P5(x1881)+~P3(x1882,a41)+~E(f38(x1881,x1882),a37) % 0.83/0.82 [191]E(x1911,x1912)+~E(f43(x1911),f43(x1912))+~P3(x1912,a41)+~P3(x1911,a41) % 0.83/0.82 [197]~P1(x1972)+~P5(x1972)+~P7(x1971,x1972)+P9(f5(x1971),f5(x1972)) % 0.83/0.82 [200]~P1(x2001)+~P5(x2001)+~P3(x2002,a41)+P5(f38(x2001,x2002)) % 0.83/0.82 [209]~P1(x2091)+~P1(x2092)+P7(x2091,x2092)+P3(f24(x2092,x2091),x2091) % 0.83/0.82 [217]P9(x2171,x2172)+P9(f43(x2172),x2171)+~P3(x2172,a41)+~P3(x2171,a41) % 0.83/0.82 [229]~P9(x2291,x2292)+~P3(x2292,a41)+~P3(x2291,a41)+P7(f4(x2291),f4(x2292)) % 0.83/0.82 [230]~P9(x2301,x2302)+~P3(x2302,a41)+~P3(x2301,a41)+P9(f43(x2301),f43(x2302)) % 0.83/0.82 [232]~P1(x2321)+~P1(x2322)+P7(x2321,x2322)+~P3(f24(x2322,x2321),x2322) % 0.83/0.82 [234]P9(x2341,x2342)+~P3(x2342,a41)+~P3(x2341,a41)+~P7(f4(x2341),f4(x2342)) % 0.83/0.82 [235]P9(x2351,x2352)+~P3(x2352,a41)+~P3(x2351,a41)+~P9(f43(x2351),f43(x2352)) % 0.83/0.82 [253]~P9(x2532,x2531)+~P3(x2532,a41)+~P3(x2531,a41)+P7(f31(a46,x2531),f31(a46,x2532)) % 0.83/0.82 [212]P3(x2122,x2121)+~P1(x2121)+~P4(x2122)+E(f35(f36(x2121,x2122),x2122),x2121) % 0.83/0.82 [220]~E(x2201,x2202)+~P3(x2202,a41)+~P3(x2201,a41)+P3(x2201,f4(f43(x2202))) % 0.83/0.82 [241]~P3(x2412,a41)+~P3(x2411,a41)+~P3(x2411,f4(x2412))+P3(x2411,f4(f43(x2412))) % 0.83/0.82 [257]E(x2571,x2572)+~P3(x2572,a41)+~P3(x2571,a41)+~E(f2(f31(a46,x2571)),f2(f31(a46,x2572))) % 0.83/0.82 [260]~P1(x2602)+~P3(x2601,a41)+E(f31(f31(a45,x2601),x2602),f18(x2601))+~P3(x2602,f38(f17(x2601),a50)) % 0.83/0.82 [240]~P1(x2401)+~P5(x2401)+~P3(x2402,x2401)+E(f43(f5(f35(x2401,x2402))),f5(x2401)) % 0.83/0.82 [270]~P1(x2702)+~P3(x2701,a41)+E(f31(f31(a45,x2701),x2702),f22(x2701))+~P3(x2702,f38(f31(a46,f43(x2701)),a50)) % 0.83/0.82 [272]~P1(x2722)+~P3(x2721,a41)+E(f31(f31(a45,x2721),x2722),f31(a52,x2721))+~P3(x2722,f38(f31(a46,f43(x2721)),a50)) % 0.83/0.82 [300]~P1(x3001)+~P3(x3002,a41)+P3(f36(x3001,f2(f31(a46,x3002))),f38(a54,a44))+~P3(x3001,f38(f35(f31(a46,x3002),f2(f31(a46,x3002))),a50)) % 0.83/0.82 [301]~P1(x3011)+~P3(x3012,a41)+~P3(x3011,f38(f35(f31(a46,x3012),f2(f31(a46,x3012))),a50))+E(f31(a55,f36(x3011,f2(f31(a46,x3012)))),f31(f31(a45,x3012),x3011)) % 0.83/0.82 [204]~P1(x2042)+~P7(x2043,x2042)+P3(x2041,x2042)+~P3(x2041,x2043) % 0.83/0.82 [175]~P1(x1752)+~P4(x1753)+P1(x1751)+~E(x1751,f36(x1752,x1753)) % 0.83/0.82 [176]~P1(x1762)+~P4(x1763)+P1(x1761)+~E(x1761,f35(x1762,x1763)) % 0.83/0.82 [177]~P4(x1773)+~P2(x1772)+P1(x1771)+~E(x1771,f32(x1772,x1773)) % 0.83/0.82 [189]~P1(x1892)+P1(x1891)+~P3(x1893,a41)+~E(x1891,f38(x1892,x1893)) % 0.83/0.82 [198]~P3(x1981,x1982)+~P3(x1983,a41)+P3(x1981,a41)+~E(x1982,f4(x1983)) % 0.83/0.82 [206]~P2(x2062)+P1(x2061)+~P7(x2063,f39(x2062))+~E(x2061,f34(x2062,x2063)) % 0.83/0.82 [207]~P2(x2072)+P2(x2071)+~P7(x2073,f39(x2072))+~E(x2071,f33(x2072,x2073)) % 0.83/0.82 [208]~P2(x2083)+~P7(x2082,f39(x2083))+E(f39(x2081),x2082)+~E(x2081,f33(x2083,x2082)) % 0.83/0.82 [214]~P3(x2141,x2143)+~P3(x2142,a41)+P9(f43(x2141),x2142)+~E(x2143,f4(x2142)) % 0.83/0.82 [195]~P1(x1952)+~P1(x1951)+~P7(x1952,x1951)+~P7(x1951,x1952)+E(x1951,x1952) % 0.83/0.82 [227]~P9(x2272,x2271)+~P9(x2271,x2272)+E(x2271,x2272)+~P3(x2272,a41)+~P3(x2271,a41) % 0.83/0.82 [183]~P5(x1831)+P3(x1832,x1831)+~E(x1832,f42(x1831))+~P7(x1831,a41)+E(x1831,a37) % 0.83/0.82 [203]~P1(x2032)+~P6(x2032)+~P3(x2031,a41)+E(x2031,a3)+P6(f38(x2032,x2031)) % 0.83/0.82 [231]~P3(x2312,x2311)+P3(f27(x2311,x2312),x2311)+~P7(x2311,a41)+E(x2311,a37)+E(x2312,f2(x2311)) % 0.83/0.82 [242]~P1(x2421)+~P5(x2421)+~P3(x2422,a41)+~P9(x2422,f5(x2421))+P7(f28(x2421,x2422),x2421) % 0.83/0.82 [244]~P1(x2441)+P3(f30(x2442,x2441),x2441)+~P3(x2442,a41)+E(x2441,f4(x2442))+P3(f30(x2442,x2441),a41) % 0.83/0.82 [245]~P3(x2452,x2451)+~P7(x2451,a41)+~P9(x2452,f27(x2451,x2452))+E(x2451,a37)+E(x2452,f2(x2451)) % 0.83/0.82 [252]~P6(x2522)+~P2(x2521)+~E(f8(x2521,x2522),f9(x2521,x2522))+~P7(x2522,f39(x2521))+P6(f34(x2521,x2522)) % 0.83/0.82 [254]~P6(x2542)+~P2(x2541)+P3(f9(x2541,x2542),f39(x2541))+~P7(x2542,f39(x2541))+P6(f34(x2541,x2542)) % 0.83/0.82 [255]~P6(x2552)+~P2(x2551)+P3(f8(x2551,x2552),f39(x2551))+~P7(x2552,f39(x2551))+P6(f34(x2551,x2552)) % 0.83/0.82 [219]P3(x2192,x2191)+~P1(x2191)+~P4(x2192)+~P5(x2191)+E(f5(f36(x2191,x2192)),f43(f5(x2191))) % 0.83/0.82 [238]~P1(x2381)+~P5(x2381)+~P3(x2382,a41)+~P9(x2382,f5(x2381))+E(f5(f28(x2381,x2382)),x2382) % 0.83/0.82 [247]E(x2471,x2472)+P3(x2471,f4(x2472))+~P3(x2472,a41)+~P3(x2471,a41)+~P3(x2471,f4(f43(x2472))) % 0.83/0.82 [259]~P1(x2591)+P3(f30(x2592,x2591),x2591)+~P3(x2592,a41)+E(x2591,f4(x2592))+P9(f43(f30(x2592,x2591)),x2592) % 0.83/0.82 [261]~P6(x2612)+~P2(x2611)+~P7(x2612,f39(x2611))+P6(f34(x2611,x2612))+E(f31(x2611,f8(x2611,x2612)),f31(x2611,f9(x2611,x2612))) % 0.83/0.82 [205]~P3(x2053,x2051)+P9(x2052,x2053)+~E(x2052,f2(x2051))+~P7(x2051,a41)+E(x2051,a37) % 0.83/0.82 [233]P3(x2331,x2332)+~P3(x2333,a41)+~P3(x2331,a41)+~P9(f43(x2331),x2333)+~E(x2332,f4(x2333)) % 0.83/0.82 [266]~P1(x2661)+~P5(x2663)+~P3(x2662,a41)+~P7(x2663,f38(x2661,x2662))+P5(f11(x2661,x2662,x2663)) % 0.83/0.82 [268]~P1(x2681)+~P5(x2683)+~P3(x2682,a41)+~P7(x2683,f38(x2681,x2682))+P7(f11(x2681,x2682,x2683),x2681) % 0.83/0.82 [287]~P1(x2872)+~P5(x2871)+~P3(x2873,a41)+~P7(x2871,f38(x2872,x2873))+P7(x2871,f38(f11(x2872,x2873,x2871),x2873)) % 0.83/0.82 [199]~P1(x1994)+~P4(x1992)+~P3(x1991,x1993)+~E(x1991,x1992)+~E(x1993,f35(x1994,x1992)) % 0.83/0.82 [201]~P1(x2013)+~P4(x2014)+~P3(x2011,x2012)+P4(x2011)+~E(x2012,f36(x2013,x2014)) % 0.83/0.82 [202]~P1(x2023)+~P4(x2024)+~P3(x2021,x2022)+P4(x2021)+~E(x2022,f35(x2023,x2024)) % 0.83/0.82 [216]~P1(x2162)+~P4(x2164)+~P3(x2161,x2163)+P3(x2161,x2162)+~E(x2163,f35(x2162,x2164)) % 0.83/0.82 [218]~P4(x2183)+~P2(x2181)+~P3(x2182,x2184)+E(f31(x2181,x2182),x2183)+~E(x2184,f32(x2181,x2183)) % 0.83/0.82 [222]~P1(x2224)+~P3(x2221,x2223)+~P3(x2222,a41)+E(f5(x2221),x2222)+~E(x2223,f38(x2224,x2222)) % 0.83/0.82 [224]~P4(x2244)+~P2(x2242)+~P3(x2241,x2243)+P3(x2241,f39(x2242))+~E(x2243,f32(x2242,x2244)) % 0.83/0.82 [228]~P1(x2282)+~P3(x2281,x2283)+P7(x2281,x2282)+~P3(x2284,a41)+~E(x2283,f38(x2282,x2284)) % 0.83/0.82 [246]~P2(x2463)+~P3(x2462,x2464)+~P7(x2464,f39(x2463))+E(f31(x2461,x2462),f31(x2463,x2462))+~E(x2461,f33(x2463,x2464)) % 0.83/0.82 [293]~P2(x2931)+~P3(x2934,x2933)+~E(x2933,f34(x2931,x2932))+~P7(x2932,f39(x2931))+P3(f15(x2931,x2932,x2933,x2934),x2932) % 0.83/0.82 [294]~P2(x2941)+~P3(x2944,x2943)+~E(x2943,f34(x2941,x2942))+~P7(x2942,f39(x2941))+E(f31(x2941,f15(x2941,x2942,x2943,x2944)),x2944) % 0.83/0.82 [237]~P5(x2371)+~P3(x2372,x2371)+P3(f29(x2371,x2372),x2371)+~P7(x2371,a41)+E(x2371,a37)+E(x2372,f42(x2371)) % 0.83/0.82 [250]~P5(x2501)+~P3(x2502,x2501)+~P7(x2501,a41)+~P9(f29(x2501,x2502),x2502)+E(x2501,a37)+E(x2502,f42(x2501)) % 0.83/0.82 [275]~P1(x2751)+~P3(x2752,a41)+~P3(f30(x2752,x2751),x2751)+E(x2751,f4(x2752))+~P3(f30(x2752,x2751),a41)+~P9(f43(f30(x2752,x2751)),x2752) % 0.83/0.82 [223]~P1(x2232)+~P1(x2231)+~P7(x2233,x2232)+~P7(x2231,x2233)+P7(x2231,x2232)+~P1(x2233) % 0.83/0.82 [251]~P9(x2511,x2513)+P9(x2511,x2512)+~P9(x2513,x2512)+~P3(x2512,a41)+~P3(x2513,a41)+~P3(x2511,a41) % 0.83/0.82 [215]~P5(x2151)+~P3(x2152,x2151)+P9(x2152,x2153)+~E(x2153,f42(x2151))+~P7(x2151,a41)+E(x2151,a37) % 0.83/0.82 [264]~P2(x2641)+~P2(x2642)+P3(f10(x2642,x2643,x2641),x2643)+~E(f39(x2641),x2643)+~P7(x2643,f39(x2642))+E(x2641,f33(x2642,x2643)) % 0.83/0.82 [271]~P1(x2711)+~P1(x2712)+~P4(x2713)+P3(f25(x2712,x2713,x2711),x2711)+~E(f25(x2712,x2713,x2711),x2713)+E(x2711,f35(x2712,x2713)) % 0.83/0.82 [273]~P1(x2731)+~P1(x2732)+~P4(x2733)+P3(f26(x2732,x2733,x2731),x2731)+E(x2731,f36(x2732,x2733))+P4(f26(x2732,x2733,x2731)) % 0.83/0.82 [274]~P1(x2741)+~P1(x2742)+~P4(x2743)+P3(f25(x2742,x2743,x2741),x2741)+E(x2741,f35(x2742,x2743))+P4(f25(x2742,x2743,x2741)) % 0.83/0.82 [276]~P1(x2761)+~P1(x2762)+~P4(x2763)+P3(f25(x2762,x2763,x2761),x2761)+P3(f25(x2762,x2763,x2761),x2762)+E(x2761,f35(x2762,x2763)) % 0.83/0.82 [279]~P1(x2791)+~P4(x2793)+~P2(x2792)+P3(f13(x2792,x2793,x2791),x2791)+P3(f13(x2792,x2793,x2791),f39(x2792))+E(x2791,f32(x2792,x2793)) % 0.83/0.82 [280]~P1(x2801)+~P1(x2802)+P3(f12(x2802,x2803,x2801),x2801)+P7(f12(x2802,x2803,x2801),x2802)+~P3(x2803,a41)+E(x2801,f38(x2802,x2803)) % 0.83/0.82 [283]~P1(x2831)+~P2(x2832)+P3(f14(x2832,x2833,x2831),x2831)+P3(f16(x2832,x2833,x2831),x2833)+~P7(x2833,f39(x2832))+E(x2831,f34(x2832,x2833)) % 0.83/0.82 [277]~P1(x2771)+~P4(x2773)+~P2(x2772)+P3(f13(x2772,x2773,x2771),x2771)+E(x2771,f32(x2772,x2773))+E(f31(x2772,f13(x2772,x2773,x2771)),x2773) % 0.83/0.82 [278]~P1(x2781)+~P1(x2782)+P3(f12(x2782,x2783,x2781),x2781)+~P3(x2783,a41)+E(x2781,f38(x2782,x2783))+E(f5(f12(x2782,x2783,x2781)),x2783) % 0.83/0.82 [288]~P1(x2881)+~P2(x2882)+P3(f14(x2882,x2883,x2881),x2881)+~P7(x2883,f39(x2882))+E(x2881,f34(x2882,x2883))+E(f31(x2882,f16(x2882,x2883,x2881)),f14(x2882,x2883,x2881)) % 0.83/0.82 [290]~P2(x2902)+~P2(x2901)+~E(f39(x2901),x2903)+~P7(x2903,f39(x2902))+E(x2901,f33(x2902,x2903))+~E(f31(x2901,f10(x2902,x2903,x2901)),f31(x2902,f10(x2902,x2903,x2901))) % 0.83/0.82 [299]~P1(x2991)+~P6(x2993)+~P3(x2992,a41)+~P3(x2991,f38(x2993,a50))+~P7(x2993,f35(f31(a46,x2992),f2(f31(a46,x2992))))+P3(x2991,f38(f35(f31(a46,x2992),f2(f31(a46,x2992))),a50)) % 0.83/0.82 [196]~P1(x1964)+~P4(x1963)+~P4(x1961)+P3(x1961,x1962)+~E(x1961,x1963)+~E(x1962,f36(x1964,x1963)) % 0.83/0.82 [221]~P1(x2213)+~P4(x2212)+~P3(x2211,x2214)+E(x2211,x2212)+P3(x2211,x2213)+~E(x2214,f36(x2213,x2212)) % 0.83/0.82 [225]~P1(x2253)+~P4(x2254)+~P4(x2251)+~P3(x2251,x2253)+P3(x2251,x2252)+~E(x2252,f36(x2253,x2254)) % 0.83/0.82 [236]~P1(x2364)+~P7(x2361,x2364)+P3(x2361,x2362)+~P3(x2363,a41)+~E(x2362,f38(x2364,x2363))+~E(f5(x2361),x2363) % 0.83/0.82 [243]~P4(x2434)+~P2(x2433)+P3(x2431,x2432)+~E(f31(x2433,x2431),x2434)+~P3(x2431,f39(x2433))+~E(x2432,f32(x2433,x2434)) % 0.83/0.82 [256]~P2(x2563)+~P3(x2565,x2564)+P3(x2561,x2562)+~P7(x2564,f39(x2563))+~E(x2562,f34(x2563,x2564))+~E(f31(x2563,x2565),x2561) % 0.83/0.82 [248]E(f2(x2482),f2(x2481))+~P7(x2481,a41)+~P7(x2482,a41)+~P3(f2(x2481),x2482)+~P3(f2(x2482),x2481)+E(x2481,a37)+E(x2482,a37) % 0.83/0.82 [263]~P1(x2633)+~P1(x2632)+P7(x2632,x2633)+~P3(x2631,a41)+~P7(f38(x2632,x2631),f38(x2633,x2631))+E(x2631,a3)+E(f38(x2632,x2631),a37) % 0.83/0.82 [285]~P1(x2851)+~P1(x2852)+~P4(x2853)+E(f26(x2852,x2853,x2851),x2853)+P3(f26(x2852,x2853,x2851),x2851)+P3(f26(x2852,x2853,x2851),x2852)+E(x2851,f36(x2852,x2853)) % 0.83/0.82 [291]~P1(x2911)+~P1(x2912)+~P4(x2913)+~E(f26(x2912,x2913,x2911),x2913)+~P3(f26(x2912,x2913,x2911),x2911)+E(x2911,f36(x2912,x2913))+~P4(f26(x2912,x2913,x2911)) % 0.83/0.82 [292]~P1(x2921)+~P1(x2922)+~P4(x2923)+~P3(f26(x2922,x2923,x2921),x2921)+~P3(f26(x2922,x2923,x2921),x2922)+E(x2921,f36(x2922,x2923))+~P4(f26(x2922,x2923,x2921)) % 0.83/0.82 [295]~P1(x2951)+~P1(x2952)+~P3(x2953,a41)+~P3(f12(x2952,x2953,x2951),x2951)+~P7(f12(x2952,x2953,x2951),x2952)+E(x2951,f38(x2952,x2953))+~E(f5(f12(x2952,x2953,x2951)),x2953) % 0.83/0.82 [296]~P1(x2961)+~P4(x2963)+~P2(x2962)+~P3(f13(x2962,x2963,x2961),x2961)+~P3(f13(x2962,x2963,x2961),f39(x2962))+E(x2961,f32(x2962,x2963))+~E(f31(x2962,f13(x2962,x2963,x2961)),x2963) % 0.83/0.82 [226]~P1(x2264)+~P4(x2262)+~P4(x2261)+~P3(x2261,x2264)+E(x2261,x2262)+P3(x2261,x2263)+~E(x2263,f35(x2264,x2262)) % 0.83/0.82 [289]~P1(x2891)+~P2(x2892)+~P3(x2894,x2893)+~P7(x2893,f39(x2892))+~P3(f14(x2892,x2893,x2891),x2891)+~E(f31(x2892,x2894),f14(x2892,x2893,x2891))+E(x2891,f34(x2892,x2893)) % 0.83/0.82 [297]~P1(x2971)+~P1(x2972)+~P4(x2973)+E(f25(x2972,x2973,x2971),x2973)+~P3(f25(x2972,x2973,x2971),x2971)+~P3(f25(x2972,x2973,x2971),x2972)+E(x2971,f35(x2972,x2973))+~P4(f25(x2972,x2973,x2971)) % 0.83/0.82 [281]~P6(x2812)+~P2(x2813)+~E(f39(x2813),f38(x2812,x2811))+~P3(x2811,a41)+~P7(x2812,a41)+~P8(x2811,a44)+P6(f19(x2811,x2812,x2813))+~P7(f34(x2813,f39(x2813)),a53) % 0.83/0.82 [282]~P6(x2822)+~P2(x2823)+~E(f39(x2823),f38(x2822,x2821))+~P3(x2821,a41)+~P7(x2822,a41)+~P8(x2821,a44)+P3(f20(x2821,x2822,x2823),a53)+~P7(f34(x2823,f39(x2823)),a53) % 0.83/0.82 [284]~P6(x2842)+~P2(x2843)+~E(f39(x2843),f38(x2842,x2841))+~P3(x2841,a41)+~P7(x2842,a41)+~P8(x2841,a44)+P7(f19(x2841,x2842,x2843),x2842)+~P7(f34(x2843,f39(x2843)),a53) % 0.83/0.82 [298]~P6(x2984)+~P2(x2981)+~E(f39(x2981),f38(x2984,x2983))+~P3(x2983,a41)+~P7(x2984,a41)+~P8(x2983,a44)+E(f31(x2981,x2982),f20(x2983,x2984,x2981))+~P3(x2982,f38(f19(x2983,x2984,x2981),x2983))+~P7(f34(x2981,f39(x2981)),a53) % 0.83/0.82 %EqnAxiom % 0.83/0.82 [1]E(x11,x11) % 0.83/0.82 [2]E(x22,x21)+~E(x21,x22) % 0.83/0.82 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.83/0.82 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.83/0.82 [5]~E(x51,x52)+E(f43(x51),f43(x52)) % 0.83/0.82 [6]~E(x61,x62)+E(f4(x61),f4(x62)) % 0.83/0.82 [7]~E(x71,x72)+E(f39(x71),f39(x72)) % 0.83/0.82 [8]~E(x81,x82)+E(f31(x81,x83),f31(x82,x83)) % 0.83/0.82 [9]~E(x91,x92)+E(f31(x93,x91),f31(x93,x92)) % 0.83/0.82 [10]~E(x101,x102)+E(f10(x101,x103,x104),f10(x102,x103,x104)) % 0.83/0.82 [11]~E(x111,x112)+E(f10(x113,x111,x114),f10(x113,x112,x114)) % 0.83/0.82 [12]~E(x121,x122)+E(f10(x123,x124,x121),f10(x123,x124,x122)) % 0.83/0.82 [13]~E(x131,x132)+E(f19(x131,x133,x134),f19(x132,x133,x134)) % 0.83/0.82 [14]~E(x141,x142)+E(f19(x143,x141,x144),f19(x143,x142,x144)) % 0.83/0.82 [15]~E(x151,x152)+E(f19(x153,x154,x151),f19(x153,x154,x152)) % 0.83/0.82 [16]~E(x161,x162)+E(f5(x161),f5(x162)) % 0.83/0.82 [17]~E(x171,x172)+E(f35(x171,x173),f35(x172,x173)) % 0.83/0.82 [18]~E(x181,x182)+E(f35(x183,x181),f35(x183,x182)) % 0.83/0.82 [19]~E(x191,x192)+E(f33(x191,x193),f33(x192,x193)) % 0.83/0.82 [20]~E(x201,x202)+E(f33(x203,x201),f33(x203,x202)) % 0.83/0.82 [21]~E(x211,x212)+E(f12(x211,x213,x214),f12(x212,x213,x214)) % 0.83/0.82 [22]~E(x221,x222)+E(f12(x223,x221,x224),f12(x223,x222,x224)) % 0.83/0.82 [23]~E(x231,x232)+E(f12(x233,x234,x231),f12(x233,x234,x232)) % 0.83/0.82 [24]~E(x241,x242)+E(f38(x241,x243),f38(x242,x243)) % 0.83/0.82 [25]~E(x251,x252)+E(f38(x253,x251),f38(x253,x252)) % 0.83/0.82 [26]~E(x261,x262)+E(f34(x261,x263),f34(x262,x263)) % 0.83/0.82 [27]~E(x271,x272)+E(f34(x273,x271),f34(x273,x272)) % 0.83/0.82 [28]~E(x281,x282)+E(f22(x281),f22(x282)) % 0.83/0.82 [29]~E(x291,x292)+E(f20(x291,x293,x294),f20(x292,x293,x294)) % 0.83/0.82 [30]~E(x301,x302)+E(f20(x303,x301,x304),f20(x303,x302,x304)) % 0.83/0.82 [31]~E(x311,x312)+E(f20(x313,x314,x311),f20(x313,x314,x312)) % 0.83/0.82 [32]~E(x321,x322)+E(f25(x321,x323,x324),f25(x322,x323,x324)) % 0.83/0.82 [33]~E(x331,x332)+E(f25(x333,x331,x334),f25(x333,x332,x334)) % 0.83/0.82 [34]~E(x341,x342)+E(f25(x343,x344,x341),f25(x343,x344,x342)) % 0.83/0.82 [35]~E(x351,x352)+E(f40(x351),f40(x352)) % 0.83/0.82 [36]~E(x361,x362)+E(f36(x361,x363),f36(x362,x363)) % 0.83/0.82 [37]~E(x371,x372)+E(f36(x373,x371),f36(x373,x372)) % 0.83/0.82 [38]~E(x381,x382)+E(f30(x381,x383),f30(x382,x383)) % 0.83/0.82 [39]~E(x391,x392)+E(f30(x393,x391),f30(x393,x392)) % 0.83/0.82 [40]~E(x401,x402)+E(f17(x401),f17(x402)) % 0.83/0.82 [41]~E(x411,x412)+E(f26(x411,x413,x414),f26(x412,x413,x414)) % 0.83/0.82 [42]~E(x421,x422)+E(f26(x423,x421,x424),f26(x423,x422,x424)) % 0.83/0.82 [43]~E(x431,x432)+E(f26(x433,x434,x431),f26(x433,x434,x432)) % 0.83/0.82 [44]~E(x441,x442)+E(f24(x441,x443),f24(x442,x443)) % 0.83/0.82 [45]~E(x451,x452)+E(f24(x453,x451),f24(x453,x452)) % 0.83/0.82 [46]~E(x461,x462)+E(f32(x461,x463),f32(x462,x463)) % 0.83/0.82 [47]~E(x471,x472)+E(f32(x473,x471),f32(x473,x472)) % 0.83/0.82 [48]~E(x481,x482)+E(f8(x481,x483),f8(x482,x483)) % 0.83/0.82 [49]~E(x491,x492)+E(f8(x493,x491),f8(x493,x492)) % 0.83/0.82 [50]~E(x501,x502)+E(f7(x501),f7(x502)) % 0.83/0.82 [51]~E(x511,x512)+E(f13(x511,x513,x514),f13(x512,x513,x514)) % 0.83/0.82 [52]~E(x521,x522)+E(f13(x523,x521,x524),f13(x523,x522,x524)) % 0.83/0.82 [53]~E(x531,x532)+E(f13(x533,x534,x531),f13(x533,x534,x532)) % 0.83/0.82 [54]~E(x541,x542)+E(f14(x541,x543,x544),f14(x542,x543,x544)) % 0.83/0.82 [55]~E(x551,x552)+E(f14(x553,x551,x554),f14(x553,x552,x554)) % 0.83/0.82 [56]~E(x561,x562)+E(f14(x563,x564,x561),f14(x563,x564,x562)) % 0.83/0.82 [57]~E(x571,x572)+E(f42(x571),f42(x572)) % 0.83/0.82 [58]~E(x581,x582)+E(f16(x581,x583,x584),f16(x582,x583,x584)) % 0.83/0.82 [59]~E(x591,x592)+E(f16(x593,x591,x594),f16(x593,x592,x594)) % 0.83/0.82 [60]~E(x601,x602)+E(f16(x603,x604,x601),f16(x603,x604,x602)) % 0.83/0.82 [61]~E(x611,x612)+E(f28(x611,x613),f28(x612,x613)) % 0.83/0.82 [62]~E(x621,x622)+E(f28(x623,x621),f28(x623,x622)) % 0.83/0.82 [63]~E(x631,x632)+E(f21(x631),f21(x632)) % 0.83/0.82 [64]~E(x641,x642)+E(f29(x641,x643),f29(x642,x643)) % 0.83/0.82 [65]~E(x651,x652)+E(f29(x653,x651),f29(x653,x652)) % 0.83/0.82 [66]~E(x661,x662)+E(f11(x661,x663,x664),f11(x662,x663,x664)) % 0.83/0.82 [67]~E(x671,x672)+E(f11(x673,x671,x674),f11(x673,x672,x674)) % 0.83/0.82 [68]~E(x681,x682)+E(f11(x683,x684,x681),f11(x683,x684,x682)) % 0.83/0.82 [69]~E(x691,x692)+E(f15(x691,x693,x694,x695),f15(x692,x693,x694,x695)) % 0.83/0.82 [70]~E(x701,x702)+E(f15(x703,x701,x704,x705),f15(x703,x702,x704,x705)) % 0.83/0.82 [71]~E(x711,x712)+E(f15(x713,x714,x711,x715),f15(x713,x714,x712,x715)) % 0.83/0.82 [72]~E(x721,x722)+E(f15(x723,x724,x725,x721),f15(x723,x724,x725,x722)) % 0.83/0.82 [73]~E(x731,x732)+E(f27(x731,x733),f27(x732,x733)) % 0.83/0.82 [74]~E(x741,x742)+E(f27(x743,x741),f27(x743,x742)) % 0.83/0.82 [75]~E(x751,x752)+E(f9(x751,x753),f9(x752,x753)) % 0.83/0.82 [76]~E(x761,x762)+E(f9(x763,x761),f9(x763,x762)) % 0.83/0.82 [77]~E(x771,x772)+E(f23(x771),f23(x772)) % 0.83/0.82 [78]~E(x781,x782)+E(f6(x781),f6(x782)) % 0.83/0.82 [79]~E(x791,x792)+E(f18(x791),f18(x792)) % 0.83/0.82 [80]~P1(x801)+P1(x802)+~E(x801,x802) % 0.83/0.82 [81]P3(x812,x813)+~E(x811,x812)+~P3(x811,x813) % 0.83/0.82 [82]P3(x823,x822)+~E(x821,x822)+~P3(x823,x821) % 0.83/0.82 [83]~P6(x831)+P6(x832)+~E(x831,x832) % 0.83/0.82 [84]P7(x842,x843)+~E(x841,x842)+~P7(x841,x843) % 0.83/0.82 [85]P7(x853,x852)+~E(x851,x852)+~P7(x853,x851) % 0.83/0.82 [86]~P2(x861)+P2(x862)+~E(x861,x862) % 0.83/0.82 [87]~P5(x871)+P5(x872)+~E(x871,x872) % 0.83/0.82 [88]~P4(x881)+P4(x882)+~E(x881,x882) % 0.83/0.82 [89]P9(x892,x893)+~E(x891,x892)+~P9(x891,x893) % 0.83/0.82 [90]P9(x903,x902)+~E(x901,x902)+~P9(x903,x901) % 0.83/0.82 [91]P8(x912,x913)+~E(x911,x912)+~P8(x911,x913) % 0.83/0.82 [92]P8(x923,x922)+~E(x921,x922)+~P8(x923,x921) % 0.83/0.82 % 0.83/0.82 %------------------------------------------- % 0.83/0.82 cnf(302,plain, % 0.83/0.82 (P1(a37)), % 0.83/0.82 inference(equality_inference,[],[143])). % 0.83/0.82 cnf(305,plain, % 0.83/0.82 (~P3(x3051,a37)), % 0.83/0.82 inference(equality_inference,[],[151])). % 0.83/0.82 cnf(306,plain, % 0.83/0.82 (P1(f4(x3061))+~P3(x3061,a41)), % 0.83/0.82 inference(equality_inference,[],[160])). % 0.83/0.82 cnf(312,plain, % 0.83/0.82 (~P1(x3121)+P1(f38(x3121,x3122))+~P3(x3122,a41)), % 0.83/0.82 inference(equality_inference,[],[189])). % 0.83/0.82 cnf(325,plain, % 0.83/0.82 (~P3(x3251,a41)+~P3(x3251,a41)+P3(x3251,f4(f43(x3251)))), % 0.83/0.82 inference(equality_inference,[],[220])). % 0.83/0.82 cnf(363,plain, % 0.83/0.82 ($false), % 0.83/0.82 inference(scs_inference,[],[142,305,302,100,104,107,118,119,120,115,95,96,132,116,2,143,151,306,164,3,146,312,325,149,173,82,87,191]), % 0.83/0.82 ['proof']). % 0.83/0.82 % SZS output end Proof % 0.83/0.82 % Total time :0.060000s %------------------------------------------------------------------------------