%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM632+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 : n001.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 12:25:33 EDT 2024 % Result : Theorem 0.56s 0.68s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM632+1 : TPTP v8.2.0. Released v4.0.0. % 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n001.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sun Jun 23 02:54:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.19/0.55 start to proof:theBenchmark % 0.56/0.66 %------------------------------------------- % 0.56/0.66 % File :CSE---1.7 % 0.56/0.66 % Problem :theBenchmark % 0.56/0.66 % Transform :cnf % 0.56/0.66 % Format :tptp:raw % 0.56/0.66 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.66 % 0.56/0.66 % Result :Theorem 0.020000s % 0.56/0.66 % Output :CNFRefutation 0.020000s % 0.56/0.66 %------------------------------------------- % 0.56/0.67 %------------------------------------------------------------------------------ % 0.56/0.67 % File : NUM632+1 : TPTP v8.2.0. Released v4.0.0. % 0.56/0.67 % Domain : Number Theory % 0.56/0.67 % Problem : Ramsey's Infinite Theorem 15_02_23_13, 00 expansion % 0.56/0.67 % Version : Especial. % 0.56/0.67 % English : % 0.56/0.67 % 0.56/0.67 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.56/0.67 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.56/0.67 % Source : [Pas08] % 0.56/0.67 % Names : ramsey_15_02_23_13.00 [Pas08] % 0.56/0.67 % 0.56/0.67 % Status : Theorem % 0.56/0.67 % Rating : 0.14 v8.1.0, 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0 % 0.56/0.67 % Syntax : Number of formulae : 115 ( 22 unt; 11 def) % 0.56/0.67 % Number of atoms : 407 ( 76 equ) % 0.56/0.67 % Maximal formula atoms : 12 ( 3 avg) % 0.56/0.67 % Number of connectives : 317 ( 25 ~; 4 |; 131 &) % 0.56/0.67 % ( 22 <=>; 135 =>; 0 <=; 0 <~>) % 0.56/0.67 % Maximal formula depth : 15 ( 5 avg) % 0.56/0.67 % Maximal term depth : 5 ( 1 avg) % 0.56/0.67 % Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty) % 0.56/0.67 % Number of functors : 31 ( 31 usr; 17 con; 0-2 aty) % 0.56/0.67 % Number of variables : 171 ( 159 !; 12 ?) % 0.56/0.67 % SPC : FOF_THM_RFO_SEQ % 0.56/0.67 % 0.56/0.67 % Comments : Problem generated by the SAD system [VLP07] % 0.56/0.67 %------------------------------------------------------------------------------ % 0.56/0.67 fof(mSetSort,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => $true ) ). % 0.56/0.67 % 0.56/0.67 fof(mElmSort,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElement0(W0) % 0.56/0.67 => $true ) ). % 0.56/0.67 % 0.56/0.67 fof(mEOfElem,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( aElementOf0(W1,W0) % 0.56/0.67 => aElement0(W1) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mFinRel,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ( isFinite0(W0) % 0.56/0.67 => $true ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mDefEmp,definition, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( W0 = slcrc0 % 0.56/0.67 <=> ( aSet0(W0) % 0.56/0.67 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mEmpFin,axiom, % 0.56/0.67 isFinite0(slcrc0) ). % 0.56/0.67 % 0.56/0.67 fof(mCntRel,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ( isCountable0(W0) % 0.56/0.67 => $true ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCountNFin,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & isCountable0(W0) ) % 0.56/0.67 => ~ isFinite0(W0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCountNFin_01,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & isCountable0(W0) ) % 0.56/0.67 => W0 != slcrc0 ) ). % 0.56/0.67 % 0.56/0.67 fof(mDefSub,definition, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( aSubsetOf0(W1,W0) % 0.56/0.67 <=> ( aSet0(W1) % 0.56/0.67 & ! [W2] : % 0.56/0.67 ( aElementOf0(W2,W1) % 0.56/0.67 => aElementOf0(W2,W0) ) ) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSubFSet,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & isFinite0(W0) ) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( aSubsetOf0(W1,W0) % 0.56/0.67 => isFinite0(W1) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSubRefl,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => aSubsetOf0(W0,W0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSubASymm,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & aSet0(W1) ) % 0.56/0.67 => ( ( aSubsetOf0(W0,W1) % 0.56/0.67 & aSubsetOf0(W1,W0) ) % 0.56/0.67 => W0 = W1 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSubTrans,axiom, % 0.56/0.67 ! [W0,W1,W2] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & aSet0(W1) % 0.56/0.67 & aSet0(W2) ) % 0.56/0.67 => ( ( aSubsetOf0(W0,W1) % 0.56/0.67 & aSubsetOf0(W1,W2) ) % 0.56/0.67 => aSubsetOf0(W0,W2) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mDefCons,definition, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & aElement0(W1) ) % 0.56/0.67 => ! [W2] : % 0.56/0.67 ( W2 = sdtpldt0(W0,W1) % 0.56/0.67 <=> ( aSet0(W2) % 0.56/0.67 & ! [W3] : % 0.56/0.67 ( aElementOf0(W3,W2) % 0.56/0.67 <=> ( aElement0(W3) % 0.56/0.67 & ( aElementOf0(W3,W0) % 0.56/0.67 | W3 = W1 ) ) ) ) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mDefDiff,definition, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & aElement0(W1) ) % 0.56/0.67 => ! [W2] : % 0.56/0.67 ( W2 = sdtmndt0(W0,W1) % 0.56/0.67 <=> ( aSet0(W2) % 0.56/0.67 & ! [W3] : % 0.56/0.67 ( aElementOf0(W3,W2) % 0.56/0.67 <=> ( aElement0(W3) % 0.56/0.67 & aElementOf0(W3,W0) % 0.56/0.67 & W3 != W1 ) ) ) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mConsDiff,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( aElementOf0(W1,W0) % 0.56/0.67 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mDiffCons,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElement0(W0) % 0.56/0.67 & aSet0(W1) ) % 0.56/0.67 => ( ~ aElementOf0(W0,W1) % 0.56/0.67 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCConsSet,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElement0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( aSet0(W1) % 0.56/0.67 & isCountable0(W1) ) % 0.56/0.67 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCDiffSet,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElement0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( aSet0(W1) % 0.56/0.67 & isCountable0(W1) ) % 0.56/0.67 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mFConsSet,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElement0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( aSet0(W1) % 0.56/0.67 & isFinite0(W1) ) % 0.56/0.67 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mFDiffSet,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElement0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( aSet0(W1) % 0.56/0.67 & isFinite0(W1) ) % 0.56/0.67 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mNATSet,axiom, % 0.56/0.67 ( aSet0(szNzAzT0) % 0.56/0.67 & isCountable0(szNzAzT0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mZeroNum,axiom, % 0.56/0.67 aElementOf0(sz00,szNzAzT0) ). % 0.56/0.67 % 0.56/0.67 fof(mSuccNum,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 0.56/0.67 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSuccEquSucc,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.56/0.67 => W0 = W1 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mNatExtra,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => ( W0 = sz00 % 0.56/0.67 | ? [W1] : % 0.56/0.67 ( aElementOf0(W1,szNzAzT0) % 0.56/0.67 & W0 = szszuzczcdt0(W1) ) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mNatNSucc,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => W0 != szszuzczcdt0(W0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessRel,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( sdtlseqdt0(W0,W1) % 0.56/0.67 => $true ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mZeroLess,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => sdtlseqdt0(sz00,W0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mNoScLessZr,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 0.56/0.67 % 0.56/0.67 fof(mSuccLess,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( sdtlseqdt0(W0,W1) % 0.56/0.67 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessSucc,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessRefl,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => sdtlseqdt0(W0,W0) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessASymm,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( ( sdtlseqdt0(W0,W1) % 0.56/0.67 & sdtlseqdt0(W1,W0) ) % 0.56/0.67 => W0 = W1 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessTrans,axiom, % 0.56/0.67 ! [W0,W1,W2] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) % 0.56/0.67 & aElementOf0(W2,szNzAzT0) ) % 0.56/0.67 => ( ( sdtlseqdt0(W0,W1) % 0.56/0.67 & sdtlseqdt0(W1,W2) ) % 0.56/0.67 => sdtlseqdt0(W0,W2) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mLessTotal,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( sdtlseqdt0(W0,W1) % 0.56/0.67 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mIHSort,axiom, % 0.56/0.67 ! [W0,W1] : % 0.56/0.67 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.67 => ( iLess0(W0,W1) % 0.56/0.67 => $true ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mIH,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aElementOf0(W0,szNzAzT0) % 0.56/0.67 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardS,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => aElement0(sbrdtbr0(W0)) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardNum,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 0.56/0.67 <=> isFinite0(W0) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardEmpty,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ( sbrdtbr0(W0) = sz00 % 0.56/0.67 <=> W0 = slcrc0 ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardCons,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( ( aSet0(W0) % 0.56/0.67 & isFinite0(W0) ) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( aElement0(W1) % 0.56/0.67 => ( ~ aElementOf0(W1,W0) % 0.56/0.67 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardDiff,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( isFinite0(W0) % 0.56/0.67 & aElementOf0(W1,W0) ) % 0.56/0.67 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardSub,axiom, % 0.56/0.67 ! [W0] : % 0.56/0.67 ( aSet0(W0) % 0.56/0.67 => ! [W1] : % 0.56/0.67 ( ( isFinite0(W0) % 0.56/0.67 & aSubsetOf0(W1,W0) ) % 0.56/0.67 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 0.56/0.67 % 0.56/0.67 fof(mCardSubEx,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ( ( isFinite0(W0) % 0.56/0.68 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 0.56/0.68 => ? [W2] : % 0.56/0.68 ( aSubsetOf0(W2,W0) % 0.56/0.68 & sbrdtbr0(W2) = W1 ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefMin,definition, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSubsetOf0(W0,szNzAzT0) % 0.56/0.68 & W0 != slcrc0 ) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( W1 = szmzizndt0(W0) % 0.56/0.68 <=> ( aElementOf0(W1,W0) % 0.56/0.68 & ! [W2] : % 0.56/0.68 ( aElementOf0(W2,W0) % 0.56/0.68 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefMax,definition, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSubsetOf0(W0,szNzAzT0) % 0.56/0.68 & isFinite0(W0) % 0.56/0.68 & W0 != slcrc0 ) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( W1 = szmzazxdt0(W0) % 0.56/0.68 <=> ( aElementOf0(W1,W0) % 0.56/0.68 & ! [W2] : % 0.56/0.68 ( aElementOf0(W2,W0) % 0.56/0.68 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mMinMin,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aSubsetOf0(W0,szNzAzT0) % 0.56/0.68 & aSubsetOf0(W1,szNzAzT0) % 0.56/0.68 & W0 != slcrc0 % 0.56/0.68 & W1 != slcrc0 ) % 0.56/0.68 => ( ( aElementOf0(szmzizndt0(W0),W1) % 0.56/0.68 & aElementOf0(szmzizndt0(W1),W0) ) % 0.56/0.68 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefSeg,definition, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( W1 = slbdtrb0(W0) % 0.56/0.68 <=> ( aSet0(W1) % 0.56/0.68 & ! [W2] : % 0.56/0.68 ( aElementOf0(W2,W1) % 0.56/0.68 <=> ( aElementOf0(W2,szNzAzT0) % 0.56/0.68 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSegFin,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => isFinite0(slbdtrb0(W0)) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSegZero,axiom, % 0.56/0.68 slbdtrb0(sz00) = slcrc0 ). % 0.56/0.68 % 0.56/0.68 fof(mSegSucc,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 0.56/0.68 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 0.56/0.68 | W0 = W1 ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSegLess,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ( sdtlseqdt0(W0,W1) % 0.56/0.68 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mFinSubSeg,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSubsetOf0(W0,szNzAzT0) % 0.56/0.68 & isFinite0(W0) ) % 0.56/0.68 => ? [W1] : % 0.56/0.68 ( aElementOf0(W1,szNzAzT0) % 0.56/0.68 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mCardSeg,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefSel,definition, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( W2 = slbdtsldtrb0(W0,W1) % 0.56/0.68 <=> ( aSet0(W2) % 0.56/0.68 & ! [W3] : % 0.56/0.68 ( aElementOf0(W3,W2) % 0.56/0.68 <=> ( aSubsetOf0(W3,W0) % 0.56/0.68 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSelFSet,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & isFinite0(W0) ) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aElementOf0(W1,szNzAzT0) % 0.56/0.68 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSelNSet,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & ~ isFinite0(W0) ) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aElementOf0(W1,szNzAzT0) % 0.56/0.68 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSelCSet,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & isCountable0(W0) ) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aElementOf0(W1,szNzAzT0) % 0.56/0.68 & W1 != sz00 ) % 0.56/0.68 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSelSub,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1,W2] : % 0.56/0.68 ( ( aSet0(W1) % 0.56/0.68 & aSet0(W2) % 0.56/0.68 & W0 != sz00 ) % 0.56/0.68 => ( ( aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0)) % 0.56/0.68 & slbdtsldtrb0(W1,W0) != slcrc0 ) % 0.56/0.68 => aSubsetOf0(W1,W2) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mSelExtra,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aSet0(W0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( ( aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) % 0.56/0.68 & isFinite0(W2) ) % 0.56/0.68 => ? [W3] : % 0.56/0.68 ( aSubsetOf0(W3,W0) % 0.56/0.68 & isFinite0(W3) % 0.56/0.68 & aSubsetOf0(W2,slbdtsldtrb0(W3,W1)) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mFunSort,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => $true ) ). % 0.56/0.68 % 0.56/0.68 fof(mDomSet,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => aSet0(szDzozmdt0(W0)) ) ). % 0.56/0.68 % 0.56/0.68 fof(mImgElm,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aElementOf0(W1,szDzozmdt0(W0)) % 0.56/0.68 => aElement0(sdtlpdtrp0(W0,W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefPtt,definition, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aFunction0(W0) % 0.56/0.68 & aElement0(W1) ) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( W2 = sdtlbdtrb0(W0,W1) % 0.56/0.68 <=> ( aSet0(W2) % 0.56/0.68 & ! [W3] : % 0.56/0.68 ( aElementOf0(W3,W2) % 0.56/0.68 <=> ( aElementOf0(W3,szDzozmdt0(W0)) % 0.56/0.68 & sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mPttSet,axiom, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aFunction0(W0) % 0.56/0.68 & aElement0(W1) ) % 0.56/0.68 => aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefSImg,definition, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( W2 = sdtlcdtrc0(W0,W1) % 0.56/0.68 <=> ( aSet0(W2) % 0.56/0.68 & ! [W3] : % 0.56/0.68 ( aElementOf0(W3,W2) % 0.56/0.68 <=> ? [W4] : % 0.56/0.68 ( aElementOf0(W4,W1) % 0.56/0.68 & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mImgRng,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aElementOf0(W1,szDzozmdt0(W0)) % 0.56/0.68 => aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDefRst,definition, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( W2 = sdtexdt0(W0,W1) % 0.56/0.68 <=> ( aFunction0(W2) % 0.56/0.68 & szDzozmdt0(W2) = W1 % 0.56/0.68 & ! [W3] : % 0.56/0.68 ( aElementOf0(W3,W1) % 0.56/0.68 => sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3) ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mImgCount,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aSubsetOf0(W1,szDzozmdt0(W0)) % 0.56/0.68 & isCountable0(W1) ) % 0.56/0.68 => ( ! [W2,W3] : % 0.56/0.68 ( ( aElementOf0(W2,szDzozmdt0(W0)) % 0.56/0.68 & aElementOf0(W3,szDzozmdt0(W0)) % 0.56/0.68 & W2 != W3 ) % 0.56/0.68 => sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) % 0.56/0.68 => isCountable0(sdtlcdtrc0(W0,W1)) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(mDirichlet,axiom, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aFunction0(W0) % 0.56/0.68 => ( ( isCountable0(szDzozmdt0(W0)) % 0.56/0.68 & isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) % 0.56/0.68 => ( aElement0(szDzizrdt0(W0)) % 0.56/0.68 & isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3291,hypothesis, % 0.56/0.68 ( aSet0(xT) % 0.56/0.68 & isFinite0(xT) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3418,hypothesis, % 0.56/0.68 aElementOf0(xK,szNzAzT0) ). % 0.56/0.68 % 0.56/0.68 fof(m__3435,hypothesis, % 0.56/0.68 ( aSubsetOf0(xS,szNzAzT0) % 0.56/0.68 & isCountable0(xS) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3453,hypothesis, % 0.56/0.68 ( aFunction0(xc) % 0.56/0.68 & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) % 0.56/0.68 & aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3398,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aSubsetOf0(W1,szNzAzT0) % 0.56/0.68 & isCountable0(W1) ) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( ( aFunction0(W2) % 0.56/0.68 & szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) % 0.56/0.68 & aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) % 0.56/0.68 => ( iLess0(W0,xK) % 0.56/0.68 => ? [W3] : % 0.56/0.68 ( aElementOf0(W3,xT) % 0.56/0.68 & ? [W4] : % 0.56/0.68 ( aSubsetOf0(W4,W1) % 0.56/0.68 & isCountable0(W4) % 0.56/0.68 & ! [W5] : % 0.56/0.68 ( aElementOf0(W5,slbdtsldtrb0(W4,W0)) % 0.56/0.68 => sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3462,hypothesis, % 0.56/0.68 xK != sz00 ). % 0.56/0.68 % 0.56/0.68 fof(m__3520,hypothesis, % 0.56/0.68 xK != sz00 ). % 0.56/0.68 % 0.56/0.68 fof(m__3533,hypothesis, % 0.56/0.68 ( aElementOf0(xk,szNzAzT0) % 0.56/0.68 & szszuzczcdt0(xk) = xK ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3623,hypothesis, % 0.56/0.68 ( aFunction0(xN) % 0.56/0.68 & szDzozmdt0(xN) = szNzAzT0 % 0.56/0.68 & sdtlpdtrp0(xN,sz00) = xS % 0.56/0.68 & ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) % 0.56/0.68 & isCountable0(sdtlpdtrp0(xN,W0)) ) % 0.56/0.68 => ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.56/0.68 & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3671,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) % 0.56/0.68 & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3754,hypothesis, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) ) % 0.56/0.68 => ( sdtlseqdt0(W1,W0) % 0.56/0.68 => aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3821,hypothesis, % 0.56/0.68 ! [W0,W1] : % 0.56/0.68 ( ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 & aElementOf0(W1,szNzAzT0) % 0.56/0.68 & W0 != W1 ) % 0.56/0.68 => szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__3965,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aSet0(W1) % 0.56/0.68 & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) % 0.56/0.68 => aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4151,hypothesis, % 0.56/0.68 ( aFunction0(xC) % 0.56/0.68 & szDzozmdt0(xC) = szNzAzT0 % 0.56/0.68 & ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ( aFunction0(sdtlpdtrp0(xC,W0)) % 0.56/0.68 & szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) % 0.56/0.68 & ! [W1] : % 0.56/0.68 ( ( aSet0(W1) % 0.56/0.68 & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) % 0.56/0.68 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4182,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4331,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.56/0.68 & isCountable0(W1) ) % 0.56/0.68 => ! [W2] : % 0.56/0.68 ( ( aSet0(W2) % 0.56/0.68 & aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) % 0.56/0.68 => aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4411,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ? [W1] : % 0.56/0.68 ( aElementOf0(W1,xT) % 0.56/0.68 & ? [W2] : % 0.56/0.68 ( aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) % 0.56/0.68 & isCountable0(W2) % 0.56/0.68 & ! [W3] : % 0.56/0.68 ( ( aSet0(W3) % 0.56/0.68 & aElementOf0(W3,slbdtsldtrb0(W2,xk)) ) % 0.56/0.68 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 ) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4618,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ? [W1] : % 0.56/0.68 ( aElementOf0(W1,xT) % 0.56/0.68 & ! [W2] : % 0.56/0.68 ( ( aSet0(W2) % 0.56/0.68 & aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) % 0.56/0.68 => sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4660,hypothesis, % 0.56/0.68 ( aFunction0(xe) % 0.56/0.68 & szDzozmdt0(xe) = szNzAzT0 % 0.56/0.68 & ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4730,hypothesis, % 0.56/0.68 ( aFunction0(xd) % 0.56/0.68 & szDzozmdt0(xd) = szNzAzT0 % 0.56/0.68 & ! [W0] : % 0.56/0.68 ( aElementOf0(W0,szNzAzT0) % 0.56/0.68 => ! [W1] : % 0.56/0.68 ( ( aSet0(W1) % 0.56/0.68 & aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) % 0.56/0.68 => sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4758,hypothesis, % 0.56/0.68 aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ). % 0.56/0.68 % 0.56/0.68 fof(m__4854,hypothesis, % 0.56/0.68 ( aElementOf0(szDzizrdt0(xd),xT) % 0.56/0.68 & isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4891,hypothesis, % 0.56/0.68 ( aSet0(xO) % 0.56/0.68 & xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4908,hypothesis, % 0.56/0.68 ( aSet0(xO) % 0.56/0.68 & isCountable0(xO) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4982,hypothesis, % 0.56/0.68 ! [W0] : % 0.56/0.68 ( aElementOf0(W0,xO) % 0.56/0.68 => ? [W1] : % 0.56/0.68 ( aElementOf0(W1,szNzAzT0) % 0.56/0.68 & aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) % 0.56/0.68 & sdtlpdtrp0(xe,W1) = W0 ) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__4998,hypothesis, % 0.56/0.68 aSubsetOf0(xO,xS) ). % 0.56/0.68 % 0.56/0.68 fof(m__5078,hypothesis, % 0.56/0.68 aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ). % 0.56/0.68 % 0.56/0.68 fof(m__5093,hypothesis, % 0.56/0.68 ( aSubsetOf0(xQ,xO) % 0.56/0.68 & xQ != slcrc0 ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5106,hypothesis, % 0.56/0.68 aSubsetOf0(xQ,szNzAzT0) ). % 0.56/0.68 % 0.56/0.68 fof(m__5116,hypothesis, % 0.56/0.68 aElementOf0(xQ,szDzozmdt0(xc)) ). % 0.56/0.68 % 0.56/0.68 fof(m__5147,hypothesis, % 0.56/0.68 xp = szmzizndt0(xQ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5164,hypothesis, % 0.56/0.68 ( aSet0(xP) % 0.56/0.68 & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5173,hypothesis, % 0.56/0.68 aElementOf0(xp,xQ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5182,hypothesis, % 0.56/0.68 aElementOf0(xp,xO) ). % 0.56/0.68 % 0.56/0.68 fof(m__5195,hypothesis, % 0.56/0.68 aSubsetOf0(xP,xQ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5208,hypothesis, % 0.56/0.68 aSubsetOf0(xP,xO) ). % 0.56/0.68 % 0.56/0.68 fof(m__5217,hypothesis, % 0.56/0.68 sbrdtbr0(xP) = xk ). % 0.56/0.68 % 0.56/0.68 fof(m__5270,hypothesis, % 0.56/0.68 aElementOf0(xP,slbdtsldtrb0(xO,xk)) ). % 0.56/0.68 % 0.56/0.68 fof(m__5309,hypothesis, % 0.56/0.68 ( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) % 0.56/0.68 & aElementOf0(xn,szNzAzT0) % 0.56/0.68 & sdtlpdtrp0(xe,xn) = xp ) ). % 0.56/0.68 % 0.56/0.68 fof(m__5321,hypothesis, % 0.56/0.68 sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) ). % 0.56/0.68 % 0.56/0.68 fof(m__5334,hypothesis, % 0.56/0.68 aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ). % 0.56/0.68 % 0.56/0.68 fof(m__5568,hypothesis, % 0.56/0.68 sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn) ). % 0.56/0.68 % 0.56/0.68 fof(m__,conjecture, % 0.56/0.68 sdtlpdtrp0(xc,xQ) = szDzizrdt0(xd) ). % 0.56/0.68 % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 %------------------------------------------- % 0.56/0.68 % Proof found % 0.56/0.68 % SZS status Theorem for theBenchmark % 0.56/0.68 % SZS output start Proof % 0.56/0.68 %ClaNum:306(EqnAxiom:92) % 0.56/0.68 %VarNum:1229(SingletonVarNum:358) % 0.56/0.68 %MaxLitNum:9 % 0.56/0.68 %MaxfuncDepth:4 % 0.56/0.68 %SharedTerms:94 % 0.56/0.68 %goalClause: 147 % 0.56/0.68 %singleGoalClaCount:1 % 0.56/0.68 [101]P1(a41) % 0.56/0.68 [102]P1(a53) % 0.56/0.68 [104]P1(a48) % 0.56/0.68 [105]P1(a46) % 0.56/0.68 [106]P5(a37) % 0.56/0.68 [107]P5(a53) % 0.56/0.68 [108]P6(a41) % 0.56/0.68 [109]P6(a54) % 0.56/0.68 [110]P6(a48) % 0.56/0.68 [111]P2(a55) % 0.56/0.68 [112]P2(a47) % 0.56/0.68 [113]P2(a45) % 0.56/0.68 [114]P2(a51) % 0.56/0.68 [115]P2(a52) % 0.56/0.68 [118]P3(a29,a41) % 0.56/0.68 [119]P3(a44,a41) % 0.56/0.68 [120]P3(a50,a41) % 0.56/0.68 [121]P3(a49,a48) % 0.56/0.68 [122]P3(a49,a1) % 0.56/0.68 [123]P3(a56,a41) % 0.56/0.68 [124]P7(a54,a41) % 0.56/0.68 [125]P7(a48,a54) % 0.56/0.68 [126]P7(a1,a41) % 0.56/0.68 [127]P7(a1,a48) % 0.56/0.68 [128]P7(a46,a48) % 0.56/0.68 [129]P7(a46,a1) % 0.56/0.68 [145]~E(a29,a44) % 0.56/0.68 [146]~E(a37,a1) % 0.56/0.68 [93]E(f2(a1),a49) % 0.56/0.68 [94]E(f43(a50),a44) % 0.56/0.68 [95]E(f3(a46),a50) % 0.56/0.68 [96]E(f30(a29),a37) % 0.56/0.68 [97]E(f39(a47),a41) % 0.56/0.68 [98]E(f39(a45),a41) % 0.56/0.68 [99]E(f39(a51),a41) % 0.56/0.68 [100]E(f39(a52),a41) % 0.56/0.68 [116]E(f31(a47,a29),a54) % 0.56/0.68 [117]E(f31(a51,a56),a49) % 0.56/0.68 [130]E(f38(a54,a44),f39(a55)) % 0.56/0.68 [131]E(f31(a52,a56),f40(a52)) % 0.56/0.68 [133]P3(a1,f39(a55)) % 0.56/0.68 [134]P3(f40(a52),a53) % 0.56/0.68 [135]E(f31(a55,a1),f31(a52,a56)) % 0.56/0.68 [136]P3(a1,f38(a48,a44)) % 0.56/0.68 [137]P3(a46,f38(a48,a50)) % 0.56/0.68 [147]~E(f31(a55,a1),f40(a52)) % 0.56/0.68 [132]E(f35(a1,f2(a1)),a46) % 0.56/0.68 [138]P6(f32(a52,f40(a52))) % 0.56/0.68 [140]P3(a56,f32(a52,f40(a52))) % 0.56/0.68 [141]P7(a46,f31(a47,f43(a56))) % 0.56/0.68 [142]P7(f34(a55,f39(a55)),a53) % 0.56/0.68 [143]P7(f34(a52,f39(a52)),a53) % 0.56/0.68 [139]E(f34(a51,f32(a52,f40(a52))),a48) % 0.56/0.68 [148]P1(x1481)+~E(x1481,a37) % 0.56/0.68 [155]~P1(x1551)+P7(x1551,x1551) % 0.56/0.68 [163]~P3(x1631,a41)+P9(a29,x1631) % 0.56/0.68 [169]P9(x1691,x1691)+~P3(x1691,a41) % 0.56/0.68 [152]~P2(x1521)+P1(f39(x1521)) % 0.56/0.68 [153]~P1(x1531)+P4(f3(x1531)) % 0.56/0.68 [157]~P3(x1571,a41)+~E(f43(x1571),a29) % 0.56/0.68 [158]~P3(x1581,a41)+~E(f43(x1581),x1581) % 0.56/0.68 [160]~P3(x1601,a41)+P5(f30(x1601)) % 0.56/0.68 [161]~P3(x1611,a41)+P6(f15(x1611)) % 0.56/0.68 [170]~P3(x1701,a41)+P3(f43(x1701),a41) % 0.56/0.68 [171]~P3(x1711,a41)+P3(f16(x1711),a53) % 0.56/0.68 [172]~P3(x1721,a41)+P3(f20(x1721),a53) % 0.56/0.68 [173]~P3(x1731,a48)+P3(f21(x1731),a41) % 0.56/0.68 [175]~P3(x1751,a41)+P9(x1751,f43(x1751)) % 0.56/0.68 [176]~P3(x1761,a41)+P8(x1761,f43(x1761)) % 0.56/0.68 [185]~P3(x1851,a41)+P6(f31(a47,x1851)) % 0.56/0.68 [186]~P3(x1861,a41)+P2(f31(a45,x1861)) % 0.56/0.68 [187]~P3(x1871,a41)+~P9(f43(x1871),a29) % 0.56/0.68 [195]~P3(x1951,a41)+P7(f31(a47,x1951),a41) % 0.56/0.68 [162]~P3(x1621,a41)+E(f3(f30(x1621)),x1621) % 0.56/0.68 [174]~P3(x1741,a48)+E(f31(a51,f21(x1741)),x1741) % 0.56/0.68 [197]~P3(x1971,a41)+E(f2(f31(a47,x1971)),f31(a51,x1971)) % 0.56/0.68 [215]~P3(x2151,a48)+P3(f21(x2151),f32(a52,f40(a52))) % 0.56/0.68 [270]~P3(x2701,a41)+P7(f34(f31(a45,x2701),f39(f31(a45,x2701))),a53) % 0.56/0.68 [272]~P3(x2721,a41)+P7(f15(x2721),f35(f31(a47,x2721),f2(f31(a47,x2721)))) % 0.56/0.68 [274]~P3(x2741,a41)+E(f38(f35(f31(a47,x2741),f2(f31(a47,x2741))),a50),f39(f31(a45,x2741))) % 0.56/0.68 [156]~P3(x1562,x1561)+~E(x1561,a37) % 0.56/0.68 [151]~P1(x1511)+~P6(x1511)+~E(x1511,a37) % 0.56/0.68 [154]~P5(x1541)+~P6(x1541)+~P1(x1541) % 0.56/0.68 [149]~P1(x1491)+~E(x1491,a37)+E(f3(x1491),a29) % 0.56/0.68 [150]~P1(x1501)+E(x1501,a37)+~E(f3(x1501),a29) % 0.56/0.68 [159]~P1(x1591)+P3(f4(x1591),x1591)+E(x1591,a37) % 0.56/0.68 [166]~P1(x1661)+~P5(x1661)+P3(f3(x1661),a41) % 0.56/0.68 [177]~P3(x1771,a41)+E(x1771,a29)+P3(f19(x1771),a41) % 0.56/0.68 [178]~P1(x1781)+P5(x1781)+~P3(f3(x1781),a41) % 0.56/0.68 [184]~P5(x1841)+~P7(x1841,a41)+P3(f5(x1841),a41) % 0.56/0.68 [164]~P3(x1641,a41)+E(x1641,a29)+E(f43(f19(x1641)),x1641) % 0.56/0.68 [198]~P5(x1981)+~P7(x1981,a41)+P7(x1981,f30(f5(x1981))) % 0.56/0.68 [167]~P7(x1671,x1672)+P1(x1671)+~P1(x1672) % 0.56/0.68 [168]~P3(x1681,x1682)+P4(x1681)+~P1(x1682) % 0.56/0.68 [165]P1(x1651)+~P3(x1652,a41)+~E(x1651,f30(x1652)) % 0.56/0.68 [199]~P4(x1992)+~P2(x1991)+P7(f32(x1991,x1992),f39(x1991)) % 0.56/0.68 [216]~P2(x2161)+~P3(x2162,f39(x2161))+P4(f31(x2161,x2162)) % 0.56/0.68 [218]~P1(x2181)+~P3(x2182,x2181)+E(f36(f35(x2181,x2182),x2182),x2181) % 0.56/0.68 [254]~P2(x2541)+~P3(x2542,f39(x2541))+P3(f31(x2541,x2542),f34(x2541,f39(x2541))) % 0.56/0.68 [244]~P2(x2441)+~P6(f39(x2441))+P4(f40(x2441))+~P5(f34(x2441,f39(x2441))) % 0.56/0.68 [263]~P2(x2631)+~P6(f39(x2631))+~P5(f34(x2631,f39(x2631)))+P6(f32(x2631,f40(x2631))) % 0.56/0.68 [267]~P3(x2671,a41)+~P7(f31(a47,x2671),a41)+~P6(f31(a47,x2671))+P6(f31(a47,f43(x2671))) % 0.56/0.68 [291]~P3(x2911,a41)+~P7(f31(a47,x2911),a41)+~P6(f31(a47,x2911))+P7(f31(a47,f43(x2911)),f35(f31(a47,x2911),f2(f31(a47,x2911)))) % 0.56/0.68 [179]~P5(x1792)+~P7(x1791,x1792)+P5(x1791)+~P1(x1792) % 0.56/0.68 [183]P3(x1832,x1831)+~E(x1832,f2(x1831))+~P7(x1831,a41)+E(x1831,a37) % 0.56/0.68 [189]~P1(x1891)+~P4(x1892)+~P5(x1891)+P5(f36(x1891,x1892)) % 0.56/0.68 [190]~P1(x1901)+~P4(x1902)+~P5(x1901)+P5(f35(x1901,x1902)) % 0.56/0.68 [191]~P1(x1911)+~P4(x1912)+~P6(x1911)+P6(f36(x1911,x1912)) % 0.56/0.68 [192]~P1(x1921)+~P4(x1922)+~P6(x1921)+P6(f35(x1921,x1922)) % 0.56/0.68 [193]~P1(x1931)+P5(x1931)+~P3(x1932,a41)+~E(f38(x1931,x1932),a37) % 0.56/0.68 [196]E(x1961,x1962)+~E(f43(x1961),f43(x1962))+~P3(x1962,a41)+~P3(x1961,a41) % 0.56/0.68 [202]~P1(x2022)+~P5(x2022)+~P7(x2021,x2022)+P9(f3(x2021),f3(x2022)) % 0.56/0.68 [205]~P1(x2051)+~P5(x2051)+~P3(x2052,a41)+P5(f38(x2051,x2052)) % 0.56/0.69 [214]~P1(x2141)+~P1(x2142)+P7(x2141,x2142)+P3(f22(x2142,x2141),x2141) % 0.56/0.69 [222]P9(x2221,x2222)+P9(f43(x2222),x2221)+~P3(x2222,a41)+~P3(x2221,a41) % 0.56/0.69 [234]~P9(x2341,x2342)+~P3(x2342,a41)+~P3(x2341,a41)+P7(f30(x2341),f30(x2342)) % 0.56/0.69 [235]~P9(x2351,x2352)+~P3(x2352,a41)+~P3(x2351,a41)+P9(f43(x2351),f43(x2352)) % 0.56/0.69 [237]~P1(x2371)+~P1(x2372)+P7(x2371,x2372)+~P3(f22(x2372,x2371),x2372) % 0.56/0.69 [239]P9(x2391,x2392)+~P3(x2392,a41)+~P3(x2391,a41)+~P7(f30(x2391),f30(x2392)) % 0.56/0.69 [240]P9(x2401,x2402)+~P3(x2402,a41)+~P3(x2401,a41)+~P9(f43(x2401),f43(x2402)) % 0.56/0.69 [258]~P9(x2582,x2581)+~P3(x2582,a41)+~P3(x2581,a41)+P7(f31(a47,x2581),f31(a47,x2582)) % 0.56/0.69 [217]P3(x2172,x2171)+~P1(x2171)+~P4(x2172)+E(f35(f36(x2171,x2172),x2172),x2171) % 0.56/0.69 [225]~E(x2251,x2252)+~P3(x2252,a41)+~P3(x2251,a41)+P3(x2251,f30(f43(x2252))) % 0.56/0.69 [246]~P3(x2462,a41)+~P3(x2461,a41)+~P3(x2461,f30(x2462))+P3(x2461,f30(f43(x2462))) % 0.56/0.69 [262]E(x2621,x2622)+~P3(x2622,a41)+~P3(x2621,a41)+~E(f2(f31(a47,x2621)),f2(f31(a47,x2622))) % 0.56/0.69 [265]~P1(x2652)+~P3(x2651,a41)+E(f31(f31(a45,x2651),x2652),f16(x2651))+~P3(x2652,f38(f15(x2651),a50)) % 0.56/0.69 [245]~P1(x2451)+~P5(x2451)+~P3(x2452,x2451)+E(f43(f3(f35(x2451,x2452))),f3(x2451)) % 0.56/0.69 [275]~P1(x2752)+~P3(x2751,a41)+E(f31(f31(a45,x2751),x2752),f20(x2751))+~P3(x2752,f38(f31(a47,f43(x2751)),a50)) % 0.56/0.69 [277]~P1(x2772)+~P3(x2771,a41)+E(f31(f31(a45,x2771),x2772),f31(a52,x2771))+~P3(x2772,f38(f31(a47,f43(x2771)),a50)) % 0.56/0.69 [305]~P1(x3051)+~P3(x3052,a41)+P3(f36(x3051,f2(f31(a47,x3052))),f38(a54,a44))+~P3(x3051,f38(f35(f31(a47,x3052),f2(f31(a47,x3052))),a50)) % 0.56/0.69 [306]~P1(x3061)+~P3(x3062,a41)+~P3(x3061,f38(f35(f31(a47,x3062),f2(f31(a47,x3062))),a50))+E(f31(a55,f36(x3061,f2(f31(a47,x3062)))),f31(f31(a45,x3062),x3061)) % 0.56/0.69 [209]~P1(x2092)+~P7(x2093,x2092)+P3(x2091,x2092)+~P3(x2091,x2093) % 0.56/0.69 [180]~P1(x1802)+~P4(x1803)+P1(x1801)+~E(x1801,f36(x1802,x1803)) % 0.56/0.69 [181]~P1(x1812)+~P4(x1813)+P1(x1811)+~E(x1811,f35(x1812,x1813)) % 0.56/0.69 [182]~P4(x1823)+~P2(x1822)+P1(x1821)+~E(x1821,f32(x1822,x1823)) % 0.56/0.69 [194]~P1(x1942)+P1(x1941)+~P3(x1943,a41)+~E(x1941,f38(x1942,x1943)) % 0.56/0.69 [203]~P3(x2031,x2032)+~P3(x2033,a41)+P3(x2031,a41)+~E(x2032,f30(x2033)) % 0.56/0.69 [211]~P2(x2112)+P1(x2111)+~P7(x2113,f39(x2112))+~E(x2111,f34(x2112,x2113)) % 0.56/0.69 [212]~P2(x2122)+P2(x2121)+~P7(x2123,f39(x2122))+~E(x2121,f33(x2122,x2123)) % 0.56/0.69 [213]~P2(x2133)+~P7(x2132,f39(x2133))+E(f39(x2131),x2132)+~E(x2131,f33(x2133,x2132)) % 0.56/0.69 [219]~P3(x2191,x2193)+~P3(x2192,a41)+P9(f43(x2191),x2192)+~E(x2193,f30(x2192)) % 0.56/0.69 [200]~P1(x2002)+~P1(x2001)+~P7(x2002,x2001)+~P7(x2001,x2002)+E(x2001,x2002) % 0.56/0.69 [232]~P9(x2322,x2321)+~P9(x2321,x2322)+E(x2321,x2322)+~P3(x2322,a41)+~P3(x2321,a41) % 0.56/0.69 [188]~P5(x1881)+P3(x1882,x1881)+~E(x1882,f42(x1881))+~P7(x1881,a41)+E(x1881,a37) % 0.56/0.69 [208]~P1(x2082)+~P6(x2082)+~P3(x2081,a41)+E(x2081,a29)+P6(f38(x2082,x2081)) % 0.56/0.69 [236]~P3(x2362,x2361)+P3(f25(x2361,x2362),x2361)+~P7(x2361,a41)+E(x2361,a37)+E(x2362,f2(x2361)) % 0.56/0.69 [247]~P1(x2471)+~P5(x2471)+~P3(x2472,a41)+~P9(x2472,f3(x2471))+P7(f26(x2471,x2472),x2471) % 0.56/0.69 [249]~P1(x2491)+P3(f28(x2492,x2491),x2491)+~P3(x2492,a41)+E(x2491,f30(x2492))+P3(f28(x2492,x2491),a41) % 0.56/0.69 [250]~P3(x2502,x2501)+~P7(x2501,a41)+~P9(x2502,f25(x2501,x2502))+E(x2501,a37)+E(x2502,f2(x2501)) % 0.56/0.69 [257]~P6(x2572)+~P2(x2571)+~E(f6(x2571,x2572),f7(x2571,x2572))+~P7(x2572,f39(x2571))+P6(f34(x2571,x2572)) % 0.56/0.69 [259]~P6(x2592)+~P2(x2591)+P3(f7(x2591,x2592),f39(x2591))+~P7(x2592,f39(x2591))+P6(f34(x2591,x2592)) % 0.56/0.69 [260]~P6(x2602)+~P2(x2601)+P3(f6(x2601,x2602),f39(x2601))+~P7(x2602,f39(x2601))+P6(f34(x2601,x2602)) % 0.56/0.69 [224]P3(x2242,x2241)+~P1(x2241)+~P4(x2242)+~P5(x2241)+E(f3(f36(x2241,x2242)),f43(f3(x2241))) % 0.56/0.69 [243]~P1(x2431)+~P5(x2431)+~P3(x2432,a41)+~P9(x2432,f3(x2431))+E(f3(f26(x2431,x2432)),x2432) % 0.56/0.69 [252]E(x2521,x2522)+P3(x2521,f30(x2522))+~P3(x2522,a41)+~P3(x2521,a41)+~P3(x2521,f30(f43(x2522))) % 0.56/0.69 [264]~P1(x2641)+P3(f28(x2642,x2641),x2641)+~P3(x2642,a41)+E(x2641,f30(x2642))+P9(f43(f28(x2642,x2641)),x2642) % 0.56/0.69 [266]~P6(x2662)+~P2(x2661)+~P7(x2662,f39(x2661))+P6(f34(x2661,x2662))+E(f31(x2661,f6(x2661,x2662)),f31(x2661,f7(x2661,x2662))) % 0.56/0.69 [210]~P3(x2103,x2101)+P9(x2102,x2103)+~E(x2102,f2(x2101))+~P7(x2101,a41)+E(x2101,a37) % 0.56/0.69 [238]P3(x2381,x2382)+~P3(x2383,a41)+~P3(x2381,a41)+~P9(f43(x2381),x2383)+~E(x2382,f30(x2383)) % 0.56/0.69 [271]~P1(x2711)+~P5(x2713)+~P3(x2712,a41)+~P7(x2713,f38(x2711,x2712))+P5(f9(x2711,x2712,x2713)) % 0.56/0.69 [273]~P1(x2731)+~P5(x2733)+~P3(x2732,a41)+~P7(x2733,f38(x2731,x2732))+P7(f9(x2731,x2732,x2733),x2731) % 0.56/0.69 [292]~P1(x2922)+~P5(x2921)+~P3(x2923,a41)+~P7(x2921,f38(x2922,x2923))+P7(x2921,f38(f9(x2922,x2923,x2921),x2923)) % 0.56/0.69 [204]~P1(x2044)+~P4(x2042)+~P3(x2041,x2043)+~E(x2041,x2042)+~E(x2043,f35(x2044,x2042)) % 0.56/0.69 [206]~P1(x2063)+~P4(x2064)+~P3(x2061,x2062)+P4(x2061)+~E(x2062,f36(x2063,x2064)) % 0.56/0.69 [207]~P1(x2073)+~P4(x2074)+~P3(x2071,x2072)+P4(x2071)+~E(x2072,f35(x2073,x2074)) % 0.56/0.69 [221]~P1(x2212)+~P4(x2214)+~P3(x2211,x2213)+P3(x2211,x2212)+~E(x2213,f35(x2212,x2214)) % 0.56/0.69 [223]~P4(x2233)+~P2(x2231)+~P3(x2232,x2234)+E(f31(x2231,x2232),x2233)+~E(x2234,f32(x2231,x2233)) % 0.56/0.69 [227]~P1(x2274)+~P3(x2271,x2273)+~P3(x2272,a41)+E(f3(x2271),x2272)+~E(x2273,f38(x2274,x2272)) % 0.56/0.69 [229]~P4(x2294)+~P2(x2292)+~P3(x2291,x2293)+P3(x2291,f39(x2292))+~E(x2293,f32(x2292,x2294)) % 0.56/0.69 [233]~P1(x2332)+~P3(x2331,x2333)+P7(x2331,x2332)+~P3(x2334,a41)+~E(x2333,f38(x2332,x2334)) % 0.56/0.69 [251]~P2(x2513)+~P3(x2512,x2514)+~P7(x2514,f39(x2513))+E(f31(x2511,x2512),f31(x2513,x2512))+~E(x2511,f33(x2513,x2514)) % 0.56/0.69 [298]~P2(x2981)+~P3(x2984,x2983)+~E(x2983,f34(x2981,x2982))+~P7(x2982,f39(x2981))+P3(f13(x2981,x2982,x2983,x2984),x2982) % 0.56/0.69 [299]~P2(x2991)+~P3(x2994,x2993)+~E(x2993,f34(x2991,x2992))+~P7(x2992,f39(x2991))+E(f31(x2991,f13(x2991,x2992,x2993,x2994)),x2994) % 0.56/0.69 [242]~P5(x2421)+~P3(x2422,x2421)+P3(f27(x2421,x2422),x2421)+~P7(x2421,a41)+E(x2421,a37)+E(x2422,f42(x2421)) % 0.56/0.69 [255]~P5(x2551)+~P3(x2552,x2551)+~P7(x2551,a41)+~P9(f27(x2551,x2552),x2552)+E(x2551,a37)+E(x2552,f42(x2551)) % 0.56/0.69 [280]~P1(x2801)+~P3(x2802,a41)+~P3(f28(x2802,x2801),x2801)+E(x2801,f30(x2802))+~P3(f28(x2802,x2801),a41)+~P9(f43(f28(x2802,x2801)),x2802) % 0.56/0.69 [228]~P1(x2282)+~P1(x2281)+~P7(x2283,x2282)+~P7(x2281,x2283)+P7(x2281,x2282)+~P1(x2283) % 0.56/0.69 [256]~P9(x2561,x2563)+P9(x2561,x2562)+~P9(x2563,x2562)+~P3(x2562,a41)+~P3(x2563,a41)+~P3(x2561,a41) % 0.56/0.69 [220]~P5(x2201)+~P3(x2202,x2201)+P9(x2202,x2203)+~E(x2203,f42(x2201))+~P7(x2201,a41)+E(x2201,a37) % 0.56/0.69 [269]~P2(x2691)+~P2(x2692)+P3(f8(x2692,x2693,x2691),x2693)+~E(f39(x2691),x2693)+~P7(x2693,f39(x2692))+E(x2691,f33(x2692,x2693)) % 0.56/0.69 [276]~P1(x2761)+~P1(x2762)+~P4(x2763)+P3(f23(x2762,x2763,x2761),x2761)+~E(f23(x2762,x2763,x2761),x2763)+E(x2761,f35(x2762,x2763)) % 0.56/0.69 [278]~P1(x2781)+~P1(x2782)+~P4(x2783)+P3(f24(x2782,x2783,x2781),x2781)+E(x2781,f36(x2782,x2783))+P4(f24(x2782,x2783,x2781)) % 0.56/0.69 [279]~P1(x2791)+~P1(x2792)+~P4(x2793)+P3(f23(x2792,x2793,x2791),x2791)+E(x2791,f35(x2792,x2793))+P4(f23(x2792,x2793,x2791)) % 0.56/0.69 [281]~P1(x2811)+~P1(x2812)+~P4(x2813)+P3(f23(x2812,x2813,x2811),x2811)+P3(f23(x2812,x2813,x2811),x2812)+E(x2811,f35(x2812,x2813)) % 0.56/0.69 [284]~P1(x2841)+~P4(x2843)+~P2(x2842)+P3(f11(x2842,x2843,x2841),x2841)+P3(f11(x2842,x2843,x2841),f39(x2842))+E(x2841,f32(x2842,x2843)) % 0.56/0.69 [285]~P1(x2851)+~P1(x2852)+P3(f10(x2852,x2853,x2851),x2851)+P7(f10(x2852,x2853,x2851),x2852)+~P3(x2853,a41)+E(x2851,f38(x2852,x2853)) % 0.56/0.69 [288]~P1(x2881)+~P2(x2882)+P3(f12(x2882,x2883,x2881),x2881)+P3(f14(x2882,x2883,x2881),x2883)+~P7(x2883,f39(x2882))+E(x2881,f34(x2882,x2883)) % 0.56/0.69 [282]~P1(x2821)+~P4(x2823)+~P2(x2822)+P3(f11(x2822,x2823,x2821),x2821)+E(x2821,f32(x2822,x2823))+E(f31(x2822,f11(x2822,x2823,x2821)),x2823) % 0.56/0.69 [283]~P1(x2831)+~P1(x2832)+P3(f10(x2832,x2833,x2831),x2831)+~P3(x2833,a41)+E(x2831,f38(x2832,x2833))+E(f3(f10(x2832,x2833,x2831)),x2833) % 0.56/0.69 [293]~P1(x2931)+~P2(x2932)+P3(f12(x2932,x2933,x2931),x2931)+~P7(x2933,f39(x2932))+E(x2931,f34(x2932,x2933))+E(f31(x2932,f14(x2932,x2933,x2931)),f12(x2932,x2933,x2931)) % 0.56/0.69 [295]~P2(x2952)+~P2(x2951)+~E(f39(x2951),x2953)+~P7(x2953,f39(x2952))+E(x2951,f33(x2952,x2953))+~E(f31(x2951,f8(x2952,x2953,x2951)),f31(x2952,f8(x2952,x2953,x2951))) % 0.56/0.69 [304]~P1(x3041)+~P6(x3043)+~P3(x3042,a41)+~P3(x3041,f38(x3043,a50))+~P7(x3043,f35(f31(a47,x3042),f2(f31(a47,x3042))))+P3(x3041,f38(f35(f31(a47,x3042),f2(f31(a47,x3042))),a50)) % 0.56/0.69 [201]~P1(x2014)+~P4(x2013)+~P4(x2011)+P3(x2011,x2012)+~E(x2011,x2013)+~E(x2012,f36(x2014,x2013)) % 0.56/0.69 [226]~P1(x2263)+~P4(x2262)+~P3(x2261,x2264)+E(x2261,x2262)+P3(x2261,x2263)+~E(x2264,f36(x2263,x2262)) % 0.56/0.69 [230]~P1(x2303)+~P4(x2304)+~P4(x2301)+~P3(x2301,x2303)+P3(x2301,x2302)+~E(x2302,f36(x2303,x2304)) % 0.56/0.69 [241]~P1(x2414)+~P7(x2411,x2414)+P3(x2411,x2412)+~P3(x2413,a41)+~E(x2412,f38(x2414,x2413))+~E(f3(x2411),x2413) % 0.56/0.69 [248]~P4(x2484)+~P2(x2483)+P3(x2481,x2482)+~E(f31(x2483,x2481),x2484)+~P3(x2481,f39(x2483))+~E(x2482,f32(x2483,x2484)) % 0.56/0.69 [261]~P2(x2613)+~P3(x2615,x2614)+P3(x2611,x2612)+~P7(x2614,f39(x2613))+~E(x2612,f34(x2613,x2614))+~E(f31(x2613,x2615),x2611) % 0.56/0.69 [253]E(f2(x2532),f2(x2531))+~P7(x2531,a41)+~P7(x2532,a41)+~P3(f2(x2531),x2532)+~P3(f2(x2532),x2531)+E(x2531,a37)+E(x2532,a37) % 0.56/0.69 [268]~P1(x2683)+~P1(x2682)+P7(x2682,x2683)+~P3(x2681,a41)+~P7(f38(x2682,x2681),f38(x2683,x2681))+E(x2681,a29)+E(f38(x2682,x2681),a37) % 0.56/0.69 [290]~P1(x2901)+~P1(x2902)+~P4(x2903)+E(f24(x2902,x2903,x2901),x2903)+P3(f24(x2902,x2903,x2901),x2901)+P3(f24(x2902,x2903,x2901),x2902)+E(x2901,f36(x2902,x2903)) % 0.56/0.69 [296]~P1(x2961)+~P1(x2962)+~P4(x2963)+~E(f24(x2962,x2963,x2961),x2963)+~P3(f24(x2962,x2963,x2961),x2961)+E(x2961,f36(x2962,x2963))+~P4(f24(x2962,x2963,x2961)) % 0.56/0.69 [297]~P1(x2971)+~P1(x2972)+~P4(x2973)+~P3(f24(x2972,x2973,x2971),x2971)+~P3(f24(x2972,x2973,x2971),x2972)+E(x2971,f36(x2972,x2973))+~P4(f24(x2972,x2973,x2971)) % 0.56/0.69 [300]~P1(x3001)+~P1(x3002)+~P3(x3003,a41)+~P3(f10(x3002,x3003,x3001),x3001)+~P7(f10(x3002,x3003,x3001),x3002)+E(x3001,f38(x3002,x3003))+~E(f3(f10(x3002,x3003,x3001)),x3003) % 0.56/0.69 [301]~P1(x3011)+~P4(x3013)+~P2(x3012)+~P3(f11(x3012,x3013,x3011),x3011)+~P3(f11(x3012,x3013,x3011),f39(x3012))+E(x3011,f32(x3012,x3013))+~E(f31(x3012,f11(x3012,x3013,x3011)),x3013) % 0.56/0.69 [231]~P1(x2314)+~P4(x2312)+~P4(x2311)+~P3(x2311,x2314)+E(x2311,x2312)+P3(x2311,x2313)+~E(x2313,f35(x2314,x2312)) % 0.56/0.69 [294]~P1(x2941)+~P2(x2942)+~P3(x2944,x2943)+~P7(x2943,f39(x2942))+~P3(f12(x2942,x2943,x2941),x2941)+~E(f31(x2942,x2944),f12(x2942,x2943,x2941))+E(x2941,f34(x2942,x2943)) % 0.56/0.69 [302]~P1(x3021)+~P1(x3022)+~P4(x3023)+E(f23(x3022,x3023,x3021),x3023)+~P3(f23(x3022,x3023,x3021),x3021)+~P3(f23(x3022,x3023,x3021),x3022)+E(x3021,f35(x3022,x3023))+~P4(f23(x3022,x3023,x3021)) % 0.56/0.69 [286]~P6(x2862)+~P2(x2863)+~E(f39(x2863),f38(x2862,x2861))+~P3(x2861,a41)+~P7(x2862,a41)+~P8(x2861,a44)+P6(f17(x2861,x2862,x2863))+~P7(f34(x2863,f39(x2863)),a53) % 0.56/0.69 [287]~P6(x2872)+~P2(x2873)+~E(f39(x2873),f38(x2872,x2871))+~P3(x2871,a41)+~P7(x2872,a41)+~P8(x2871,a44)+P3(f18(x2871,x2872,x2873),a53)+~P7(f34(x2873,f39(x2873)),a53) % 0.56/0.69 [289]~P6(x2892)+~P2(x2893)+~E(f39(x2893),f38(x2892,x2891))+~P3(x2891,a41)+~P7(x2892,a41)+~P8(x2891,a44)+P7(f17(x2891,x2892,x2893),x2892)+~P7(f34(x2893,f39(x2893)),a53) % 0.56/0.69 [303]~P6(x3034)+~P2(x3031)+~E(f39(x3031),f38(x3034,x3033))+~P3(x3033,a41)+~P7(x3034,a41)+~P8(x3033,a44)+E(f31(x3031,x3032),f18(x3033,x3034,x3031))+~P3(x3032,f38(f17(x3033,x3034,x3031),x3033))+~P7(f34(x3031,f39(x3031)),a53) % 0.56/0.69 %EqnAxiom % 0.56/0.69 [1]E(x11,x11) % 0.56/0.69 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.69 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.56/0.69 [5]~E(x51,x52)+E(f43(x51),f43(x52)) % 0.56/0.69 [6]~E(x61,x62)+E(f3(x61),f3(x62)) % 0.56/0.69 [7]~E(x71,x72)+E(f30(x71),f30(x72)) % 0.56/0.69 [8]~E(x81,x82)+E(f39(x81),f39(x82)) % 0.56/0.69 [9]~E(x91,x92)+E(f38(x91,x93),f38(x92,x93)) % 0.56/0.69 [10]~E(x101,x102)+E(f38(x103,x101),f38(x103,x102)) % 0.56/0.69 [11]~E(x111,x112)+E(f35(x111,x113),f35(x112,x113)) % 0.56/0.69 [12]~E(x121,x122)+E(f35(x123,x121),f35(x123,x122)) % 0.56/0.69 [13]~E(x131,x132)+E(f9(x131,x133,x134),f9(x132,x133,x134)) % 0.56/0.69 [14]~E(x141,x142)+E(f9(x143,x141,x144),f9(x143,x142,x144)) % 0.56/0.69 [15]~E(x151,x152)+E(f9(x153,x154,x151),f9(x153,x154,x152)) % 0.56/0.69 [16]~E(x161,x162)+E(f31(x161,x163),f31(x162,x163)) % 0.56/0.69 [17]~E(x171,x172)+E(f31(x173,x171),f31(x173,x172)) % 0.56/0.69 [18]~E(x181,x182)+E(f11(x181,x183,x184),f11(x182,x183,x184)) % 0.56/0.69 [19]~E(x191,x192)+E(f11(x193,x191,x194),f11(x193,x192,x194)) % 0.56/0.69 [20]~E(x201,x202)+E(f11(x203,x204,x201),f11(x203,x204,x202)) % 0.56/0.69 [21]~E(x211,x212)+E(f34(x211,x213),f34(x212,x213)) % 0.56/0.69 [22]~E(x221,x222)+E(f34(x223,x221),f34(x223,x222)) % 0.56/0.69 [23]~E(x231,x232)+E(f33(x231,x233),f33(x232,x233)) % 0.56/0.69 [24]~E(x241,x242)+E(f33(x243,x241),f33(x243,x242)) % 0.56/0.69 [25]~E(x251,x252)+E(f7(x251,x253),f7(x252,x253)) % 0.56/0.69 [26]~E(x261,x262)+E(f7(x263,x261),f7(x263,x262)) % 0.56/0.69 [27]~E(x271,x272)+E(f40(x271),f40(x272)) % 0.56/0.69 [28]~E(x281,x282)+E(f28(x281,x283),f28(x282,x283)) % 0.56/0.69 [29]~E(x291,x292)+E(f28(x293,x291),f28(x293,x292)) % 0.56/0.69 [30]~E(x301,x302)+E(f6(x301,x303),f6(x302,x303)) % 0.56/0.69 [31]~E(x311,x312)+E(f6(x313,x311),f6(x313,x312)) % 0.56/0.69 [32]~E(x321,x322)+E(f15(x321),f15(x322)) % 0.56/0.69 [33]~E(x331,x332)+E(f36(x331,x333),f36(x332,x333)) % 0.56/0.69 [34]~E(x341,x342)+E(f36(x343,x341),f36(x343,x342)) % 0.56/0.69 [35]~E(x351,x352)+E(f16(x351),f16(x352)) % 0.56/0.69 [36]~E(x361,x362)+E(f18(x361,x363,x364),f18(x362,x363,x364)) % 0.56/0.69 [37]~E(x371,x372)+E(f18(x373,x371,x374),f18(x373,x372,x374)) % 0.56/0.69 [38]~E(x381,x382)+E(f18(x383,x384,x381),f18(x383,x384,x382)) % 0.56/0.69 [39]~E(x391,x392)+E(f17(x391,x393,x394),f17(x392,x393,x394)) % 0.56/0.69 [40]~E(x401,x402)+E(f17(x403,x401,x404),f17(x403,x402,x404)) % 0.56/0.69 [41]~E(x411,x412)+E(f17(x413,x414,x411),f17(x413,x414,x412)) % 0.56/0.69 [42]~E(x421,x422)+E(f25(x421,x423),f25(x422,x423)) % 0.56/0.69 [43]~E(x431,x432)+E(f25(x433,x431),f25(x433,x432)) % 0.56/0.69 [44]~E(x441,x442)+E(f32(x441,x443),f32(x442,x443)) % 0.56/0.69 [45]~E(x451,x452)+E(f32(x453,x451),f32(x453,x452)) % 0.56/0.69 [46]~E(x461,x462)+E(f10(x461,x463,x464),f10(x462,x463,x464)) % 0.56/0.69 [47]~E(x471,x472)+E(f10(x473,x471,x474),f10(x473,x472,x474)) % 0.56/0.69 [48]~E(x481,x482)+E(f10(x483,x484,x481),f10(x483,x484,x482)) % 0.56/0.69 [49]~E(x491,x492)+E(f12(x491,x493,x494),f12(x492,x493,x494)) % 0.56/0.69 [50]~E(x501,x502)+E(f12(x503,x501,x504),f12(x503,x502,x504)) % 0.56/0.69 [51]~E(x511,x512)+E(f12(x513,x514,x511),f12(x513,x514,x512)) % 0.56/0.69 [52]~E(x521,x522)+E(f24(x521,x523,x524),f24(x522,x523,x524)) % 0.56/0.69 [53]~E(x531,x532)+E(f24(x533,x531,x534),f24(x533,x532,x534)) % 0.56/0.69 [54]~E(x541,x542)+E(f24(x543,x544,x541),f24(x543,x544,x542)) % 0.56/0.69 [55]~E(x551,x552)+E(f23(x551,x553,x554),f23(x552,x553,x554)) % 0.56/0.69 [56]~E(x561,x562)+E(f23(x563,x561,x564),f23(x563,x562,x564)) % 0.56/0.69 [57]~E(x571,x572)+E(f23(x573,x574,x571),f23(x573,x574,x572)) % 0.56/0.69 [58]~E(x581,x582)+E(f8(x581,x583,x584),f8(x582,x583,x584)) % 0.56/0.69 [59]~E(x591,x592)+E(f8(x593,x591,x594),f8(x593,x592,x594)) % 0.56/0.69 [60]~E(x601,x602)+E(f8(x603,x604,x601),f8(x603,x604,x602)) % 0.56/0.69 [61]~E(x611,x612)+E(f42(x611),f42(x612)) % 0.56/0.69 [62]~E(x621,x622)+E(f5(x621),f5(x622)) % 0.56/0.69 [63]~E(x631,x632)+E(f26(x631,x633),f26(x632,x633)) % 0.56/0.69 [64]~E(x641,x642)+E(f26(x643,x641),f26(x643,x642)) % 0.56/0.69 [65]~E(x651,x652)+E(f14(x651,x653,x654),f14(x652,x653,x654)) % 0.56/0.69 [66]~E(x661,x662)+E(f14(x663,x661,x664),f14(x663,x662,x664)) % 0.56/0.69 [67]~E(x671,x672)+E(f14(x673,x674,x671),f14(x673,x674,x672)) % 0.56/0.69 [68]~E(x681,x682)+E(f13(x681,x683,x684,x685),f13(x682,x683,x684,x685)) % 0.56/0.69 [69]~E(x691,x692)+E(f13(x693,x691,x694,x695),f13(x693,x692,x694,x695)) % 0.56/0.69 [70]~E(x701,x702)+E(f13(x703,x704,x701,x705),f13(x703,x704,x702,x705)) % 0.56/0.69 [71]~E(x711,x712)+E(f13(x713,x714,x715,x711),f13(x713,x714,x715,x712)) % 0.56/0.69 [72]~E(x721,x722)+E(f21(x721),f21(x722)) % 0.56/0.69 [73]~E(x731,x732)+E(f27(x731,x733),f27(x732,x733)) % 0.56/0.69 [74]~E(x741,x742)+E(f27(x743,x741),f27(x743,x742)) % 0.56/0.69 [75]~E(x751,x752)+E(f19(x751),f19(x752)) % 0.56/0.69 [76]~E(x761,x762)+E(f22(x761,x763),f22(x762,x763)) % 0.56/0.69 [77]~E(x771,x772)+E(f22(x773,x771),f22(x773,x772)) % 0.56/0.69 [78]~E(x781,x782)+E(f20(x781),f20(x782)) % 0.56/0.69 [79]~E(x791,x792)+E(f4(x791),f4(x792)) % 0.56/0.69 [80]~P1(x801)+P1(x802)+~E(x801,x802) % 0.56/0.69 [81]P3(x812,x813)+~E(x811,x812)+~P3(x811,x813) % 0.56/0.69 [82]P3(x823,x822)+~E(x821,x822)+~P3(x823,x821) % 0.56/0.69 [83]~P6(x831)+P6(x832)+~E(x831,x832) % 0.56/0.69 [84]P7(x842,x843)+~E(x841,x842)+~P7(x841,x843) % 0.56/0.69 [85]P7(x853,x852)+~E(x851,x852)+~P7(x853,x851) % 0.56/0.69 [86]~P2(x861)+P2(x862)+~E(x861,x862) % 0.56/0.69 [87]~P5(x871)+P5(x872)+~E(x871,x872) % 0.56/0.69 [88]~P4(x881)+P4(x882)+~E(x881,x882) % 0.56/0.69 [89]P9(x892,x893)+~E(x891,x892)+~P9(x891,x893) % 0.56/0.69 [90]P9(x903,x902)+~E(x901,x902)+~P9(x903,x901) % 0.56/0.69 [91]P8(x912,x913)+~E(x911,x912)+~P8(x911,x913) % 0.56/0.69 [92]P8(x923,x922)+~E(x921,x922)+~P8(x923,x921) % 0.56/0.69 % 0.56/0.69 %------------------------------------------- % 0.56/0.69 cnf(311,plain, % 0.56/0.69 (P1(f30(x3111))+~P3(x3111,a41)), % 0.56/0.69 inference(equality_inference,[],[165])). % 0.56/0.69 cnf(354,plain, % 0.56/0.69 ($false), % 0.56/0.69 inference(scs_inference,[],[147,135,118,119,131,96,2,148,156,311,169,3]), % 0.56/0.69 ['proof']). % 0.56/0.69 % SZS output end Proof % 0.56/0.69 % Total time :0.020000s %------------------------------------------------------------------------------