%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM548+1 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 12:24:57 EDT 2024 % Result : Theorem 8.29s 8.43s % Output : CNFRefutation 8.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : NUM548+1 : TPTP v8.2.0. Released v4.0.0. % 0.00/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 300 % 0.09/0.28 % DateTime : Sat Jun 22 21:36:53 EDT 2024 % 0.09/0.28 % CPUTime : % 0.14/0.46 start to proof:theBenchmark % 8.29/8.41 %------------------------------------------- % 8.29/8.41 % File :CSE---1.7 % 8.29/8.41 % Problem :theBenchmark % 8.29/8.41 % Transform :cnf % 8.29/8.41 % Format :tptp:raw % 8.29/8.41 % Command :java -jar mcs_scs.jar %d %s % 8.29/8.41 % 8.29/8.41 % Result :Theorem 7.890000s % 8.29/8.41 % Output :CNFRefutation 7.890000s % 8.29/8.41 %------------------------------------------- % 8.29/8.41 %------------------------------------------------------------------------------ % 8.29/8.41 % File : NUM548+1 : TPTP v8.2.0. Released v4.0.0. % 8.29/8.41 % Domain : Number Theory % 8.29/8.41 % Problem : Ramsey's Infinite Theorem 12_02, 00 expansion % 8.29/8.41 % Version : Especial. % 8.29/8.41 % English : % 8.29/8.41 % 8.29/8.41 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 8.29/8.41 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 8.29/8.41 % Source : [Pas08] % 8.29/8.41 % Names : ramsey_12_02.00 [Pas08] % 8.29/8.42 % 8.29/8.42 % Status : Theorem % 8.29/8.42 % Rating : 0.33 v8.1.0, 0.31 v7.4.0, 0.27 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.26 v7.0.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.29 v6.2.0, 0.40 v6.1.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0, 0.40 v5.1.0, 0.57 v5.0.0, 0.58 v4.1.0, 0.70 v4.0.1, 0.83 v4.0.0 % 8.29/8.42 % Syntax : Number of formulae : 66 ( 7 unt; 8 def) % 8.29/8.42 % Number of atoms : 237 ( 38 equ) % 8.29/8.42 % Maximal formula atoms : 8 ( 3 avg) % 8.29/8.42 % Number of connectives : 189 ( 18 ~; 4 |; 66 &) % 8.29/8.42 % ( 17 <=>; 84 =>; 0 <=; 0 <~>) % 8.29/8.42 % Maximal formula depth : 12 ( 5 avg) % 8.29/8.42 % Maximal term depth : 4 ( 1 avg) % 8.29/8.42 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 8.29/8.42 % Number of functors : 16 ( 16 usr; 8 con; 0-2 aty) % 8.29/8.42 % Number of variables : 106 ( 102 !; 4 ?) % 8.29/8.42 % SPC : FOF_THM_RFO_SEQ % 8.29/8.42 % 8.29/8.42 % Comments : Problem generated by the SAD system [VLP07] % 8.29/8.42 %------------------------------------------------------------------------------ % 8.29/8.42 fof(mSetSort,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => $true ) ). % 8.29/8.42 % 8.29/8.42 fof(mElmSort,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElement0(W0) % 8.29/8.42 => $true ) ). % 8.29/8.42 % 8.29/8.42 fof(mEOfElem,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( aElementOf0(W1,W0) % 8.29/8.42 => aElement0(W1) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mFinRel,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => ( isFinite0(W0) % 8.29/8.42 => $true ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mDefEmp,definition, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( W0 = slcrc0 % 8.29/8.42 <=> ( aSet0(W0) % 8.29/8.42 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mEmpFin,axiom, % 8.29/8.42 isFinite0(slcrc0) ). % 8.29/8.42 % 8.29/8.42 fof(mCntRel,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => ( isCountable0(W0) % 8.29/8.42 => $true ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mCountNFin,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & isCountable0(W0) ) % 8.29/8.42 => ~ isFinite0(W0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mCountNFin_01,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & isCountable0(W0) ) % 8.29/8.42 => W0 != slcrc0 ) ). % 8.29/8.42 % 8.29/8.42 fof(mDefSub,definition, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( aSubsetOf0(W1,W0) % 8.29/8.42 <=> ( aSet0(W1) % 8.29/8.42 & ! [W2] : % 8.29/8.42 ( aElementOf0(W2,W1) % 8.29/8.42 => aElementOf0(W2,W0) ) ) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSubFSet,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & isFinite0(W0) ) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( aSubsetOf0(W1,W0) % 8.29/8.42 => isFinite0(W1) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSubRefl,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => aSubsetOf0(W0,W0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSubASymm,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & aSet0(W1) ) % 8.29/8.42 => ( ( aSubsetOf0(W0,W1) % 8.29/8.42 & aSubsetOf0(W1,W0) ) % 8.29/8.42 => W0 = W1 ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSubTrans,axiom, % 8.29/8.42 ! [W0,W1,W2] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & aSet0(W1) % 8.29/8.42 & aSet0(W2) ) % 8.29/8.42 => ( ( aSubsetOf0(W0,W1) % 8.29/8.42 & aSubsetOf0(W1,W2) ) % 8.29/8.42 => aSubsetOf0(W0,W2) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mDefCons,definition, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & aElement0(W1) ) % 8.29/8.42 => ! [W2] : % 8.29/8.42 ( W2 = sdtpldt0(W0,W1) % 8.29/8.42 <=> ( aSet0(W2) % 8.29/8.42 & ! [W3] : % 8.29/8.42 ( aElementOf0(W3,W2) % 8.29/8.42 <=> ( aElement0(W3) % 8.29/8.42 & ( aElementOf0(W3,W0) % 8.29/8.42 | W3 = W1 ) ) ) ) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mDefDiff,definition, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aSet0(W0) % 8.29/8.42 & aElement0(W1) ) % 8.29/8.42 => ! [W2] : % 8.29/8.42 ( W2 = sdtmndt0(W0,W1) % 8.29/8.42 <=> ( aSet0(W2) % 8.29/8.42 & ! [W3] : % 8.29/8.42 ( aElementOf0(W3,W2) % 8.29/8.42 <=> ( aElement0(W3) % 8.29/8.42 & aElementOf0(W3,W0) % 8.29/8.42 & W3 != W1 ) ) ) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mConsDiff,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aSet0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( aElementOf0(W1,W0) % 8.29/8.42 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mDiffCons,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aElement0(W0) % 8.29/8.42 & aSet0(W1) ) % 8.29/8.42 => ( ~ aElementOf0(W0,W1) % 8.29/8.42 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mCConsSet,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElement0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( ( aSet0(W1) % 8.29/8.42 & isCountable0(W1) ) % 8.29/8.42 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mCDiffSet,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElement0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( ( aSet0(W1) % 8.29/8.42 & isCountable0(W1) ) % 8.29/8.42 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mFConsSet,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElement0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( ( aSet0(W1) % 8.29/8.42 & isFinite0(W1) ) % 8.29/8.42 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mFDiffSet,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElement0(W0) % 8.29/8.42 => ! [W1] : % 8.29/8.42 ( ( aSet0(W1) % 8.29/8.42 & isFinite0(W1) ) % 8.29/8.42 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mNATSet,axiom, % 8.29/8.42 ( aSet0(szNzAzT0) % 8.29/8.42 & isCountable0(szNzAzT0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mZeroNum,axiom, % 8.29/8.42 aElementOf0(sz00,szNzAzT0) ). % 8.29/8.42 % 8.29/8.42 fof(mSuccNum,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 8.29/8.42 & szszuzczcdt0(W0) != sz00 ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSuccEquSucc,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.42 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 8.29/8.42 => W0 = W1 ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mNatExtra,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => ( W0 = sz00 % 8.29/8.42 | ? [W1] : % 8.29/8.42 ( aElementOf0(W1,szNzAzT0) % 8.29/8.42 & W0 = szszuzczcdt0(W1) ) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mNatNSucc,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => W0 != szszuzczcdt0(W0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mLessRel,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.42 => ( sdtlseqdt0(W0,W1) % 8.29/8.42 => $true ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mZeroLess,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => sdtlseqdt0(sz00,W0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mNoScLessZr,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 8.29/8.42 % 8.29/8.42 fof(mSuccLess,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.42 => ( sdtlseqdt0(W0,W1) % 8.29/8.42 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 8.29/8.42 % 8.29/8.42 fof(mLessSucc,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 8.29/8.42 % 8.29/8.42 fof(mLessRefl,axiom, % 8.29/8.42 ! [W0] : % 8.29/8.42 ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 => sdtlseqdt0(W0,W0) ) ). % 8.29/8.42 % 8.29/8.42 fof(mLessASymm,axiom, % 8.29/8.42 ! [W0,W1] : % 8.29/8.42 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.42 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.42 => ( ( sdtlseqdt0(W0,W1) % 8.29/8.42 & sdtlseqdt0(W1,W0) ) % 8.29/8.42 => W0 = W1 ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mLessTrans,axiom, % 8.29/8.43 ! [W0,W1,W2] : % 8.29/8.43 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) % 8.29/8.43 & aElementOf0(W2,szNzAzT0) ) % 8.29/8.43 => ( ( sdtlseqdt0(W0,W1) % 8.29/8.43 & sdtlseqdt0(W1,W2) ) % 8.29/8.43 => sdtlseqdt0(W0,W2) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mLessTotal,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ( sdtlseqdt0(W0,W1) % 8.29/8.43 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mIHSort,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ( iLess0(W0,W1) % 8.29/8.43 => $true ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mIH,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardS,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aSet0(W0) % 8.29/8.43 => aElement0(sbrdtbr0(W0)) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardNum,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aSet0(W0) % 8.29/8.43 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 8.29/8.43 <=> isFinite0(W0) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardEmpty,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aSet0(W0) % 8.29/8.43 => ( sbrdtbr0(W0) = sz00 % 8.29/8.43 <=> W0 = slcrc0 ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardCons,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & isFinite0(W0) ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( aElement0(W1) % 8.29/8.43 => ( ~ aElementOf0(W1,W0) % 8.29/8.43 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardDiff,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aSet0(W0) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( ( isFinite0(W0) % 8.29/8.43 & aElementOf0(W1,W0) ) % 8.29/8.43 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardSub,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aSet0(W0) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( ( isFinite0(W0) % 8.29/8.43 & aSubsetOf0(W1,W0) ) % 8.29/8.43 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardSubEx,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ( ( isFinite0(W0) % 8.29/8.43 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 8.29/8.43 => ? [W2] : % 8.29/8.43 ( aSubsetOf0(W2,W0) % 8.29/8.43 & sbrdtbr0(W2) = W1 ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mDefMin,definition, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSubsetOf0(W0,szNzAzT0) % 8.29/8.43 & W0 != slcrc0 ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( W1 = szmzizndt0(W0) % 8.29/8.43 <=> ( aElementOf0(W1,W0) % 8.29/8.43 & ! [W2] : % 8.29/8.43 ( aElementOf0(W2,W0) % 8.29/8.43 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mDefMax,definition, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSubsetOf0(W0,szNzAzT0) % 8.29/8.43 & isFinite0(W0) % 8.29/8.43 & W0 != slcrc0 ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( W1 = szmzazxdt0(W0) % 8.29/8.43 <=> ( aElementOf0(W1,W0) % 8.29/8.43 & ! [W2] : % 8.29/8.43 ( aElementOf0(W2,W0) % 8.29/8.43 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mMinMin,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aSubsetOf0(W0,szNzAzT0) % 8.29/8.43 & aSubsetOf0(W1,szNzAzT0) % 8.29/8.43 & W0 != slcrc0 % 8.29/8.43 & W1 != slcrc0 ) % 8.29/8.43 => ( ( aElementOf0(szmzizndt0(W0),W1) % 8.29/8.43 & aElementOf0(szmzizndt0(W1),W0) ) % 8.29/8.43 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mDefSeg,definition, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( W1 = slbdtrb0(W0) % 8.29/8.43 <=> ( aSet0(W1) % 8.29/8.43 & ! [W2] : % 8.29/8.43 ( aElementOf0(W2,W1) % 8.29/8.43 <=> ( aElementOf0(W2,szNzAzT0) % 8.29/8.43 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSegFin,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 => isFinite0(slbdtrb0(W0)) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSegZero,axiom, % 8.29/8.43 slbdtrb0(sz00) = slcrc0 ). % 8.29/8.43 % 8.29/8.43 fof(mSegSucc,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 8.29/8.43 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 8.29/8.43 | W0 = W1 ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSegLess,axiom, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ( sdtlseqdt0(W0,W1) % 8.29/8.43 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mFinSubSeg,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSubsetOf0(W0,szNzAzT0) % 8.29/8.43 & isFinite0(W0) ) % 8.29/8.43 => ? [W1] : % 8.29/8.43 ( aElementOf0(W1,szNzAzT0) % 8.29/8.43 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mCardSeg,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( aElementOf0(W0,szNzAzT0) % 8.29/8.43 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 8.29/8.43 % 8.29/8.43 fof(mDefSel,definition, % 8.29/8.43 ! [W0,W1] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & aElementOf0(W1,szNzAzT0) ) % 8.29/8.43 => ! [W2] : % 8.29/8.43 ( W2 = slbdtsldtrb0(W0,W1) % 8.29/8.43 <=> ( aSet0(W2) % 8.29/8.43 & ! [W3] : % 8.29/8.43 ( aElementOf0(W3,W2) % 8.29/8.43 <=> ( aSubsetOf0(W3,W0) % 8.29/8.43 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSelFSet,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & isFinite0(W0) ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( aElementOf0(W1,szNzAzT0) % 8.29/8.43 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSelNSet,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & ~ isFinite0(W0) ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( aElementOf0(W1,szNzAzT0) % 8.29/8.43 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 8.29/8.43 % 8.29/8.43 fof(mSelCSet,axiom, % 8.29/8.43 ! [W0] : % 8.29/8.43 ( ( aSet0(W0) % 8.29/8.43 & isCountable0(W0) ) % 8.29/8.43 => ! [W1] : % 8.29/8.43 ( ( aElementOf0(W1,szNzAzT0) % 8.29/8.43 & W1 != sz00 ) % 8.29/8.43 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 8.29/8.43 % 8.29/8.43 fof(m__2202,hypothesis, % 8.29/8.43 aElementOf0(xk,szNzAzT0) ). % 8.29/8.43 % 8.29/8.43 fof(m__2202_02,hypothesis, % 8.29/8.43 ( aSet0(xS) % 8.29/8.43 & aSet0(xT) % 8.29/8.43 & xk != sz00 ) ). % 8.29/8.43 % 8.29/8.43 fof(m__2227,hypothesis, % 8.29/8.43 ( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) % 8.29/8.43 & slbdtsldtrb0(xS,xk) != slcrc0 ) ). % 8.29/8.43 % 8.29/8.43 fof(m__2256,hypothesis, % 8.29/8.43 aElementOf0(xx,xS) ). % 8.29/8.43 % 8.29/8.43 fof(m__2270,hypothesis, % 8.29/8.43 aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ). % 8.29/8.43 % 8.29/8.43 fof(m__,conjecture, % 8.29/8.43 isFinite0(xQ) ). % 8.29/8.43 % 8.29/8.43 %------------------------------------------------------------------------------ % 8.29/8.43 %------------------------------------------- % 8.29/8.43 % Proof found % 8.29/8.43 % SZS status Theorem for theBenchmark % 8.29/8.43 % SZS output start Proof % 8.29/8.43 %ClaNum:161(EqnAxiom:48) % 8.29/8.43 %VarNum:714(SingletonVarNum:218) % 8.29/8.43 %MaxLitNum:8 % 8.29/8.43 %MaxfuncDepth:3 % 8.29/8.43 %SharedTerms:25 % 8.29/8.43 %goalClause: 61 % 8.29/8.43 %singleGoalClaCount:1 % 8.29/8.43 [50]P1(a19) % 8.29/8.43 [51]P1(a20) % 8.29/8.43 [52]P1(a25) % 8.29/8.43 [53]P4(a17) % 8.29/8.43 [54]P5(a19) % 8.29/8.43 [55]P2(a1,a19) % 8.29/8.43 [56]P2(a26,a19) % 8.29/8.43 [57]P2(a27,a20) % 8.29/8.43 [60]~E(a26,a1) % 8.29/8.43 [61]~P4(a21) % 8.29/8.43 [49]E(f2(a1),a17) % 8.29/8.43 [58]P2(a21,f18(a20,a26)) % 8.29/8.43 [59]P6(f18(a20,a26),f18(a25,a26)) % 8.29/8.43 [62]~E(f18(a20,a26),a17) % 8.29/8.43 [63]P1(x631)+~E(x631,a17) % 8.29/8.43 [69]~P1(x691)+P6(x691,x691) % 8.29/8.43 [76]~P2(x761,a19)+P8(a1,x761) % 8.29/8.43 [82]P8(x821,x821)+~P2(x821,a19) % 8.29/8.43 [67]~P1(x671)+P3(f3(x671)) % 8.29/8.43 [71]~P2(x711,a19)+~E(f22(x711),a1) % 8.29/8.43 [72]~P2(x721,a19)+~E(f22(x721),x721) % 8.29/8.43 [74]~P2(x741,a19)+P4(f2(x741)) % 8.29/8.43 [83]~P2(x831,a19)+P2(f22(x831),a19) % 8.29/8.43 [84]~P2(x841,a19)+P8(x841,f22(x841)) % 8.29/8.43 [85]~P2(x851,a19)+P7(x851,f22(x851)) % 8.29/8.43 [93]~P2(x931,a19)+~P8(f22(x931),a1) % 8.29/8.43 [75]~P2(x751,a19)+E(f3(f2(x751)),x751) % 8.29/8.43 [70]~P2(x702,x701)+~E(x701,a17) % 8.29/8.43 [66]~P1(x661)+~P5(x661)+~E(x661,a17) % 8.29/8.43 [68]~P4(x681)+~P5(x681)+~P1(x681) % 8.29/8.43 [64]~P1(x641)+~E(x641,a17)+E(f3(x641),a1) % 8.29/8.43 [65]~P1(x651)+E(x651,a17)+~E(f3(x651),a1) % 8.29/8.43 [73]~P1(x731)+P2(f4(x731),x731)+E(x731,a17) % 8.29/8.43 [79]~P1(x791)+~P4(x791)+P2(f3(x791),a19) % 8.29/8.43 [86]~P2(x861,a19)+E(x861,a1)+P2(f7(x861),a19) % 8.29/8.43 [87]~P1(x871)+P4(x871)+~P2(f3(x871),a19) % 8.29/8.43 [92]~P4(x921)+~P6(x921,a19)+P2(f5(x921),a19) % 8.29/8.43 [77]~P2(x771,a19)+E(x771,a1)+E(f22(f7(x771)),x771) % 8.29/8.43 [102]~P4(x1021)+~P6(x1021,a19)+P6(x1021,f2(f5(x1021))) % 8.29/8.43 [80]~P6(x801,x802)+P1(x801)+~P1(x802) % 8.29/8.43 [81]~P2(x811,x812)+P3(x811)+~P1(x812) % 8.29/8.43 [78]P1(x781)+~P2(x782,a19)+~E(x781,f2(x782)) % 8.29/8.43 [116]~P1(x1161)+~P2(x1162,x1161)+E(f15(f16(x1161,x1162),x1162),x1161) % 8.29/8.43 [88]~P4(x882)+~P6(x881,x882)+P4(x881)+~P1(x882) % 8.29/8.43 [91]P2(x912,x911)+~E(x912,f23(x911))+~P6(x911,a19)+E(x911,a17) % 8.29/8.43 [95]~P1(x951)+~P3(x952)+~P4(x951)+P4(f15(x951,x952)) % 8.29/8.43 [96]~P1(x961)+~P3(x962)+~P4(x961)+P4(f16(x961,x962)) % 8.29/8.43 [97]~P1(x971)+~P3(x972)+~P5(x971)+P5(f15(x971,x972)) % 8.29/8.43 [98]~P1(x981)+~P3(x982)+~P5(x981)+P5(f16(x981,x982)) % 8.29/8.43 [99]~P1(x991)+P4(x991)+~P2(x992,a19)+~E(f18(x991,x992),a17) % 8.29/8.43 [101]E(x1011,x1012)+~E(f22(x1011),f22(x1012))+~P2(x1012,a19)+~P2(x1011,a19) % 8.29/8.43 [105]~P1(x1052)+~P4(x1052)+~P6(x1051,x1052)+P8(f3(x1051),f3(x1052)) % 8.29/8.43 [108]~P1(x1081)+~P4(x1081)+~P2(x1082,a19)+P4(f18(x1081,x1082)) % 8.29/8.43 [114]~P1(x1141)+~P1(x1142)+P6(x1141,x1142)+P2(f8(x1142,x1141),x1141) % 8.29/8.43 [120]P8(x1201,x1202)+P8(f22(x1202),x1201)+~P2(x1202,a19)+~P2(x1201,a19) % 8.29/8.43 [130]~P8(x1301,x1302)+~P2(x1302,a19)+~P2(x1301,a19)+P6(f2(x1301),f2(x1302)) % 8.29/8.43 [131]~P8(x1311,x1312)+~P2(x1312,a19)+~P2(x1311,a19)+P8(f22(x1311),f22(x1312)) % 8.29/8.43 [133]~P1(x1331)+~P1(x1332)+P6(x1331,x1332)+~P2(f8(x1332,x1331),x1332) % 8.29/8.43 [135]P8(x1351,x1352)+~P2(x1352,a19)+~P2(x1351,a19)+~P6(f2(x1351),f2(x1352)) % 8.29/8.43 [136]P8(x1361,x1362)+~P2(x1362,a19)+~P2(x1361,a19)+~P8(f22(x1361),f22(x1362)) % 8.29/8.43 [115]P2(x1152,x1151)+~P1(x1151)+~P3(x1152)+E(f16(f15(x1151,x1152),x1152),x1151) % 8.29/8.43 [122]~E(x1221,x1222)+~P2(x1222,a19)+~P2(x1221,a19)+P2(x1221,f2(f22(x1222))) % 8.29/8.43 [141]~P2(x1412,a19)+~P2(x1411,a19)+~P2(x1411,f2(x1412))+P2(x1411,f2(f22(x1412))) % 8.29/8.43 [140]~P1(x1401)+~P4(x1401)+~P2(x1402,x1401)+E(f22(f3(f16(x1401,x1402))),f3(x1401)) % 8.29/8.43 [112]~P1(x1122)+~P6(x1123,x1122)+P2(x1121,x1122)+~P2(x1121,x1123) % 8.29/8.43 [89]~P1(x892)+~P3(x893)+P1(x891)+~E(x891,f15(x892,x893)) % 8.29/8.43 [90]~P1(x902)+~P3(x903)+P1(x901)+~E(x901,f16(x902,x903)) % 8.29/8.43 [100]~P1(x1002)+P1(x1001)+~P2(x1003,a19)+~E(x1001,f18(x1002,x1003)) % 8.29/8.43 [106]~P2(x1061,x1062)+~P2(x1063,a19)+P2(x1061,a19)+~E(x1062,f2(x1063)) % 8.29/8.43 [117]~P2(x1171,x1173)+~P2(x1172,a19)+P8(f22(x1171),x1172)+~E(x1173,f2(x1172)) % 8.29/8.43 [103]~P1(x1032)+~P1(x1031)+~P6(x1032,x1031)+~P6(x1031,x1032)+E(x1031,x1032) % 8.29/8.43 [128]~P8(x1282,x1281)+~P8(x1281,x1282)+E(x1281,x1282)+~P2(x1282,a19)+~P2(x1281,a19) % 8.29/8.43 [94]~P4(x941)+P2(x942,x941)+~E(x942,f24(x941))+~P6(x941,a19)+E(x941,a17) % 8.29/8.43 [111]~P1(x1112)+~P5(x1112)+~P2(x1111,a19)+E(x1111,a1)+P5(f18(x1112,x1111)) % 8.29/8.43 [132]~P2(x1322,x1321)+P2(f11(x1321,x1322),x1321)+~P6(x1321,a19)+E(x1321,a17)+E(x1322,f23(x1321)) % 8.29/8.43 [142]~P1(x1421)+~P4(x1421)+~P2(x1422,a19)+~P8(x1422,f3(x1421))+P6(f12(x1421,x1422),x1421) % 8.29/8.43 [143]~P1(x1431)+P2(f14(x1432,x1431),x1431)+~P2(x1432,a19)+E(x1431,f2(x1432))+P2(f14(x1432,x1431),a19) % 8.29/8.43 [144]~P2(x1442,x1441)+~P6(x1441,a19)+~P8(x1442,f11(x1441,x1442))+E(x1441,a17)+E(x1442,f23(x1441)) % 8.29/8.43 [121]P2(x1212,x1211)+~P1(x1211)+~P3(x1212)+~P4(x1211)+E(f3(f15(x1211,x1212)),f22(f3(x1211))) % 8.29/8.43 [139]~P1(x1391)+~P4(x1391)+~P2(x1392,a19)+~P8(x1392,f3(x1391))+E(f3(f12(x1391,x1392)),x1392) % 8.29/8.43 [145]E(x1451,x1452)+P2(x1451,f2(x1452))+~P2(x1452,a19)+~P2(x1451,a19)+~P2(x1451,f2(f22(x1452))) % 8.29/8.43 [149]~P1(x1491)+P2(f14(x1492,x1491),x1491)+~P2(x1492,a19)+E(x1491,f2(x1492))+P8(f22(f14(x1492,x1491)),x1492) % 8.29/8.43 [113]~P2(x1133,x1131)+P8(x1132,x1133)+~E(x1132,f23(x1131))+~P6(x1131,a19)+E(x1131,a17) % 8.29/8.43 [134]P2(x1341,x1342)+~P2(x1343,a19)+~P2(x1341,a19)+~P8(f22(x1341),x1343)+~E(x1342,f2(x1343)) % 8.29/8.43 [107]~P1(x1074)+~P3(x1072)+~P2(x1071,x1073)+~E(x1071,x1072)+~E(x1073,f16(x1074,x1072)) % 8.29/8.43 [109]~P1(x1093)+~P3(x1094)+~P2(x1091,x1092)+P3(x1091)+~E(x1092,f15(x1093,x1094)) % 8.29/8.43 [110]~P1(x1103)+~P3(x1104)+~P2(x1101,x1102)+P3(x1101)+~E(x1102,f16(x1103,x1104)) % 8.29/8.43 [119]~P1(x1192)+~P3(x1194)+~P2(x1191,x1193)+P2(x1191,x1192)+~E(x1193,f16(x1192,x1194)) % 8.29/8.43 [124]~P1(x1244)+~P2(x1241,x1243)+~P2(x1242,a19)+E(f3(x1241),x1242)+~E(x1243,f18(x1244,x1242)) % 8.29/8.43 [129]~P1(x1292)+~P2(x1291,x1293)+P6(x1291,x1292)+~P2(x1294,a19)+~E(x1293,f18(x1292,x1294)) % 8.29/8.43 [138]~P4(x1381)+~P2(x1382,x1381)+P2(f13(x1381,x1382),x1381)+~P6(x1381,a19)+E(x1381,a17)+E(x1382,f24(x1381)) % 8.29/8.43 [147]~P4(x1471)+~P2(x1472,x1471)+~P6(x1471,a19)+~P8(f13(x1471,x1472),x1472)+E(x1471,a17)+E(x1472,f24(x1471)) % 8.29/8.43 [153]~P1(x1531)+~P2(x1532,a19)+~P2(f14(x1532,x1531),x1531)+E(x1531,f2(x1532))+~P2(f14(x1532,x1531),a19)+~P8(f22(f14(x1532,x1531)),x1532) % 8.29/8.43 [125]~P1(x1252)+~P1(x1251)+~P6(x1253,x1252)+~P6(x1251,x1253)+P6(x1251,x1252)+~P1(x1253) % 8.29/8.43 [148]~P8(x1481,x1483)+P8(x1481,x1482)+~P8(x1483,x1482)+~P2(x1482,a19)+~P2(x1483,a19)+~P2(x1481,a19) % 8.29/8.43 [118]~P4(x1181)+~P2(x1182,x1181)+P8(x1182,x1183)+~E(x1183,f24(x1181))+~P6(x1181,a19)+E(x1181,a17) % 8.29/8.43 [150]~P1(x1501)+~P1(x1502)+~P3(x1503)+P2(f9(x1502,x1503,x1501),x1501)+~E(f9(x1502,x1503,x1501),x1503)+E(x1501,f16(x1502,x1503)) % 8.29/8.43 [151]~P1(x1511)+~P1(x1512)+~P3(x1513)+P2(f10(x1512,x1513,x1511),x1511)+E(x1511,f15(x1512,x1513))+P3(f10(x1512,x1513,x1511)) % 8.29/8.43 [152]~P1(x1521)+~P1(x1522)+~P3(x1523)+P2(f9(x1522,x1523,x1521),x1521)+E(x1521,f16(x1522,x1523))+P3(f9(x1522,x1523,x1521)) % 8.29/8.43 [154]~P1(x1541)+~P1(x1542)+~P3(x1543)+P2(f9(x1542,x1543,x1541),x1541)+P2(f9(x1542,x1543,x1541),x1542)+E(x1541,f16(x1542,x1543)) % 8.29/8.43 [156]~P1(x1561)+~P1(x1562)+P2(f6(x1562,x1563,x1561),x1561)+P6(f6(x1562,x1563,x1561),x1562)+~P2(x1563,a19)+E(x1561,f18(x1562,x1563)) % 8.29/8.43 [155]~P1(x1551)+~P1(x1552)+P2(f6(x1552,x1553,x1551),x1551)+~P2(x1553,a19)+E(x1551,f18(x1552,x1553))+E(f3(f6(x1552,x1553,x1551)),x1553) % 8.29/8.43 [104]~P1(x1044)+~P3(x1043)+~P3(x1041)+P2(x1041,x1042)+~E(x1041,x1043)+~E(x1042,f15(x1044,x1043)) % 8.29/8.43 [123]~P1(x1233)+~P3(x1232)+~P2(x1231,x1234)+E(x1231,x1232)+P2(x1231,x1233)+~E(x1234,f15(x1233,x1232)) % 8.29/8.43 [126]~P1(x1263)+~P3(x1264)+~P3(x1261)+~P2(x1261,x1263)+P2(x1261,x1262)+~E(x1262,f15(x1263,x1264)) % 8.29/8.43 [137]~P1(x1374)+~P6(x1371,x1374)+P2(x1371,x1372)+~P2(x1373,a19)+~E(x1372,f18(x1374,x1373))+~E(f3(x1371),x1373) % 8.29/8.43 [146]E(f23(x1462),f23(x1461))+~P6(x1461,a19)+~P6(x1462,a19)+~P2(f23(x1461),x1462)+~P2(f23(x1462),x1461)+E(x1461,a17)+E(x1462,a17) % 8.29/8.43 [157]~P1(x1571)+~P1(x1572)+~P3(x1573)+E(f10(x1572,x1573,x1571),x1573)+P2(f10(x1572,x1573,x1571),x1571)+P2(f10(x1572,x1573,x1571),x1572)+E(x1571,f15(x1572,x1573)) % 8.29/8.43 [158]~P1(x1581)+~P1(x1582)+~P3(x1583)+~E(f10(x1582,x1583,x1581),x1583)+~P2(f10(x1582,x1583,x1581),x1581)+E(x1581,f15(x1582,x1583))+~P3(f10(x1582,x1583,x1581)) % 8.29/8.43 [159]~P1(x1591)+~P1(x1592)+~P3(x1593)+~P2(f10(x1592,x1593,x1591),x1591)+~P2(f10(x1592,x1593,x1591),x1592)+E(x1591,f15(x1592,x1593))+~P3(f10(x1592,x1593,x1591)) % 8.29/8.43 [160]~P1(x1601)+~P1(x1602)+~P2(x1603,a19)+~P2(f6(x1602,x1603,x1601),x1601)+~P6(f6(x1602,x1603,x1601),x1602)+E(x1601,f18(x1602,x1603))+~E(f3(f6(x1602,x1603,x1601)),x1603) % 8.29/8.43 [127]~P1(x1274)+~P3(x1272)+~P3(x1271)+~P2(x1271,x1274)+E(x1271,x1272)+P2(x1271,x1273)+~E(x1273,f16(x1274,x1272)) % 8.29/8.43 [161]~P1(x1611)+~P1(x1612)+~P3(x1613)+E(f9(x1612,x1613,x1611),x1613)+~P2(f9(x1612,x1613,x1611),x1611)+~P2(f9(x1612,x1613,x1611),x1612)+E(x1611,f16(x1612,x1613))+~P3(f9(x1612,x1613,x1611)) % 8.29/8.43 %EqnAxiom % 8.29/8.43 [1]E(x11,x11) % 8.29/8.43 [2]E(x22,x21)+~E(x21,x22) % 8.29/8.43 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 8.29/8.43 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 8.29/8.43 [5]~E(x51,x52)+E(f18(x51,x53),f18(x52,x53)) % 8.29/8.43 [6]~E(x61,x62)+E(f18(x63,x61),f18(x63,x62)) % 8.29/8.43 [7]~E(x71,x72)+E(f10(x71,x73,x74),f10(x72,x73,x74)) % 8.29/8.43 [8]~E(x81,x82)+E(f10(x83,x81,x84),f10(x83,x82,x84)) % 8.29/8.43 [9]~E(x91,x92)+E(f10(x93,x94,x91),f10(x93,x94,x92)) % 8.29/8.43 [10]~E(x101,x102)+E(f22(x101),f22(x102)) % 8.29/8.43 [11]~E(x111,x112)+E(f15(x111,x113),f15(x112,x113)) % 8.29/8.43 [12]~E(x121,x122)+E(f15(x123,x121),f15(x123,x122)) % 8.29/8.43 [13]~E(x131,x132)+E(f3(x131),f3(x132)) % 8.29/8.43 [14]~E(x141,x142)+E(f24(x141),f24(x142)) % 8.29/8.43 [15]~E(x151,x152)+E(f16(x151,x153),f16(x152,x153)) % 8.29/8.43 [16]~E(x161,x162)+E(f16(x163,x161),f16(x163,x162)) % 8.29/8.43 [17]~E(x171,x172)+E(f14(x171,x173),f14(x172,x173)) % 8.29/8.43 [18]~E(x181,x182)+E(f14(x183,x181),f14(x183,x182)) % 8.29/8.43 [19]~E(x191,x192)+E(f9(x191,x193,x194),f9(x192,x193,x194)) % 8.29/8.43 [20]~E(x201,x202)+E(f9(x203,x201,x204),f9(x203,x202,x204)) % 8.29/8.43 [21]~E(x211,x212)+E(f9(x213,x214,x211),f9(x213,x214,x212)) % 8.29/8.43 [22]~E(x221,x222)+E(f4(x221),f4(x222)) % 8.29/8.43 [23]~E(x231,x232)+E(f23(x231),f23(x232)) % 8.29/8.43 [24]~E(x241,x242)+E(f11(x241,x243),f11(x242,x243)) % 8.29/8.43 [25]~E(x251,x252)+E(f11(x253,x251),f11(x253,x252)) % 8.29/8.43 [26]~E(x261,x262)+E(f5(x261),f5(x262)) % 8.29/8.43 [27]~E(x271,x272)+E(f7(x271),f7(x272)) % 8.29/8.43 [28]~E(x281,x282)+E(f6(x281,x283,x284),f6(x282,x283,x284)) % 8.29/8.43 [29]~E(x291,x292)+E(f6(x293,x291,x294),f6(x293,x292,x294)) % 8.29/8.43 [30]~E(x301,x302)+E(f6(x303,x304,x301),f6(x303,x304,x302)) % 8.29/8.43 [31]~E(x311,x312)+E(f13(x311,x313),f13(x312,x313)) % 8.29/8.43 [32]~E(x321,x322)+E(f13(x323,x321),f13(x323,x322)) % 8.29/8.43 [33]~E(x331,x332)+E(f8(x331,x333),f8(x332,x333)) % 8.29/8.43 [34]~E(x341,x342)+E(f8(x343,x341),f8(x343,x342)) % 8.29/8.43 [35]~E(x351,x352)+E(f12(x351,x353),f12(x352,x353)) % 8.29/8.43 [36]~E(x361,x362)+E(f12(x363,x361),f12(x363,x362)) % 8.29/8.43 [37]~P1(x371)+P1(x372)+~E(x371,x372) % 8.29/8.43 [38]P2(x382,x383)+~E(x381,x382)+~P2(x381,x383) % 8.29/8.43 [39]P2(x393,x392)+~E(x391,x392)+~P2(x393,x391) % 8.29/8.43 [40]P6(x402,x403)+~E(x401,x402)+~P6(x401,x403) % 8.29/8.44 [41]P6(x413,x412)+~E(x411,x412)+~P6(x413,x411) % 8.29/8.44 [42]~P4(x421)+P4(x422)+~E(x421,x422) % 8.29/8.44 [43]~P5(x431)+P5(x432)+~E(x431,x432) % 8.29/8.44 [44]P8(x442,x443)+~E(x441,x442)+~P8(x441,x443) % 8.29/8.44 [45]P8(x453,x452)+~E(x451,x452)+~P8(x453,x451) % 8.29/8.44 [46]~P3(x461)+P3(x462)+~E(x461,x462) % 8.29/8.44 [47]P7(x472,x473)+~E(x471,x472)+~P7(x471,x473) % 8.29/8.44 [48]P7(x483,x482)+~E(x481,x482)+~P7(x483,x481) % 8.29/8.44 % 8.29/8.44 %------------------------------------------- % 8.29/8.44 cnf(162,plain, % 8.29/8.44 (P1(a17)), % 8.29/8.44 inference(equality_inference,[],[63])). % 8.29/8.44 cnf(163,plain, % 8.29/8.44 (~P1(a17)+E(f3(a17),a1)), % 8.29/8.44 inference(equality_inference,[],[64])). % 8.29/8.44 cnf(165,plain, % 8.29/8.44 (~P2(x1651,a17)), % 8.29/8.44 inference(equality_inference,[],[70])). % 8.29/8.44 cnf(166,plain, % 8.29/8.44 (P1(f2(x1661))+~P2(x1661,a19)), % 8.29/8.44 inference(equality_inference,[],[78])). % 8.29/8.44 cnf(169,plain, % 8.29/8.44 (P2(f23(x1691),x1691)+~P6(x1691,a19)+E(x1691,a17)), % 8.29/8.44 inference(equality_inference,[],[91])). % 8.29/8.44 cnf(171,plain, % 8.29/8.44 (~P1(x1711)+P1(f18(x1711,x1712))+~P2(x1712,a19)), % 8.29/8.44 inference(equality_inference,[],[100])). % 8.29/8.44 cnf(177,plain, % 8.29/8.44 (~P2(x1771,f2(x1772))+P8(f22(x1771),x1772)+~P2(x1772,a19)), % 8.29/8.44 inference(equality_inference,[],[117])). % 8.29/8.44 cnf(180,plain, % 8.29/8.44 (~P2(x1801,a19)+~P2(x1801,a19)+P2(x1801,f2(f22(x1801)))), % 8.29/8.44 inference(equality_inference,[],[122])). % 8.29/8.44 cnf(182,plain, % 8.29/8.44 (~P1(x1821)+~P2(x1822,f18(x1821,x1823))+E(f3(x1822),x1823)+~P2(x1823,a19)), % 8.29/8.44 inference(equality_inference,[],[124])). % 8.29/8.44 cnf(185,plain, % 8.29/8.44 (P6(x1851,x1852)+~P1(x1852)+~P2(x1851,f18(x1852,x1853))+~P2(x1853,a19)), % 8.29/8.44 inference(equality_inference,[],[129])). % 8.29/8.44 cnf(186,plain, % 8.29/8.44 (P2(x1861,f2(x1862))+~P2(x1861,a19)+~P8(f22(x1861),x1862)+~P2(x1862,a19)), % 8.29/8.44 inference(equality_inference,[],[134])). % 8.29/8.44 cnf(187,plain, % 8.29/8.44 (E(f3(a17),a1)), % 8.29/8.44 inference(scs_inference,[],[162,163])). % 8.29/8.44 cnf(189,plain, % 8.29/8.44 (P1(f2(a1))), % 8.29/8.44 inference(scs_inference,[],[49,63])). % 8.29/8.44 cnf(193,plain, % 8.29/8.44 (~P2(x1931,f2(a1))), % 8.29/8.44 inference(scs_inference,[],[56,49,63,166,70])). % 8.29/8.44 cnf(195,plain, % 8.29/8.44 (P8(a1,a1)), % 8.29/8.44 inference(scs_inference,[],[55,56,49,63,166,70,82])). % 8.29/8.44 cnf(197,plain, % 8.29/8.44 (E(a17,f2(a1))), % 8.29/8.44 inference(scs_inference,[],[55,56,49,63,166,70,82,2])). % 8.29/8.44 cnf(205,plain, % 8.29/8.44 (P2(a1,f2(f22(a1)))), % 8.29/8.44 inference(scs_inference,[],[50,53,54,55,56,49,63,166,70,82,2,42,68,171,66,180])). % 8.29/8.44 cnf(208,plain, % 8.29/8.44 (~E(a19,a17)), % 8.29/8.44 inference(scs_inference,[],[50,165,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39])). % 8.29/8.44 cnf(209,plain, % 8.29/8.44 (~P2(x2091,a17)), % 8.29/8.44 inference(rename_variables,[],[165])). % 8.29/8.44 cnf(212,plain, % 8.29/8.44 (P6(a17,a19)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114])). % 8.29/8.44 cnf(213,plain, % 8.29/8.44 (~P2(x2131,a17)), % 8.29/8.44 inference(rename_variables,[],[165])). % 8.29/8.44 cnf(215,plain, % 8.29/8.44 (P6(f2(a1),f2(a1))), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130])). % 8.29/8.44 cnf(219,plain, % 8.29/8.44 (~P8(f22(a26),a1)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,213,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130,131,134])). % 8.29/8.44 cnf(222,plain, % 8.29/8.44 (~P6(a19,a17)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,213,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130,131,134,103])). % 8.29/8.44 cnf(226,plain, % 8.29/8.44 (P6(f2(a1),a19)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,213,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130,131,134,103,177,40])). % 8.29/8.44 cnf(229,plain, % 8.29/8.44 (~E(f22(a1),a1)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,213,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130,131,134,103,177,40,41,44,45])). % 8.29/8.44 cnf(230,plain, % 8.29/8.44 (P8(a1,a26)), % 8.29/8.44 inference(scs_inference,[],[50,162,165,209,213,53,54,55,56,62,49,63,166,70,82,2,42,68,171,66,180,3,39,186,114,130,131,134,103,177,40,41,44,45,120])). % 8.29/8.44 cnf(238,plain, % 8.29/8.44 (P8(a26,a26)), % 8.29/8.44 inference(scs_inference,[],[56,82])). % 8.29/8.44 cnf(240,plain, % 8.29/8.44 (E(a1,f3(a17))), % 8.29/8.44 inference(scs_inference,[],[187,56,82,2])). % 8.29/8.44 cnf(241,plain, % 8.29/8.44 (P2(a26,f2(f22(a26)))), % 8.29/8.44 inference(scs_inference,[],[187,56,82,2,180])). % 8.29/8.44 cnf(243,plain, % 8.29/8.44 (P2(f3(a17),a19)), % 8.29/8.44 inference(scs_inference,[],[55,187,56,82,2,180,38])). % 8.29/8.44 cnf(248,plain, % 8.29/8.44 (P8(f3(a17),a26)), % 8.29/8.44 inference(scs_inference,[],[50,55,193,187,230,56,82,2,180,38,39,171,44])). % 8.29/8.44 cnf(251,plain, % 8.29/8.44 (P6(a17,f2(a1))), % 8.29/8.44 inference(scs_inference,[],[50,55,49,195,193,215,187,229,230,56,82,2,180,38,39,171,44,45,3,40])). % 8.29/8.44 cnf(252,plain, % 8.29/8.44 (P8(f22(a26),f22(a26))), % 8.29/8.44 inference(scs_inference,[],[50,55,49,195,193,215,187,229,230,56,82,2,180,38,39,171,44,45,3,40,131])). % 8.29/8.44 cnf(256,plain, % 8.29/8.44 (P6(f12(a17,a1),a17)), % 8.29/8.44 inference(scs_inference,[],[50,162,55,49,195,193,215,187,229,230,53,56,82,2,180,38,39,171,44,45,3,40,131,130,142])). % 8.29/8.44 cnf(258,plain, % 8.29/8.44 (~P8(f22(f3(a17)),a1)), % 8.29/8.44 inference(scs_inference,[],[50,162,55,49,195,193,215,187,197,229,230,165,53,56,82,2,180,38,39,171,44,45,3,40,131,130,142,134])). % 8.29/8.44 cnf(261,plain, % 8.29/8.44 (~P6(a19,f2(a1))), % 8.29/8.44 inference(scs_inference,[],[50,189,162,55,49,195,226,193,215,187,197,229,230,165,53,56,82,2,180,38,39,171,44,45,3,40,131,130,142,134,103])). % 8.29/8.44 cnf(276,plain, % 8.29/8.44 (P2(f3(a17),f2(f22(f3(a17))))), % 8.29/8.44 inference(scs_inference,[],[243,82,180])). % 8.29/8.44 cnf(289,plain, % 8.29/8.44 (P8(f22(f3(a17)),f22(f3(a17)))), % 8.29/8.44 inference(scs_inference,[],[50,219,256,197,243,205,252,240,60,222,193,187,82,180,171,41,38,40,39,3,45,130,131])). % 8.29/8.44 cnf(311,plain, % 8.29/8.44 (~E(f22(f3(a17)),a1)), % 8.29/8.44 inference(scs_inference,[],[258,289,45])). % 8.29/8.44 cnf(327,plain, % 8.29/8.44 (P2(x3271,a19)+~E(a26,x3271)), % 8.29/8.44 inference(scs_inference,[],[56,197,226,251,187,193,261,311,241,3,40,39,41,46,38])). % 8.29/8.44 cnf(344,plain, % 8.29/8.44 (P8(a1,x3441)+~E(a26,x3441)), % 8.29/8.44 inference(scs_inference,[],[240,230,212,165,276,58,39,38,41,46,45])). % 8.29/8.44 cnf(352,plain, % 8.29/8.44 (~E(a20,f2(a1))), % 8.29/8.44 inference(scs_inference,[],[193,57,39])). % 8.29/8.44 cnf(376,plain, % 8.29/8.44 (P8(a26,x3761)+~E(a26,x3761)), % 8.29/8.44 inference(scs_inference,[],[238,45])). % 8.29/8.44 cnf(550,plain, % 8.29/8.44 (P2(f23(a19),a19)), % 8.29/8.44 inference(scs_inference,[],[50,208,69,169])). % 8.29/8.44 cnf(1700,plain, % 8.29/8.44 (P6(a21,a20)), % 8.29/8.44 inference(scs_inference,[],[51,550,58,56,171,185])). % 8.29/8.44 cnf(1725,plain, % 8.29/8.44 (~P1(a21)), % 8.29/8.44 inference(scs_inference,[],[51,61,162,189,550,251,193,248,58,241,56,238,352,171,185,88,182,114,103,125,2,41,38,44,45,327,344,376,82,166,87])). % 8.29/8.44 cnf(1737,plain, % 8.29/8.44 ($false), % 8.29/8.44 inference(scs_inference,[],[51,1725,55,1700,171,80]), % 8.29/8.44 ['proof']). % 8.29/8.44 % SZS output end Proof % 8.29/8.44 % Total time :7.890000s %------------------------------------------------------------------------------