%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM557+3 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : 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 12:25:01 EDT 2024 % Result : Theorem 0.46s 0.54s % Output : CNFRefutation 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.09 % Problem : NUM557+3 : TPTP v8.2.0. Released v4.0.0. % 0.05/0.09 % Command : java -jar /export/starexec/sandbox2/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 : Sun Jun 23 01:39:08 EDT 2024 % 0.09/0.28 % CPUTime : % 0.14/0.45 start to proof:theBenchmark % 0.14/0.52 %------------------------------------------- % 0.14/0.52 % File :CSE---1.7 % 0.14/0.52 % Problem :theBenchmark % 0.14/0.52 % Transform :cnf % 0.14/0.52 % Format :tptp:raw % 0.14/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.14/0.52 % 0.14/0.52 % Result :Theorem 0.010000s % 0.14/0.52 % Output :CNFRefutation 0.010000s % 0.14/0.52 %------------------------------------------- % 0.14/0.52 %------------------------------------------------------------------------------ % 0.14/0.52 % File : NUM557+3 : TPTP v8.2.0. Released v4.0.0. % 0.14/0.52 % Domain : Number Theory % 0.14/0.52 % Problem : Ramsey's Infinite Theorem 12_05_02_03, 02 expansion % 0.14/0.52 % Version : Especial. % 0.14/0.52 % English : % 0.14/0.52 % 0.14/0.52 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.14/0.52 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.14/0.52 % Source : [Pas08] % 0.14/0.52 % Names : ramsey_12_05_02_03.02 [Pas08] % 0.14/0.52 % 0.14/0.52 % Status : Theorem % 0.14/0.52 % Rating : 0.08 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.10 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.70 v4.0.0 % 0.14/0.52 % Syntax : Number of formulae : 73 ( 7 unt; 8 def) % 0.14/0.52 % Number of atoms : 315 ( 52 equ) % 0.14/0.52 % Maximal formula atoms : 43 ( 4 avg) % 0.14/0.52 % Number of connectives : 266 ( 24 ~; 11 |; 110 &) % 0.14/0.52 % ( 20 <=>; 101 =>; 0 <=; 0 <~>) % 0.14/0.52 % Maximal formula depth : 17 ( 5 avg) % 0.14/0.52 % Maximal term depth : 4 ( 1 avg) % 0.14/0.52 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 0.14/0.52 % Number of functors : 18 ( 18 usr; 10 con; 0-2 aty) % 0.14/0.52 % Number of variables : 123 ( 118 !; 5 ?) % 0.14/0.52 % SPC : FOF_THM_RFO_SEQ % 0.14/0.52 % 0.14/0.52 % Comments : Problem generated by the SAD system [VLP07] % 0.14/0.52 %------------------------------------------------------------------------------ % 0.14/0.52 fof(mSetSort,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( aSet0(W0) % 0.14/0.52 => $true ) ). % 0.14/0.52 % 0.14/0.52 fof(mElmSort,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( aElement0(W0) % 0.14/0.52 => $true ) ). % 0.14/0.52 % 0.14/0.52 fof(mEOfElem,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( aSet0(W0) % 0.14/0.52 => ! [W1] : % 0.14/0.52 ( aElementOf0(W1,W0) % 0.14/0.52 => aElement0(W1) ) ) ). % 0.14/0.52 % 0.14/0.52 fof(mFinRel,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( aSet0(W0) % 0.14/0.52 => ( isFinite0(W0) % 0.14/0.52 => $true ) ) ). % 0.14/0.52 % 0.14/0.52 fof(mDefEmp,definition, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( W0 = slcrc0 % 0.14/0.52 <=> ( aSet0(W0) % 0.14/0.52 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 0.14/0.52 % 0.14/0.52 fof(mEmpFin,axiom, % 0.14/0.52 isFinite0(slcrc0) ). % 0.14/0.52 % 0.14/0.52 fof(mCntRel,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( aSet0(W0) % 0.14/0.52 => ( isCountable0(W0) % 0.14/0.52 => $true ) ) ). % 0.14/0.52 % 0.14/0.52 fof(mCountNFin,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( ( aSet0(W0) % 0.14/0.52 & isCountable0(W0) ) % 0.14/0.52 => ~ isFinite0(W0) ) ). % 0.14/0.52 % 0.14/0.52 fof(mCountNFin_01,axiom, % 0.14/0.52 ! [W0] : % 0.14/0.52 ( ( aSet0(W0) % 0.14/0.53 & isCountable0(W0) ) % 0.14/0.53 => W0 != slcrc0 ) ). % 0.14/0.53 % 0.14/0.53 fof(mDefSub,definition, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aSet0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( aSubsetOf0(W1,W0) % 0.14/0.53 <=> ( aSet0(W1) % 0.14/0.53 & ! [W2] : % 0.14/0.53 ( aElementOf0(W2,W1) % 0.14/0.53 => aElementOf0(W2,W0) ) ) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSubFSet,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( ( aSet0(W0) % 0.14/0.53 & isFinite0(W0) ) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( aSubsetOf0(W1,W0) % 0.14/0.53 => isFinite0(W1) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSubRefl,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aSet0(W0) % 0.14/0.53 => aSubsetOf0(W0,W0) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSubASymm,axiom, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aSet0(W0) % 0.14/0.53 & aSet0(W1) ) % 0.14/0.53 => ( ( aSubsetOf0(W0,W1) % 0.14/0.53 & aSubsetOf0(W1,W0) ) % 0.14/0.53 => W0 = W1 ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSubTrans,axiom, % 0.14/0.53 ! [W0,W1,W2] : % 0.14/0.53 ( ( aSet0(W0) % 0.14/0.53 & aSet0(W1) % 0.14/0.53 & aSet0(W2) ) % 0.14/0.53 => ( ( aSubsetOf0(W0,W1) % 0.14/0.53 & aSubsetOf0(W1,W2) ) % 0.14/0.53 => aSubsetOf0(W0,W2) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mDefCons,definition, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aSet0(W0) % 0.14/0.53 & aElement0(W1) ) % 0.14/0.53 => ! [W2] : % 0.14/0.53 ( W2 = sdtpldt0(W0,W1) % 0.14/0.53 <=> ( aSet0(W2) % 0.14/0.53 & ! [W3] : % 0.14/0.53 ( aElementOf0(W3,W2) % 0.14/0.53 <=> ( aElement0(W3) % 0.14/0.53 & ( aElementOf0(W3,W0) % 0.14/0.53 | W3 = W1 ) ) ) ) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mDefDiff,definition, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aSet0(W0) % 0.14/0.53 & aElement0(W1) ) % 0.14/0.53 => ! [W2] : % 0.14/0.53 ( W2 = sdtmndt0(W0,W1) % 0.14/0.53 <=> ( aSet0(W2) % 0.14/0.53 & ! [W3] : % 0.14/0.53 ( aElementOf0(W3,W2) % 0.14/0.53 <=> ( aElement0(W3) % 0.14/0.53 & aElementOf0(W3,W0) % 0.14/0.53 & W3 != W1 ) ) ) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mConsDiff,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aSet0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( aElementOf0(W1,W0) % 0.14/0.53 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mDiffCons,axiom, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aElement0(W0) % 0.14/0.53 & aSet0(W1) ) % 0.14/0.53 => ( ~ aElementOf0(W0,W1) % 0.14/0.53 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mCConsSet,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElement0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( ( aSet0(W1) % 0.14/0.53 & isCountable0(W1) ) % 0.14/0.53 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mCDiffSet,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElement0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( ( aSet0(W1) % 0.14/0.53 & isCountable0(W1) ) % 0.14/0.53 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mFConsSet,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElement0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( ( aSet0(W1) % 0.14/0.53 & isFinite0(W1) ) % 0.14/0.53 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mFDiffSet,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElement0(W0) % 0.14/0.53 => ! [W1] : % 0.14/0.53 ( ( aSet0(W1) % 0.14/0.53 & isFinite0(W1) ) % 0.14/0.53 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mNATSet,axiom, % 0.14/0.53 ( aSet0(szNzAzT0) % 0.14/0.53 & isCountable0(szNzAzT0) ) ). % 0.14/0.53 % 0.14/0.53 fof(mZeroNum,axiom, % 0.14/0.53 aElementOf0(sz00,szNzAzT0) ). % 0.14/0.53 % 0.14/0.53 fof(mSuccNum,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 0.14/0.53 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSuccEquSucc,axiom, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.14/0.53 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.14/0.53 => W0 = W1 ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mNatExtra,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 => ( W0 = sz00 % 0.14/0.53 | ? [W1] : % 0.14/0.53 ( aElementOf0(W1,szNzAzT0) % 0.14/0.53 & W0 = szszuzczcdt0(W1) ) ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mNatNSucc,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 => W0 != szszuzczcdt0(W0) ) ). % 0.14/0.53 % 0.14/0.53 fof(mLessRel,axiom, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.14/0.53 => ( sdtlseqdt0(W0,W1) % 0.14/0.53 => $true ) ) ). % 0.14/0.53 % 0.14/0.53 fof(mZeroLess,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 => sdtlseqdt0(sz00,W0) ) ). % 0.14/0.53 % 0.14/0.53 fof(mNoScLessZr,axiom, % 0.14/0.53 ! [W0] : % 0.14/0.53 ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 0.14/0.53 % 0.14/0.53 fof(mSuccLess,axiom, % 0.14/0.53 ! [W0,W1] : % 0.14/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.14/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( sdtlseqdt0(W0,W1) % 0.46/0.53 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mLessSucc,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 0.46/0.53 % 0.46/0.53 fof(mLessRefl,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => sdtlseqdt0(W0,W0) ) ). % 0.46/0.53 % 0.46/0.53 fof(mLessASymm,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( ( sdtlseqdt0(W0,W1) % 0.46/0.53 & sdtlseqdt0(W1,W0) ) % 0.46/0.53 => W0 = W1 ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mLessTrans,axiom, % 0.46/0.53 ! [W0,W1,W2] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) % 0.46/0.53 & aElementOf0(W2,szNzAzT0) ) % 0.46/0.53 => ( ( sdtlseqdt0(W0,W1) % 0.46/0.53 & sdtlseqdt0(W1,W2) ) % 0.46/0.53 => sdtlseqdt0(W0,W2) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mLessTotal,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( sdtlseqdt0(W0,W1) % 0.46/0.53 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mIHSort,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( iLess0(W0,W1) % 0.46/0.53 => $true ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mIH,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardS,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aSet0(W0) % 0.46/0.53 => aElement0(sbrdtbr0(W0)) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardNum,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aSet0(W0) % 0.46/0.53 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 0.46/0.53 <=> isFinite0(W0) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardEmpty,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aSet0(W0) % 0.46/0.53 => ( sbrdtbr0(W0) = sz00 % 0.46/0.53 <=> W0 = slcrc0 ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardCons,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & isFinite0(W0) ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( aElement0(W1) % 0.46/0.53 => ( ~ aElementOf0(W1,W0) % 0.46/0.53 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardDiff,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aSet0(W0) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( ( isFinite0(W0) % 0.46/0.53 & aElementOf0(W1,W0) ) % 0.46/0.53 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardSub,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aSet0(W0) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( ( isFinite0(W0) % 0.46/0.53 & aSubsetOf0(W1,W0) ) % 0.46/0.53 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardSubEx,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( ( isFinite0(W0) % 0.46/0.53 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 0.46/0.53 => ? [W2] : % 0.46/0.53 ( aSubsetOf0(W2,W0) % 0.46/0.53 & sbrdtbr0(W2) = W1 ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mDefMin,definition, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSubsetOf0(W0,szNzAzT0) % 0.46/0.53 & W0 != slcrc0 ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( W1 = szmzizndt0(W0) % 0.46/0.53 <=> ( aElementOf0(W1,W0) % 0.46/0.53 & ! [W2] : % 0.46/0.53 ( aElementOf0(W2,W0) % 0.46/0.53 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mDefMax,definition, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSubsetOf0(W0,szNzAzT0) % 0.46/0.53 & isFinite0(W0) % 0.46/0.53 & W0 != slcrc0 ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( W1 = szmzazxdt0(W0) % 0.46/0.53 <=> ( aElementOf0(W1,W0) % 0.46/0.53 & ! [W2] : % 0.46/0.53 ( aElementOf0(W2,W0) % 0.46/0.53 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mMinMin,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aSubsetOf0(W0,szNzAzT0) % 0.46/0.53 & aSubsetOf0(W1,szNzAzT0) % 0.46/0.53 & W0 != slcrc0 % 0.46/0.53 & W1 != slcrc0 ) % 0.46/0.53 => ( ( aElementOf0(szmzizndt0(W0),W1) % 0.46/0.53 & aElementOf0(szmzizndt0(W1),W0) ) % 0.46/0.53 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mDefSeg,definition, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( W1 = slbdtrb0(W0) % 0.46/0.53 <=> ( aSet0(W1) % 0.46/0.53 & ! [W2] : % 0.46/0.53 ( aElementOf0(W2,W1) % 0.46/0.53 <=> ( aElementOf0(W2,szNzAzT0) % 0.46/0.53 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSegFin,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => isFinite0(slbdtrb0(W0)) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSegZero,axiom, % 0.46/0.53 slbdtrb0(sz00) = slcrc0 ). % 0.46/0.53 % 0.46/0.53 fof(mSegSucc,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 0.46/0.53 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 0.46/0.53 | W0 = W1 ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSegLess,axiom, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ( sdtlseqdt0(W0,W1) % 0.46/0.53 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mFinSubSeg,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSubsetOf0(W0,szNzAzT0) % 0.46/0.53 & isFinite0(W0) ) % 0.46/0.53 => ? [W1] : % 0.46/0.53 ( aElementOf0(W1,szNzAzT0) % 0.46/0.53 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mCardSeg,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( aElementOf0(W0,szNzAzT0) % 0.46/0.53 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 0.46/0.53 % 0.46/0.53 fof(mDefSel,definition, % 0.46/0.53 ! [W0,W1] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & aElementOf0(W1,szNzAzT0) ) % 0.46/0.53 => ! [W2] : % 0.46/0.53 ( W2 = slbdtsldtrb0(W0,W1) % 0.46/0.53 <=> ( aSet0(W2) % 0.46/0.53 & ! [W3] : % 0.46/0.53 ( aElementOf0(W3,W2) % 0.46/0.53 <=> ( aSubsetOf0(W3,W0) % 0.46/0.53 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSelFSet,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & isFinite0(W0) ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( aElementOf0(W1,szNzAzT0) % 0.46/0.53 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSelNSet,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & ~ isFinite0(W0) ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( aElementOf0(W1,szNzAzT0) % 0.46/0.53 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 0.46/0.53 % 0.46/0.53 fof(mSelCSet,axiom, % 0.46/0.53 ! [W0] : % 0.46/0.53 ( ( aSet0(W0) % 0.46/0.53 & isCountable0(W0) ) % 0.46/0.53 => ! [W1] : % 0.46/0.53 ( ( aElementOf0(W1,szNzAzT0) % 0.46/0.53 & W1 != sz00 ) % 0.46/0.53 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2202,hypothesis, % 0.46/0.53 aElementOf0(xk,szNzAzT0) ). % 0.46/0.53 % 0.46/0.53 fof(m__2202_02,hypothesis, % 0.46/0.53 ( aSet0(xS) % 0.46/0.53 & aSet0(xT) % 0.46/0.53 & xk != sz00 ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2227,hypothesis, % 0.46/0.53 ( aSet0(slbdtsldtrb0(xS,xk)) % 0.46/0.53 & ! [W0] : % 0.46/0.53 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.46/0.53 => ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xS) ) % 0.46/0.53 & aSubsetOf0(W0,xS) % 0.46/0.53 & sbrdtbr0(W0) = xk ) ) % 0.46/0.53 & ( ( ( ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xS) ) ) % 0.46/0.53 | aSubsetOf0(W0,xS) ) % 0.46/0.53 & sbrdtbr0(W0) = xk ) % 0.46/0.53 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.46/0.53 & aSet0(slbdtsldtrb0(xT,xk)) % 0.46/0.53 & ! [W0] : % 0.46/0.53 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk)) % 0.46/0.53 => ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xT) ) % 0.46/0.53 & aSubsetOf0(W0,xT) % 0.46/0.53 & sbrdtbr0(W0) = xk ) ) % 0.46/0.53 & ( ( ( ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xT) ) ) % 0.46/0.53 | aSubsetOf0(W0,xT) ) % 0.46/0.53 & sbrdtbr0(W0) = xk ) % 0.46/0.53 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) % 0.46/0.53 & ! [W0] : % 0.46/0.53 ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.46/0.53 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) % 0.46/0.53 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) % 0.46/0.53 & ~ ( ! [W0] : % 0.46/0.53 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.46/0.53 => ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xS) ) % 0.46/0.53 & aSubsetOf0(W0,xS) % 0.46/0.53 & sbrdtbr0(W0) = xk ) ) % 0.46/0.53 & ( ( ( ( aSet0(W0) % 0.46/0.53 & ! [W1] : % 0.46/0.53 ( aElementOf0(W1,W0) % 0.46/0.53 => aElementOf0(W1,xS) ) ) % 0.46/0.53 | aSubsetOf0(W0,xS) ) % 0.46/0.53 & sbrdtbr0(W0) = xk ) % 0.46/0.53 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.46/0.53 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.46/0.53 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2256,hypothesis, % 0.46/0.53 aElementOf0(xx,xS) ). % 0.46/0.53 % 0.46/0.53 fof(m__2270,hypothesis, % 0.46/0.53 ( aSet0(xQ) % 0.46/0.53 & ! [W0] : % 0.46/0.53 ( aElementOf0(W0,xQ) % 0.46/0.53 => aElementOf0(W0,xS) ) % 0.46/0.53 & aSubsetOf0(xQ,xS) % 0.46/0.53 & sbrdtbr0(xQ) = xk % 0.46/0.53 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2291,hypothesis, % 0.46/0.53 ( aSet0(xQ) % 0.46/0.53 & isFinite0(xQ) % 0.46/0.53 & sbrdtbr0(xQ) = xk ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2304,hypothesis, % 0.46/0.53 ( aElement0(xy) % 0.46/0.53 & aElementOf0(xy,xQ) ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2323,hypothesis, % 0.46/0.53 ~ aElementOf0(xx,xQ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2338,hypothesis, % 0.46/0.53 ~ aElementOf0(xx,xQ) ). % 0.46/0.53 % 0.46/0.53 fof(m__2357,hypothesis, % 0.46/0.53 ( aSet0(sdtmndt0(xQ,xy)) % 0.46/0.53 & ! [W0] : % 0.46/0.53 ( aElementOf0(W0,sdtmndt0(xQ,xy)) % 0.46/0.53 <=> ( aElement0(W0) % 0.46/0.53 & aElementOf0(W0,xQ) % 0.46/0.53 & W0 != xy ) ) % 0.46/0.54 & aSet0(xP) % 0.46/0.54 & ! [W0] : % 0.46/0.54 ( aElementOf0(W0,xP) % 0.46/0.54 <=> ( aElement0(W0) % 0.46/0.54 & ( aElementOf0(W0,sdtmndt0(xQ,xy)) % 0.46/0.54 | W0 = xx ) ) ) % 0.46/0.54 & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ). % 0.46/0.54 % 0.46/0.54 fof(m__2411,hypothesis, % 0.46/0.54 ( ~ aElementOf0(xx,sdtmndt0(xQ,xy)) % 0.46/0.54 & aSet0(sdtmndt0(xQ,xy)) % 0.46/0.54 & ! [W0] : % 0.46/0.54 ( aElementOf0(W0,sdtmndt0(xQ,xy)) % 0.46/0.54 <=> ( aElement0(W0) % 0.46/0.54 & aElementOf0(W0,xQ) % 0.46/0.54 & W0 != xy ) ) ) ). % 0.46/0.54 % 0.46/0.54 fof(m__2431,hypothesis, % 0.46/0.54 ( ! [W0] : % 0.46/0.54 ( aElementOf0(W0,xP) % 0.46/0.54 => aElementOf0(W0,xS) ) % 0.46/0.54 & aSubsetOf0(xP,xS) % 0.46/0.54 & sbrdtbr0(xP) = xk ) ). % 0.46/0.54 % 0.46/0.54 fof(m__,conjecture, % 0.46/0.54 ( ( ( ! [W0] : % 0.46/0.54 ( aElementOf0(W0,xP) % 0.46/0.54 => aElementOf0(W0,xS) ) % 0.46/0.54 | aSubsetOf0(xP,xS) ) % 0.46/0.54 & sbrdtbr0(xP) = xk ) % 0.46/0.54 | aElementOf0(xP,slbdtsldtrb0(xS,xk)) ) ). % 0.46/0.54 % 0.46/0.54 %------------------------------------------------------------------------------ % 0.46/0.54 %------------------------------------------- % 0.46/0.54 % Proof found % 0.46/0.54 % SZS status Theorem for theBenchmark % 0.46/0.54 % SZS output start Proof % 0.46/0.54 %ClaNum:223(EqnAxiom:51) % 0.46/0.54 %VarNum:794(SingletonVarNum:247) % 0.46/0.54 %MaxLitNum:8 % 0.46/0.54 %MaxfuncDepth:3 % 0.46/0.54 %SharedTerms:53 % 0.46/0.54 %goalClause: 85 89 95 96 % 0.46/0.54 %singleGoalClaCount:1 % 0.46/0.54 [56]P1(a26) % 0.46/0.54 [57]P1(a31) % 0.46/0.54 [58]P1(a32) % 0.46/0.54 [60]P1(a1) % 0.46/0.54 [61]P1(a19) % 0.46/0.54 [62]P2(a33) % 0.46/0.54 [63]P4(a24) % 0.46/0.54 [64]P4(a1) % 0.46/0.54 [65]P5(a26) % 0.46/0.54 [66]P3(a20,a26) % 0.46/0.54 [67]P3(a30,a26) % 0.46/0.54 [68]P3(a34,a31) % 0.46/0.54 [69]P3(a33,a1) % 0.46/0.54 [70]P6(a1,a31) % 0.46/0.54 [71]P6(a19,a31) % 0.46/0.54 [80]~E(a20,a30) % 0.46/0.54 [83]~P3(a34,a1) % 0.46/0.54 [53]E(f2(a1),a30) % 0.46/0.54 [54]E(f2(a19),a30) % 0.46/0.54 [55]E(f21(a20),a24) % 0.46/0.54 [73]P1(f22(a1,a33)) % 0.46/0.54 [74]P1(f25(a31,a30)) % 0.46/0.54 [75]P1(f25(a32,a30)) % 0.46/0.54 [77]P3(a1,f25(a31,a30)) % 0.46/0.54 [78]P3(a3,f25(a31,a30)) % 0.46/0.54 [79]P6(f25(a31,a30),f25(a32,a30)) % 0.46/0.54 [81]~E(f25(a31,a30),a24) % 0.46/0.54 [84]~P3(a34,f22(a1,a33)) % 0.46/0.54 [85]~P3(a19,f25(a31,a30)) % 0.46/0.54 [76]E(f23(f22(a1,a33),a34),a19) % 0.46/0.54 [89]P3(a9,a19)+~E(f2(a19),a30) % 0.46/0.54 [95]~P3(a9,a31)+~E(f2(a19),a30) % 0.46/0.54 [96]~P6(a19,a31)+~E(f2(a19),a30) % 0.46/0.54 [86]P1(x861)+~E(x861,a24) % 0.46/0.54 [93]~P1(x931)+P6(x931,x931) % 0.46/0.54 [97]P2(x971)+~P3(x971,a19) % 0.46/0.54 [104]~P3(x1041,a1)+P3(x1041,a31) % 0.46/0.54 [105]~P3(x1051,a19)+P3(x1051,a31) % 0.46/0.54 [106]~P3(x1061,a26)+P8(a20,x1061) % 0.46/0.54 [112]P8(x1121,x1121)+~P3(x1121,a26) % 0.46/0.54 [91]~P1(x911)+P2(f2(x911)) % 0.46/0.54 [99]~P3(x991,a26)+~E(f27(x991),a20) % 0.46/0.54 [100]~P3(x1001,a26)+~E(f27(x1001),x1001) % 0.46/0.54 [102]~P3(x1021,a26)+P4(f21(x1021)) % 0.46/0.54 [113]~P3(x1131,a26)+P3(f27(x1131),a26) % 0.46/0.54 [114]~P3(x1141,a26)+P8(x1141,f27(x1141)) % 0.46/0.54 [115]~P3(x1151,a26)+P7(x1151,f27(x1151)) % 0.46/0.54 [123]~P3(x1231,a26)+~P8(f27(x1231),a20) % 0.46/0.54 [134]~E(x1341,a33)+~P3(x1341,f22(a1,a33)) % 0.46/0.54 [136]~P3(x1361,f25(a31,a30))+E(f2(x1361),a30) % 0.46/0.54 [137]~P3(x1371,f25(a32,a30))+E(f2(x1371),a30) % 0.46/0.54 [139]P1(x1391)+~P3(x1391,f25(a31,a30)) % 0.46/0.54 [140]P1(x1401)+~P3(x1401,f25(a32,a30)) % 0.46/0.54 [142]P2(x1421)+~P3(x1421,f22(a1,a33)) % 0.46/0.54 [159]P3(x1591,a1)+~P3(x1591,f22(a1,a33)) % 0.46/0.54 [161]P6(x1611,a31)+~P3(x1611,f25(a31,a30)) % 0.46/0.54 [162]P6(x1621,a32)+~P3(x1621,f25(a32,a30)) % 0.46/0.54 [186]~P3(x1861,f25(a31,a30))+P3(x1861,f25(a32,a30)) % 0.46/0.54 [103]~P3(x1031,a26)+E(f2(f21(x1031)),x1031) % 0.46/0.54 [98]~P3(x982,x981)+~E(x981,a24) % 0.46/0.54 [90]~P1(x901)+~P5(x901)+~E(x901,a24) % 0.46/0.54 [92]~P4(x921)+~P5(x921)+~P1(x921) % 0.46/0.54 [94]~P2(x941)+~E(x941,a34)+P3(x941,a19) % 0.46/0.54 [87]~P1(x871)+~E(x871,a24)+E(f2(x871),a20) % 0.46/0.54 [88]~P1(x881)+E(x881,a24)+~E(f2(x881),a20) % 0.46/0.54 [101]~P1(x1011)+P3(f10(x1011),x1011)+E(x1011,a24) % 0.46/0.54 [109]~P1(x1091)+~P4(x1091)+P3(f2(x1091),a26) % 0.46/0.54 [116]~P3(x1161,a26)+E(x1161,a20)+P3(f11(x1161),a26) % 0.46/0.54 [117]~P1(x1171)+P4(x1171)+~P3(f2(x1171),a26) % 0.46/0.54 [122]~P4(x1221)+~P6(x1221,a26)+P3(f4(x1221),a26) % 0.46/0.54 [131]~P3(x1311,a19)+E(x1311,a34)+P3(x1311,f22(a1,a33)) % 0.46/0.54 [145]~P6(x1451,a31)+P3(x1451,f25(a31,a30))+~E(f2(x1451),a30) % 0.46/0.54 [146]~P6(x1461,a32)+P3(x1461,f25(a32,a30))+~E(f2(x1461),a30) % 0.46/0.54 [172]~P2(x1721)+P3(x1721,a19)+~P3(x1721,f22(a1,a33)) % 0.46/0.54 [107]~P3(x1071,a26)+E(x1071,a20)+E(f27(f11(x1071)),x1071) % 0.46/0.54 [143]~P4(x1431)+~P6(x1431,a26)+P6(x1431,f21(f4(x1431))) % 0.46/0.54 [110]~P6(x1101,x1102)+P1(x1101)+~P1(x1102) % 0.46/0.54 [111]~P3(x1111,x1112)+P2(x1111)+~P1(x1112) % 0.46/0.54 [108]P1(x1081)+~P3(x1082,a26)+~E(x1081,f21(x1082)) % 0.46/0.54 [190]~P3(x1901,x1902)+P3(x1901,a31)+~P3(x1902,f25(a31,a30)) % 0.46/0.54 [191]~P3(x1911,x1912)+P3(x1911,a32)+~P3(x1912,f25(a32,a30)) % 0.46/0.54 [170]~P1(x1701)+~P3(x1702,x1701)+E(f23(f22(x1701,x1702),x1702),x1701) % 0.46/0.54 [149]~P2(x1491)+~P3(x1491,a1)+E(x1491,a33)+P3(x1491,f22(a1,a33)) % 0.46/0.54 [166]~P1(x1661)+P3(f5(x1661),x1661)+P3(x1661,f25(a31,a30))+~E(f2(x1661),a30) % 0.46/0.54 [167]~P1(x1671)+P3(f7(x1671),x1671)+P3(x1671,f25(a32,a30))+~E(f2(x1671),a30) % 0.46/0.54 [168]~P1(x1681)+P3(f8(x1681),x1681)+P3(x1681,f25(a31,a30))+~E(f2(x1681),a30) % 0.46/0.54 [179]~P1(x1791)+P3(x1791,f25(a31,a30))+~E(f2(x1791),a30)+~P3(f5(x1791),a31) % 0.46/0.54 [180]~P1(x1801)+P3(x1801,f25(a31,a30))+~E(f2(x1801),a30)+~P3(f8(x1801),a31) % 0.46/0.54 [181]~P1(x1811)+P3(x1811,f25(a32,a30))+~E(f2(x1811),a30)+~P3(f7(x1811),a32) % 0.46/0.54 [118]~P4(x1182)+~P6(x1181,x1182)+P4(x1181)+~P1(x1182) % 0.46/0.54 [121]P3(x1212,x1211)+~E(x1212,f28(x1211))+~P6(x1211,a26)+E(x1211,a24) % 0.46/0.54 [125]~P1(x1251)+~P2(x1252)+~P4(x1251)+P4(f23(x1251,x1252)) % 0.46/0.54 [126]~P1(x1261)+~P2(x1262)+~P4(x1261)+P4(f22(x1261,x1262)) % 0.46/0.54 [127]~P1(x1271)+~P2(x1272)+~P5(x1271)+P5(f23(x1271,x1272)) % 0.46/0.54 [128]~P1(x1281)+~P2(x1282)+~P5(x1281)+P5(f22(x1281,x1282)) % 0.46/0.54 [129]~P1(x1291)+P4(x1291)+~P3(x1292,a26)+~E(f25(x1291,x1292),a24) % 0.46/0.54 [132]E(x1321,x1322)+~E(f27(x1321),f27(x1322))+~P3(x1322,a26)+~P3(x1321,a26) % 0.46/0.54 [151]~P1(x1512)+~P4(x1512)+~P6(x1511,x1512)+P8(f2(x1511),f2(x1512)) % 0.46/0.54 [154]~P1(x1541)+~P4(x1541)+~P3(x1542,a26)+P4(f25(x1541,x1542)) % 0.46/0.54 [165]~P1(x1651)+~P1(x1652)+P6(x1651,x1652)+P3(f12(x1652,x1651),x1651) % 0.46/0.54 [175]P8(x1751,x1752)+P8(f27(x1752),x1751)+~P3(x1752,a26)+~P3(x1751,a26) % 0.46/0.54 [192]~P8(x1921,x1922)+~P3(x1922,a26)+~P3(x1921,a26)+P6(f21(x1921),f21(x1922)) % 0.46/0.54 [193]~P8(x1931,x1932)+~P3(x1932,a26)+~P3(x1931,a26)+P8(f27(x1931),f27(x1932)) % 0.46/0.54 [195]~P1(x1951)+~P1(x1952)+P6(x1951,x1952)+~P3(f12(x1952,x1951),x1952) % 0.46/0.54 [197]P8(x1971,x1972)+~P3(x1972,a26)+~P3(x1971,a26)+~P6(f21(x1971),f21(x1972)) % 0.46/0.54 [198]P8(x1981,x1982)+~P3(x1982,a26)+~P3(x1981,a26)+~P8(f27(x1981),f27(x1982)) % 0.46/0.54 [169]P3(x1692,x1691)+~P1(x1691)+~P2(x1692)+E(f22(f23(x1691,x1692),x1692),x1691) % 0.46/0.54 [177]~E(x1771,x1772)+~P3(x1772,a26)+~P3(x1771,a26)+P3(x1771,f21(f27(x1772))) % 0.46/0.54 [203]~P3(x2032,a26)+~P3(x2031,a26)+~P3(x2031,f21(x2032))+P3(x2031,f21(f27(x2032))) % 0.46/0.54 [202]~P1(x2021)+~P4(x2021)+~P3(x2022,x2021)+E(f27(f2(f22(x2021,x2022))),f2(x2021)) % 0.46/0.54 [163]~P1(x1632)+~P6(x1633,x1632)+P3(x1631,x1632)+~P3(x1631,x1633) % 0.46/0.54 [119]~P1(x1192)+~P2(x1193)+P1(x1191)+~E(x1191,f23(x1192,x1193)) % 0.46/0.54 [120]~P1(x1202)+~P2(x1203)+P1(x1201)+~E(x1201,f22(x1202,x1203)) % 0.46/0.54 [130]~P1(x1302)+P1(x1301)+~P3(x1303,a26)+~E(x1301,f25(x1302,x1303)) % 0.46/0.54 [152]~P3(x1521,x1522)+~P3(x1523,a26)+P3(x1521,a26)+~E(x1522,f21(x1523)) % 0.46/0.54 [171]~P3(x1711,x1713)+~P3(x1712,a26)+P8(f27(x1711),x1712)+~E(x1713,f21(x1712)) % 0.46/0.54 [147]~P1(x1472)+~P1(x1471)+~P6(x1472,x1471)+~P6(x1471,x1472)+E(x1471,x1472) % 0.46/0.54 [187]~P8(x1872,x1871)+~P8(x1871,x1872)+E(x1871,x1872)+~P3(x1872,a26)+~P3(x1871,a26) % 0.46/0.54 [124]~P4(x1241)+P3(x1242,x1241)+~E(x1242,f29(x1241))+~P6(x1241,a26)+E(x1241,a24) % 0.46/0.54 [157]~P1(x1572)+~P5(x1572)+~P3(x1571,a26)+E(x1571,a20)+P5(f25(x1572,x1571)) % 0.46/0.54 [194]~P3(x1942,x1941)+P3(f15(x1941,x1942),x1941)+~P6(x1941,a26)+E(x1941,a24)+E(x1942,f28(x1941)) % 0.46/0.54 [204]~P1(x2041)+~P4(x2041)+~P3(x2042,a26)+~P8(x2042,f2(x2041))+P6(f16(x2041,x2042),x2041) % 0.46/0.54 [205]~P1(x2051)+P3(f18(x2052,x2051),x2051)+~P3(x2052,a26)+E(x2051,f21(x2052))+P3(f18(x2052,x2051),a26) % 0.46/0.54 [206]~P3(x2062,x2061)+~P6(x2061,a26)+~P8(x2062,f15(x2061,x2062))+E(x2061,a24)+E(x2062,f28(x2061)) % 0.46/0.54 [176]P3(x1762,x1761)+~P1(x1761)+~P2(x1762)+~P4(x1761)+E(f2(f23(x1761,x1762)),f27(f2(x1761))) % 0.46/0.54 [201]~P1(x2011)+~P4(x2011)+~P3(x2012,a26)+~P8(x2012,f2(x2011))+E(f2(f16(x2011,x2012)),x2012) % 0.46/0.54 [207]E(x2071,x2072)+P3(x2071,f21(x2072))+~P3(x2072,a26)+~P3(x2071,a26)+~P3(x2071,f21(f27(x2072))) % 0.46/0.54 [211]~P1(x2111)+P3(f18(x2112,x2111),x2111)+~P3(x2112,a26)+E(x2111,f21(x2112))+P8(f27(f18(x2112,x2111)),x2112) % 0.46/0.54 [164]~P3(x1643,x1641)+P8(x1642,x1643)+~E(x1642,f28(x1641))+~P6(x1641,a26)+E(x1641,a24) % 0.46/0.54 [196]P3(x1961,x1962)+~P3(x1963,a26)+~P3(x1961,a26)+~P8(f27(x1961),x1963)+~E(x1962,f21(x1963)) % 0.46/0.54 [153]~P1(x1534)+~P2(x1532)+~P3(x1531,x1533)+~E(x1531,x1532)+~E(x1533,f22(x1534,x1532)) % 0.46/0.54 [155]~P1(x1553)+~P2(x1554)+~P3(x1551,x1552)+P2(x1551)+~E(x1552,f23(x1553,x1554)) % 0.46/0.54 [156]~P1(x1563)+~P2(x1564)+~P3(x1561,x1562)+P2(x1561)+~E(x1562,f22(x1563,x1564)) % 0.46/0.54 [174]~P1(x1742)+~P2(x1744)+~P3(x1741,x1743)+P3(x1741,x1742)+~E(x1743,f22(x1742,x1744)) % 0.46/0.54 [182]~P1(x1824)+~P3(x1821,x1823)+~P3(x1822,a26)+E(f2(x1821),x1822)+~E(x1823,f25(x1824,x1822)) % 0.46/0.54 [188]~P1(x1882)+~P3(x1881,x1883)+P6(x1881,x1882)+~P3(x1884,a26)+~E(x1883,f25(x1882,x1884)) % 0.46/0.54 [200]~P4(x2001)+~P3(x2002,x2001)+P3(f17(x2001,x2002),x2001)+~P6(x2001,a26)+E(x2001,a24)+E(x2002,f29(x2001)) % 0.46/0.54 [209]~P4(x2091)+~P3(x2092,x2091)+~P6(x2091,a26)+~P8(f17(x2091,x2092),x2092)+E(x2091,a24)+E(x2092,f29(x2091)) % 0.46/0.54 [215]~P1(x2151)+~P3(x2152,a26)+~P3(f18(x2152,x2151),x2151)+E(x2151,f21(x2152))+~P3(f18(x2152,x2151),a26)+~P8(f27(f18(x2152,x2151)),x2152) % 0.46/0.54 [183]~P1(x1832)+~P1(x1831)+~P6(x1833,x1832)+~P6(x1831,x1833)+P6(x1831,x1832)+~P1(x1833) % 0.46/0.54 [210]~P8(x2101,x2103)+P8(x2101,x2102)+~P8(x2103,x2102)+~P3(x2102,a26)+~P3(x2103,a26)+~P3(x2101,a26) % 0.46/0.54 [173]~P4(x1731)+~P3(x1732,x1731)+P8(x1732,x1733)+~E(x1733,f29(x1731))+~P6(x1731,a26)+E(x1731,a24) % 0.46/0.54 [212]~P1(x2121)+~P1(x2122)+~P2(x2123)+P3(f13(x2122,x2123,x2121),x2121)+~E(f13(x2122,x2123,x2121),x2123)+E(x2121,f22(x2122,x2123)) % 0.46/0.54 [213]~P1(x2131)+~P1(x2132)+~P2(x2133)+P3(f14(x2132,x2133,x2131),x2131)+E(x2131,f23(x2132,x2133))+P2(f14(x2132,x2133,x2131)) % 0.46/0.54 [214]~P1(x2141)+~P1(x2142)+~P2(x2143)+P3(f13(x2142,x2143,x2141),x2141)+E(x2141,f22(x2142,x2143))+P2(f13(x2142,x2143,x2141)) % 0.46/0.54 [216]~P1(x2161)+~P1(x2162)+~P2(x2163)+P3(f13(x2162,x2163,x2161),x2161)+P3(f13(x2162,x2163,x2161),x2162)+E(x2161,f22(x2162,x2163)) % 0.46/0.54 [218]~P1(x2181)+~P1(x2182)+P3(f6(x2182,x2183,x2181),x2181)+P6(f6(x2182,x2183,x2181),x2182)+~P3(x2183,a26)+E(x2181,f25(x2182,x2183)) % 0.46/0.54 [217]~P1(x2171)+~P1(x2172)+P3(f6(x2172,x2173,x2171),x2171)+~P3(x2173,a26)+E(x2171,f25(x2172,x2173))+E(f2(f6(x2172,x2173,x2171)),x2173) % 0.46/0.54 [150]~P1(x1504)+~P2(x1503)+~P2(x1501)+P3(x1501,x1502)+~E(x1501,x1503)+~E(x1502,f23(x1504,x1503)) % 0.46/0.54 [178]~P1(x1783)+~P2(x1782)+~P3(x1781,x1784)+E(x1781,x1782)+P3(x1781,x1783)+~E(x1784,f23(x1783,x1782)) % 0.46/0.54 [184]~P1(x1843)+~P2(x1844)+~P2(x1841)+~P3(x1841,x1843)+P3(x1841,x1842)+~E(x1842,f23(x1843,x1844)) % 0.46/0.54 [199]~P1(x1994)+~P6(x1991,x1994)+P3(x1991,x1992)+~P3(x1993,a26)+~E(x1992,f25(x1994,x1993))+~E(f2(x1991),x1993) % 0.46/0.54 [208]E(f28(x2082),f28(x2081))+~P6(x2081,a26)+~P6(x2082,a26)+~P3(f28(x2081),x2082)+~P3(f28(x2082),x2081)+E(x2081,a24)+E(x2082,a24) % 0.46/0.54 [219]~P1(x2191)+~P1(x2192)+~P2(x2193)+E(f14(x2192,x2193,x2191),x2193)+P3(f14(x2192,x2193,x2191),x2191)+P3(f14(x2192,x2193,x2191),x2192)+E(x2191,f23(x2192,x2193)) % 0.46/0.54 [220]~P1(x2201)+~P1(x2202)+~P2(x2203)+~E(f14(x2202,x2203,x2201),x2203)+~P3(f14(x2202,x2203,x2201),x2201)+E(x2201,f23(x2202,x2203))+~P2(f14(x2202,x2203,x2201)) % 0.46/0.54 [221]~P1(x2211)+~P1(x2212)+~P2(x2213)+~P3(f14(x2212,x2213,x2211),x2211)+~P3(f14(x2212,x2213,x2211),x2212)+E(x2211,f23(x2212,x2213))+~P2(f14(x2212,x2213,x2211)) % 0.46/0.54 [222]~P1(x2221)+~P1(x2222)+~P3(x2223,a26)+~P3(f6(x2222,x2223,x2221),x2221)+~P6(f6(x2222,x2223,x2221),x2222)+E(x2221,f25(x2222,x2223))+~E(f2(f6(x2222,x2223,x2221)),x2223) % 0.46/0.54 [185]~P1(x1854)+~P2(x1852)+~P2(x1851)+~P3(x1851,x1854)+E(x1851,x1852)+P3(x1851,x1853)+~E(x1853,f22(x1854,x1852)) % 0.46/0.54 [223]~P1(x2231)+~P1(x2232)+~P2(x2233)+E(f13(x2232,x2233,x2231),x2233)+~P3(f13(x2232,x2233,x2231),x2231)+~P3(f13(x2232,x2233,x2231),x2232)+E(x2231,f22(x2232,x2233))+~P2(f13(x2232,x2233,x2231)) % 0.46/0.54 %EqnAxiom % 0.46/0.54 [1]E(x11,x11) % 0.46/0.54 [2]E(x22,x21)+~E(x21,x22) % 0.46/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.46/0.54 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.46/0.54 [5]~E(x51,x52)+E(f13(x51,x53,x54),f13(x52,x53,x54)) % 0.46/0.54 [6]~E(x61,x62)+E(f13(x63,x61,x64),f13(x63,x62,x64)) % 0.46/0.54 [7]~E(x71,x72)+E(f13(x73,x74,x71),f13(x73,x74,x72)) % 0.46/0.54 [8]~E(x81,x82)+E(f21(x81),f21(x82)) % 0.46/0.54 [9]~E(x91,x92)+E(f22(x91,x93),f22(x92,x93)) % 0.46/0.54 [10]~E(x101,x102)+E(f22(x103,x101),f22(x103,x102)) % 0.46/0.54 [11]~E(x111,x112)+E(f18(x111,x113),f18(x112,x113)) % 0.46/0.54 [12]~E(x121,x122)+E(f18(x123,x121),f18(x123,x122)) % 0.46/0.54 [13]~E(x131,x132)+E(f16(x131,x133),f16(x132,x133)) % 0.46/0.54 [14]~E(x141,x142)+E(f16(x143,x141),f16(x143,x142)) % 0.46/0.54 [15]~E(x151,x152)+E(f25(x151,x153),f25(x152,x153)) % 0.46/0.54 [16]~E(x161,x162)+E(f25(x163,x161),f25(x163,x162)) % 0.46/0.54 [17]~E(x171,x172)+E(f27(x171),f27(x172)) % 0.46/0.54 [18]~E(x181,x182)+E(f28(x181),f28(x182)) % 0.46/0.54 [19]~E(x191,x192)+E(f23(x191,x193),f23(x192,x193)) % 0.46/0.54 [20]~E(x201,x202)+E(f23(x203,x201),f23(x203,x202)) % 0.46/0.54 [21]~E(x211,x212)+E(f15(x211,x213),f15(x212,x213)) % 0.46/0.54 [22]~E(x221,x222)+E(f15(x223,x221),f15(x223,x222)) % 0.46/0.54 [23]~E(x231,x232)+E(f14(x231,x233,x234),f14(x232,x233,x234)) % 0.46/0.54 [24]~E(x241,x242)+E(f14(x243,x241,x244),f14(x243,x242,x244)) % 0.46/0.54 [25]~E(x251,x252)+E(f14(x253,x254,x251),f14(x253,x254,x252)) % 0.46/0.54 [26]~E(x261,x262)+E(f7(x261),f7(x262)) % 0.46/0.54 [27]~E(x271,x272)+E(f8(x271),f8(x272)) % 0.46/0.54 [28]~E(x281,x282)+E(f6(x281,x283,x284),f6(x282,x283,x284)) % 0.46/0.54 [29]~E(x291,x292)+E(f6(x293,x291,x294),f6(x293,x292,x294)) % 0.46/0.54 [30]~E(x301,x302)+E(f6(x303,x304,x301),f6(x303,x304,x302)) % 0.46/0.54 [31]~E(x311,x312)+E(f11(x311),f11(x312)) % 0.46/0.54 [32]~E(x321,x322)+E(f5(x321),f5(x322)) % 0.46/0.54 [33]~E(x331,x332)+E(f12(x331,x333),f12(x332,x333)) % 0.46/0.54 [34]~E(x341,x342)+E(f12(x343,x341),f12(x343,x342)) % 0.46/0.54 [35]~E(x351,x352)+E(f17(x351,x353),f17(x352,x353)) % 0.46/0.54 [36]~E(x361,x362)+E(f17(x363,x361),f17(x363,x362)) % 0.46/0.54 [37]~E(x371,x372)+E(f29(x371),f29(x372)) % 0.46/0.54 [38]~E(x381,x382)+E(f4(x381),f4(x382)) % 0.46/0.54 [39]~E(x391,x392)+E(f10(x391),f10(x392)) % 0.46/0.54 [40]~P1(x401)+P1(x402)+~E(x401,x402) % 0.46/0.54 [41]P3(x412,x413)+~E(x411,x412)+~P3(x411,x413) % 0.46/0.54 [42]P3(x423,x422)+~E(x421,x422)+~P3(x423,x421) % 0.46/0.54 [43]~P4(x431)+P4(x432)+~E(x431,x432) % 0.46/0.54 [44]~P2(x441)+P2(x442)+~E(x441,x442) % 0.46/0.54 [45]P8(x452,x453)+~E(x451,x452)+~P8(x451,x453) % 0.46/0.54 [46]P8(x463,x462)+~E(x461,x462)+~P8(x463,x461) % 0.46/0.54 [47]P6(x472,x473)+~E(x471,x472)+~P6(x471,x473) % 0.46/0.54 [48]P6(x483,x482)+~E(x481,x482)+~P6(x483,x481) % 0.46/0.54 [49]~P5(x491)+P5(x492)+~E(x491,x492) % 0.46/0.54 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503) % 0.46/0.54 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511) % 0.46/0.54 % 0.46/0.54 %------------------------------------------- % 0.46/0.54 cnf(251,plain, % 0.46/0.54 ($false), % 0.46/0.54 inference(scs_inference,[],[71,54,96]), % 0.46/0.54 ['proof']). % 0.46/0.54 % SZS output end Proof % 0.46/0.54 % Total time :0.010000s %------------------------------------------------------------------------------