%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM551+3 : 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 : 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 12:24:59 EDT 2024 % Result : Theorem 5.94s 6.01s % Output : CNFRefutation 5.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : NUM551+3 : TPTP v8.2.0. Released v4.0.0. % 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n001.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Jun 22 20:44:08 EDT 2024 % 0.14/0.36 % CPUTime : % 0.24/0.60 start to proof:theBenchmark % 5.94/5.98 %------------------------------------------- % 5.94/5.98 % File :CSE---1.7 % 5.94/5.98 % Problem :theBenchmark % 5.94/5.98 % Transform :cnf % 5.94/5.98 % Format :tptp:raw % 5.94/5.98 % Command :java -jar mcs_scs.jar %d %s % 5.94/5.98 % 5.94/5.98 % Result :Theorem 5.300000s % 5.94/5.98 % Output :CNFRefutation 5.300000s % 5.94/5.99 %------------------------------------------- % 5.94/5.99 %------------------------------------------------------------------------------ % 5.94/5.99 % File : NUM551+3 : TPTP v8.2.0. Released v4.0.0. % 5.94/5.99 % Domain : Number Theory % 5.94/5.99 % Problem : Ramsey's Infinite Theorem 12_03_02, 02 expansion % 5.94/5.99 % Version : Especial. % 5.94/5.99 % English : % 5.94/5.99 % 5.94/5.99 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 5.94/5.99 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 5.94/5.99 % Source : [Pas08] % 5.94/5.99 % Names : ramsey_12_03_02.02 [Pas08] % 5.94/5.99 % 5.94/5.99 % Status : Theorem % 5.94/5.99 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.70 v4.0.0 % 5.94/5.99 % Syntax : Number of formulae : 68 ( 5 unt; 8 def) % 5.94/5.99 % Number of atoms : 289 ( 47 equ) % 5.94/5.99 % Maximal formula atoms : 43 ( 4 avg) % 5.94/5.99 % Number of connectives : 242 ( 21 ~; 9 |; 96 &) % 5.94/5.99 % ( 17 <=>; 99 =>; 0 <=; 0 <~>) % 5.94/5.99 % Maximal formula depth : 17 ( 5 avg) % 5.94/5.99 % Maximal term depth : 4 ( 1 avg) % 5.94/5.99 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 5.94/5.99 % Number of functors : 16 ( 16 usr; 8 con; 0-2 aty) % 5.94/5.99 % Number of variables : 120 ( 113 !; 7 ?) % 5.94/5.99 % SPC : FOF_THM_RFO_SEQ % 5.94/5.99 % 5.94/5.99 % Comments : Problem generated by the SAD system [VLP07] % 5.94/5.99 %------------------------------------------------------------------------------ % 5.94/5.99 fof(mSetSort,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => $true ) ). % 5.94/5.99 % 5.94/5.99 fof(mElmSort,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aElement0(W0) % 5.94/5.99 => $true ) ). % 5.94/5.99 % 5.94/5.99 fof(mEOfElem,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => ! [W1] : % 5.94/5.99 ( aElementOf0(W1,W0) % 5.94/5.99 => aElement0(W1) ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mFinRel,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => ( isFinite0(W0) % 5.94/5.99 => $true ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mDefEmp,definition, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( W0 = slcrc0 % 5.94/5.99 <=> ( aSet0(W0) % 5.94/5.99 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mEmpFin,axiom, % 5.94/5.99 isFinite0(slcrc0) ). % 5.94/5.99 % 5.94/5.99 fof(mCntRel,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => ( isCountable0(W0) % 5.94/5.99 => $true ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mCountNFin,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( ( aSet0(W0) % 5.94/5.99 & isCountable0(W0) ) % 5.94/5.99 => ~ isFinite0(W0) ) ). % 5.94/5.99 % 5.94/5.99 fof(mCountNFin_01,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( ( aSet0(W0) % 5.94/5.99 & isCountable0(W0) ) % 5.94/5.99 => W0 != slcrc0 ) ). % 5.94/5.99 % 5.94/5.99 fof(mDefSub,definition, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => ! [W1] : % 5.94/5.99 ( aSubsetOf0(W1,W0) % 5.94/5.99 <=> ( aSet0(W1) % 5.94/5.99 & ! [W2] : % 5.94/5.99 ( aElementOf0(W2,W1) % 5.94/5.99 => aElementOf0(W2,W0) ) ) ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mSubFSet,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( ( aSet0(W0) % 5.94/5.99 & isFinite0(W0) ) % 5.94/5.99 => ! [W1] : % 5.94/5.99 ( aSubsetOf0(W1,W0) % 5.94/5.99 => isFinite0(W1) ) ) ). % 5.94/5.99 % 5.94/5.99 fof(mSubRefl,axiom, % 5.94/5.99 ! [W0] : % 5.94/5.99 ( aSet0(W0) % 5.94/5.99 => aSubsetOf0(W0,W0) ) ). % 5.94/5.99 % 5.94/5.99 fof(mSubASymm,axiom, % 5.94/5.99 ! [W0,W1] : % 5.94/5.99 ( ( aSet0(W0) % 5.94/5.99 & aSet0(W1) ) % 5.94/5.99 => ( ( aSubsetOf0(W0,W1) % 5.94/5.99 & aSubsetOf0(W1,W0) ) % 5.94/5.99 => W0 = W1 ) ) ). % 5.94/5.99 % 5.94/6.00 fof(mSubTrans,axiom, % 5.94/6.00 ! [W0,W1,W2] : % 5.94/6.00 ( ( aSet0(W0) % 5.94/6.00 & aSet0(W1) % 5.94/6.00 & aSet0(W2) ) % 5.94/6.00 => ( ( aSubsetOf0(W0,W1) % 5.94/6.00 & aSubsetOf0(W1,W2) ) % 5.94/6.00 => aSubsetOf0(W0,W2) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDefCons,definition, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aSet0(W0) % 5.94/6.00 & aElement0(W1) ) % 5.94/6.00 => ! [W2] : % 5.94/6.00 ( W2 = sdtpldt0(W0,W1) % 5.94/6.00 <=> ( aSet0(W2) % 5.94/6.00 & ! [W3] : % 5.94/6.00 ( aElementOf0(W3,W2) % 5.94/6.00 <=> ( aElement0(W3) % 5.94/6.00 & ( aElementOf0(W3,W0) % 5.94/6.00 | W3 = W1 ) ) ) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDefDiff,definition, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aSet0(W0) % 5.94/6.00 & aElement0(W1) ) % 5.94/6.00 => ! [W2] : % 5.94/6.00 ( W2 = sdtmndt0(W0,W1) % 5.94/6.00 <=> ( aSet0(W2) % 5.94/6.00 & ! [W3] : % 5.94/6.00 ( aElementOf0(W3,W2) % 5.94/6.00 <=> ( aElement0(W3) % 5.94/6.00 & aElementOf0(W3,W0) % 5.94/6.00 & W3 != W1 ) ) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mConsDiff,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( aElementOf0(W1,W0) % 5.94/6.00 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDiffCons,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElement0(W0) % 5.94/6.00 & aSet0(W1) ) % 5.94/6.00 => ( ~ aElementOf0(W0,W1) % 5.94/6.00 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCConsSet,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElement0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( aSet0(W1) % 5.94/6.00 & isCountable0(W1) ) % 5.94/6.00 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCDiffSet,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElement0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( aSet0(W1) % 5.94/6.00 & isCountable0(W1) ) % 5.94/6.00 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mFConsSet,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElement0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( aSet0(W1) % 5.94/6.00 & isFinite0(W1) ) % 5.94/6.00 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mFDiffSet,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElement0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( aSet0(W1) % 5.94/6.00 & isFinite0(W1) ) % 5.94/6.00 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mNATSet,axiom, % 5.94/6.00 ( aSet0(szNzAzT0) % 5.94/6.00 & isCountable0(szNzAzT0) ) ). % 5.94/6.00 % 5.94/6.00 fof(mZeroNum,axiom, % 5.94/6.00 aElementOf0(sz00,szNzAzT0) ). % 5.94/6.00 % 5.94/6.00 fof(mSuccNum,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 5.94/6.00 & szszuzczcdt0(W0) != sz00 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mSuccEquSucc,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 5.94/6.00 => W0 = W1 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mNatExtra,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => ( W0 = sz00 % 5.94/6.00 | ? [W1] : % 5.94/6.00 ( aElementOf0(W1,szNzAzT0) % 5.94/6.00 & W0 = szszuzczcdt0(W1) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mNatNSucc,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => W0 != szszuzczcdt0(W0) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessRel,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( sdtlseqdt0(W0,W1) % 5.94/6.00 => $true ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mZeroLess,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => sdtlseqdt0(sz00,W0) ) ). % 5.94/6.00 % 5.94/6.00 fof(mNoScLessZr,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 5.94/6.00 % 5.94/6.00 fof(mSuccLess,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( sdtlseqdt0(W0,W1) % 5.94/6.00 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessSucc,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessRefl,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => sdtlseqdt0(W0,W0) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessASymm,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( ( sdtlseqdt0(W0,W1) % 5.94/6.00 & sdtlseqdt0(W1,W0) ) % 5.94/6.00 => W0 = W1 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessTrans,axiom, % 5.94/6.00 ! [W0,W1,W2] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) % 5.94/6.00 & aElementOf0(W2,szNzAzT0) ) % 5.94/6.00 => ( ( sdtlseqdt0(W0,W1) % 5.94/6.00 & sdtlseqdt0(W1,W2) ) % 5.94/6.00 => sdtlseqdt0(W0,W2) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mLessTotal,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( sdtlseqdt0(W0,W1) % 5.94/6.00 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mIHSort,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( iLess0(W0,W1) % 5.94/6.00 => $true ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mIH,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardS,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => aElement0(sbrdtbr0(W0)) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardNum,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 5.94/6.00 <=> isFinite0(W0) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardEmpty,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => ( sbrdtbr0(W0) = sz00 % 5.94/6.00 <=> W0 = slcrc0 ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardCons,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( ( aSet0(W0) % 5.94/6.00 & isFinite0(W0) ) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( aElement0(W1) % 5.94/6.00 => ( ~ aElementOf0(W1,W0) % 5.94/6.00 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardDiff,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( isFinite0(W0) % 5.94/6.00 & aElementOf0(W1,W0) ) % 5.94/6.00 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardSub,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aSet0(W0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( ( isFinite0(W0) % 5.94/6.00 & aSubsetOf0(W1,W0) ) % 5.94/6.00 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mCardSubEx,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aSet0(W0) % 5.94/6.00 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.00 => ( ( isFinite0(W0) % 5.94/6.00 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 5.94/6.00 => ? [W2] : % 5.94/6.00 ( aSubsetOf0(W2,W0) % 5.94/6.00 & sbrdtbr0(W2) = W1 ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDefMin,definition, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( ( aSubsetOf0(W0,szNzAzT0) % 5.94/6.00 & W0 != slcrc0 ) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( W1 = szmzizndt0(W0) % 5.94/6.00 <=> ( aElementOf0(W1,W0) % 5.94/6.00 & ! [W2] : % 5.94/6.00 ( aElementOf0(W2,W0) % 5.94/6.00 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDefMax,definition, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( ( aSubsetOf0(W0,szNzAzT0) % 5.94/6.00 & isFinite0(W0) % 5.94/6.00 & W0 != slcrc0 ) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( W1 = szmzazxdt0(W0) % 5.94/6.00 <=> ( aElementOf0(W1,W0) % 5.94/6.00 & ! [W2] : % 5.94/6.00 ( aElementOf0(W2,W0) % 5.94/6.00 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mMinMin,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aSubsetOf0(W0,szNzAzT0) % 5.94/6.00 & aSubsetOf0(W1,szNzAzT0) % 5.94/6.00 & W0 != slcrc0 % 5.94/6.00 & W1 != slcrc0 ) % 5.94/6.00 => ( ( aElementOf0(szmzizndt0(W0),W1) % 5.94/6.00 & aElementOf0(szmzizndt0(W1),W0) ) % 5.94/6.00 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mDefSeg,definition, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => ! [W1] : % 5.94/6.00 ( W1 = slbdtrb0(W0) % 5.94/6.00 <=> ( aSet0(W1) % 5.94/6.00 & ! [W2] : % 5.94/6.00 ( aElementOf0(W2,W1) % 5.94/6.00 <=> ( aElementOf0(W2,szNzAzT0) % 5.94/6.00 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 5.94/6.00 % 5.94/6.00 fof(mSegFin,axiom, % 5.94/6.00 ! [W0] : % 5.94/6.00 ( aElementOf0(W0,szNzAzT0) % 5.94/6.00 => isFinite0(slbdtrb0(W0)) ) ). % 5.94/6.00 % 5.94/6.00 fof(mSegZero,axiom, % 5.94/6.00 slbdtrb0(sz00) = slcrc0 ). % 5.94/6.00 % 5.94/6.00 fof(mSegSucc,axiom, % 5.94/6.00 ! [W0,W1] : % 5.94/6.00 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.01 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.01 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 5.94/6.01 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 5.94/6.01 | W0 = W1 ) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mSegLess,axiom, % 5.94/6.01 ! [W0,W1] : % 5.94/6.01 ( ( aElementOf0(W0,szNzAzT0) % 5.94/6.01 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.01 => ( sdtlseqdt0(W0,W1) % 5.94/6.01 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mFinSubSeg,axiom, % 5.94/6.01 ! [W0] : % 5.94/6.01 ( ( aSubsetOf0(W0,szNzAzT0) % 5.94/6.01 & isFinite0(W0) ) % 5.94/6.01 => ? [W1] : % 5.94/6.01 ( aElementOf0(W1,szNzAzT0) % 5.94/6.01 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mCardSeg,axiom, % 5.94/6.01 ! [W0] : % 5.94/6.01 ( aElementOf0(W0,szNzAzT0) % 5.94/6.01 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 5.94/6.01 % 5.94/6.01 fof(mDefSel,definition, % 5.94/6.01 ! [W0,W1] : % 5.94/6.01 ( ( aSet0(W0) % 5.94/6.01 & aElementOf0(W1,szNzAzT0) ) % 5.94/6.01 => ! [W2] : % 5.94/6.01 ( W2 = slbdtsldtrb0(W0,W1) % 5.94/6.01 <=> ( aSet0(W2) % 5.94/6.01 & ! [W3] : % 5.94/6.01 ( aElementOf0(W3,W2) % 5.94/6.01 <=> ( aSubsetOf0(W3,W0) % 5.94/6.01 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mSelFSet,axiom, % 5.94/6.01 ! [W0] : % 5.94/6.01 ( ( aSet0(W0) % 5.94/6.01 & isFinite0(W0) ) % 5.94/6.01 => ! [W1] : % 5.94/6.01 ( aElementOf0(W1,szNzAzT0) % 5.94/6.01 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mSelNSet,axiom, % 5.94/6.01 ! [W0] : % 5.94/6.01 ( ( aSet0(W0) % 5.94/6.01 & ~ isFinite0(W0) ) % 5.94/6.01 => ! [W1] : % 5.94/6.01 ( aElementOf0(W1,szNzAzT0) % 5.94/6.01 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 5.94/6.01 % 5.94/6.01 fof(mSelCSet,axiom, % 5.94/6.01 ! [W0] : % 5.94/6.01 ( ( aSet0(W0) % 5.94/6.01 & isCountable0(W0) ) % 5.94/6.01 => ! [W1] : % 5.94/6.01 ( ( aElementOf0(W1,szNzAzT0) % 5.94/6.01 & W1 != sz00 ) % 5.94/6.01 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(m__2202,hypothesis, % 5.94/6.01 aElementOf0(xk,szNzAzT0) ). % 5.94/6.01 % 5.94/6.01 fof(m__2202_02,hypothesis, % 5.94/6.01 ( aSet0(xS) % 5.94/6.01 & aSet0(xT) % 5.94/6.01 & xk != sz00 ) ). % 5.94/6.01 % 5.94/6.01 fof(m__2227,hypothesis, % 5.94/6.01 ( aSet0(slbdtsldtrb0(xS,xk)) % 5.94/6.01 & ! [W0] : % 5.94/6.01 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 5.94/6.01 => ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xS) ) % 5.94/6.01 & aSubsetOf0(W0,xS) % 5.94/6.01 & sbrdtbr0(W0) = xk ) ) % 5.94/6.01 & ( ( ( ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xS) ) ) % 5.94/6.01 | aSubsetOf0(W0,xS) ) % 5.94/6.01 & sbrdtbr0(W0) = xk ) % 5.94/6.01 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 5.94/6.01 & aSet0(slbdtsldtrb0(xT,xk)) % 5.94/6.01 & ! [W0] : % 5.94/6.01 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk)) % 5.94/6.01 => ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xT) ) % 5.94/6.01 & aSubsetOf0(W0,xT) % 5.94/6.01 & sbrdtbr0(W0) = xk ) ) % 5.94/6.01 & ( ( ( ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xT) ) ) % 5.94/6.01 | aSubsetOf0(W0,xT) ) % 5.94/6.01 & sbrdtbr0(W0) = xk ) % 5.94/6.01 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) % 5.94/6.01 & ! [W0] : % 5.94/6.01 ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 5.94/6.01 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) % 5.94/6.01 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) % 5.94/6.01 & ~ ( ! [W0] : % 5.94/6.01 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 5.94/6.01 => ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xS) ) % 5.94/6.01 & aSubsetOf0(W0,xS) % 5.94/6.01 & sbrdtbr0(W0) = xk ) ) % 5.94/6.01 & ( ( ( ( aSet0(W0) % 5.94/6.01 & ! [W1] : % 5.94/6.01 ( aElementOf0(W1,W0) % 5.94/6.01 => aElementOf0(W1,xS) ) ) % 5.94/6.01 | aSubsetOf0(W0,xS) ) % 5.94/6.01 & sbrdtbr0(W0) = xk ) % 5.94/6.01 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 5.94/6.01 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 5.94/6.01 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ). % 5.94/6.01 % 5.94/6.01 fof(m__2256,hypothesis, % 5.94/6.01 aElementOf0(xx,xS) ). % 5.94/6.01 % 5.94/6.01 fof(m__2270,hypothesis, % 5.94/6.01 ( aSet0(xQ) % 5.94/6.01 & ! [W0] : % 5.94/6.01 ( aElementOf0(W0,xQ) % 5.94/6.01 => aElementOf0(W0,xS) ) % 5.94/6.01 & aSubsetOf0(xQ,xS) % 5.94/6.01 & sbrdtbr0(xQ) = xk % 5.94/6.01 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ). % 5.94/6.01 % 5.94/6.01 fof(m__2291,hypothesis, % 5.94/6.01 ( aSet0(xQ) % 5.94/6.01 & isFinite0(xQ) % 5.94/6.01 & sbrdtbr0(xQ) = xk ) ). % 5.94/6.01 % 5.94/6.01 fof(m__2313,hypothesis, % 5.94/6.01 ~ ( ~ ? [W0] : aElementOf0(W0,xQ) % 5.94/6.01 | xQ = slcrc0 ) ). % 5.94/6.01 % 5.94/6.01 fof(m__,conjecture, % 5.94/6.01 ? [W0] : % 5.94/6.01 ( aElement0(W0) % 5.94/6.01 & aElementOf0(W0,xQ) ) ). % 5.94/6.01 % 5.94/6.01 %------------------------------------------------------------------------------ % 5.94/6.01 %------------------------------------------- % 5.94/6.01 % Proof found % 5.94/6.01 % SZS status Theorem for theBenchmark % 5.94/6.01 % SZS output start Proof % 5.94/6.01 %ClaNum:198(EqnAxiom:51) % 5.94/6.01 %VarNum:773(SingletonVarNum:239) % 5.94/6.01 %MaxLitNum:8 % 5.94/6.01 %MaxfuncDepth:3 % 5.94/6.01 %SharedTerms:36 % 5.94/6.01 %goalClause: 85 % 5.94/6.01 [55]P1(a25) % 5.94/6.01 [56]P1(a30) % 5.94/6.01 [57]P1(a31) % 5.94/6.01 [59]P1(a1) % 5.94/6.01 [60]P4(a23) % 5.94/6.01 [61]P4(a1) % 5.94/6.01 [62]P5(a25) % 5.94/6.01 [63]P2(a19,a25) % 5.94/6.01 [64]P2(a29,a25) % 5.94/6.01 [65]P2(a32,a30) % 5.94/6.01 [66]P2(a3,a1) % 5.94/6.01 [67]P6(a1,a30) % 5.94/6.01 [73]~E(a19,a29) % 5.94/6.01 [74]~E(a23,a1) % 5.94/6.01 [53]E(f2(a1),a29) % 5.94/6.01 [54]E(f20(a19),a23) % 5.94/6.01 [68]P1(f24(a30,a29)) % 5.94/6.01 [69]P1(f24(a31,a29)) % 5.94/6.01 [70]P2(a1,f24(a30,a29)) % 5.94/6.01 [71]P2(a4,f24(a30,a29)) % 5.94/6.01 [72]P6(f24(a30,a29),f24(a31,a29)) % 5.94/6.01 [75]~E(f24(a30,a29),a23) % 5.94/6.01 [76]P1(x761)+~E(x761,a23) % 5.94/6.01 [82]~P1(x821)+P6(x821,x821) % 5.94/6.01 [85]~P3(x851)+~P2(x851,a1) % 5.94/6.01 [90]~P2(x901,a1)+P2(x901,a30) % 5.94/6.01 [91]~P2(x911,a25)+P8(a19,x911) % 5.94/6.01 [97]P8(x971,x971)+~P2(x971,a25) % 5.94/6.01 [80]~P1(x801)+P3(f2(x801)) % 5.94/6.01 [84]~P2(x841,a25)+~E(f26(x841),a19) % 5.94/6.01 [86]~P2(x861,a25)+~E(f26(x861),x861) % 5.94/6.01 [88]~P2(x881,a25)+P4(f20(x881)) % 5.94/6.01 [98]~P2(x981,a25)+P2(f26(x981),a25) % 5.94/6.01 [99]~P2(x991,a25)+P8(x991,f26(x991)) % 5.94/6.01 [100]~P2(x1001,a25)+P7(x1001,f26(x1001)) % 5.94/6.01 [108]~P2(x1081,a25)+~P8(f26(x1081),a19) % 5.94/6.01 [118]~P2(x1181,f24(a30,a29))+E(f2(x1181),a29) % 5.94/6.01 [119]~P2(x1191,f24(a31,a29))+E(f2(x1191),a29) % 5.94/6.01 [121]P1(x1211)+~P2(x1211,f24(a30,a29)) % 5.94/6.01 [122]P1(x1221)+~P2(x1221,f24(a31,a29)) % 5.94/6.01 [137]P6(x1371,a30)+~P2(x1371,f24(a30,a29)) % 5.94/6.01 [138]P6(x1381,a31)+~P2(x1381,f24(a31,a29)) % 5.94/6.01 [161]~P2(x1611,f24(a30,a29))+P2(x1611,f24(a31,a29)) % 5.94/6.01 [89]~P2(x891,a25)+E(f2(f20(x891)),x891) % 5.94/6.01 [83]~P2(x832,x831)+~E(x831,a23) % 5.94/6.01 [79]~P1(x791)+~P5(x791)+~E(x791,a23) % 5.94/6.01 [81]~P4(x811)+~P5(x811)+~P1(x811) % 5.94/6.01 [77]~P1(x771)+~E(x771,a23)+E(f2(x771),a19) % 5.94/6.01 [78]~P1(x781)+E(x781,a23)+~E(f2(x781),a19) % 5.94/6.01 [87]~P1(x871)+P2(f10(x871),x871)+E(x871,a23) % 5.94/6.01 [94]~P1(x941)+~P4(x941)+P2(f2(x941),a25) % 5.94/6.01 [101]~P2(x1011,a25)+E(x1011,a19)+P2(f11(x1011),a25) % 5.94/6.01 [102]~P1(x1021)+P4(x1021)+~P2(f2(x1021),a25) % 5.94/6.01 [107]~P4(x1071)+~P6(x1071,a25)+P2(f5(x1071),a25) % 5.94/6.01 [125]~P6(x1251,a30)+P2(x1251,f24(a30,a29))+~E(f2(x1251),a29) % 5.94/6.01 [126]~P6(x1261,a31)+P2(x1261,f24(a31,a29))+~E(f2(x1261),a29) % 5.94/6.01 [92]~P2(x921,a25)+E(x921,a19)+E(f26(f11(x921)),x921) % 5.94/6.01 [123]~P4(x1231)+~P6(x1231,a25)+P6(x1231,f20(f5(x1231))) % 5.94/6.01 [95]~P6(x951,x952)+P1(x951)+~P1(x952) % 5.94/6.01 [96]~P2(x961,x962)+P3(x961)+~P1(x962) % 5.94/6.01 [93]P1(x931)+~P2(x932,a25)+~E(x931,f20(x932)) % 5.94/6.01 [165]~P2(x1651,x1652)+P2(x1651,a30)+~P2(x1652,f24(a30,a29)) % 5.94/6.01 [166]~P2(x1661,x1662)+P2(x1661,a31)+~P2(x1662,f24(a31,a29)) % 5.94/6.01 [146]~P1(x1461)+~P2(x1462,x1461)+E(f21(f22(x1461,x1462),x1462),x1461) % 5.94/6.01 [142]~P1(x1421)+P2(f6(x1421),x1421)+P2(x1421,f24(a30,a29))+~E(f2(x1421),a29) % 5.94/6.01 [143]~P1(x1431)+P2(f8(x1431),x1431)+P2(x1431,f24(a31,a29))+~E(f2(x1431),a29) % 5.94/6.01 [144]~P1(x1441)+P2(f9(x1441),x1441)+P2(x1441,f24(a30,a29))+~E(f2(x1441),a29) % 5.94/6.01 [154]~P1(x1541)+P2(x1541,f24(a30,a29))+~E(f2(x1541),a29)+~P2(f6(x1541),a30) % 5.94/6.01 [155]~P1(x1551)+P2(x1551,f24(a30,a29))+~E(f2(x1551),a29)+~P2(f9(x1551),a30) % 5.94/6.01 [156]~P1(x1561)+P2(x1561,f24(a31,a29))+~E(f2(x1561),a29)+~P2(f8(x1561),a31) % 5.94/6.01 [103]~P4(x1032)+~P6(x1031,x1032)+P4(x1031)+~P1(x1032) % 5.94/6.01 [106]P2(x1062,x1061)+~E(x1062,f27(x1061))+~P6(x1061,a25)+E(x1061,a23) % 5.94/6.01 [110]~P1(x1101)+~P3(x1102)+~P4(x1101)+P4(f21(x1101,x1102)) % 5.94/6.01 [111]~P1(x1111)+~P3(x1112)+~P4(x1111)+P4(f22(x1111,x1112)) % 5.94/6.01 [112]~P1(x1121)+~P3(x1122)+~P5(x1121)+P5(f21(x1121,x1122)) % 5.94/6.01 [113]~P1(x1131)+~P3(x1132)+~P5(x1131)+P5(f22(x1131,x1132)) % 5.94/6.01 [114]~P1(x1141)+P4(x1141)+~P2(x1142,a25)+~E(f24(x1141,x1142),a23) % 5.94/6.01 [116]E(x1161,x1162)+~E(f26(x1161),f26(x1162))+~P2(x1162,a25)+~P2(x1161,a25) % 5.94/6.01 [129]~P1(x1292)+~P4(x1292)+~P6(x1291,x1292)+P8(f2(x1291),f2(x1292)) % 5.94/6.01 [132]~P1(x1321)+~P4(x1321)+~P2(x1322,a25)+P4(f24(x1321,x1322)) % 5.94/6.01 [141]~P1(x1411)+~P1(x1412)+P6(x1411,x1412)+P2(f12(x1412,x1411),x1411) % 5.94/6.01 [150]P8(x1501,x1502)+P8(f26(x1502),x1501)+~P2(x1502,a25)+~P2(x1501,a25) % 5.94/6.01 [167]~P8(x1671,x1672)+~P2(x1672,a25)+~P2(x1671,a25)+P6(f20(x1671),f20(x1672)) % 5.94/6.01 [168]~P8(x1681,x1682)+~P2(x1682,a25)+~P2(x1681,a25)+P8(f26(x1681),f26(x1682)) % 5.94/6.01 [170]~P1(x1701)+~P1(x1702)+P6(x1701,x1702)+~P2(f12(x1702,x1701),x1702) % 5.94/6.01 [172]P8(x1721,x1722)+~P2(x1722,a25)+~P2(x1721,a25)+~P6(f20(x1721),f20(x1722)) % 5.94/6.01 [173]P8(x1731,x1732)+~P2(x1732,a25)+~P2(x1731,a25)+~P8(f26(x1731),f26(x1732)) % 5.94/6.01 [145]P2(x1452,x1451)+~P1(x1451)+~P3(x1452)+E(f22(f21(x1451,x1452),x1452),x1451) % 5.94/6.01 [152]~E(x1521,x1522)+~P2(x1522,a25)+~P2(x1521,a25)+P2(x1521,f20(f26(x1522))) % 5.94/6.01 [178]~P2(x1782,a25)+~P2(x1781,a25)+~P2(x1781,f20(x1782))+P2(x1781,f20(f26(x1782))) % 5.94/6.01 [177]~P1(x1771)+~P4(x1771)+~P2(x1772,x1771)+E(f26(f2(f22(x1771,x1772))),f2(x1771)) % 5.94/6.01 [139]~P1(x1392)+~P6(x1393,x1392)+P2(x1391,x1392)+~P2(x1391,x1393) % 5.94/6.01 [104]~P1(x1042)+~P3(x1043)+P1(x1041)+~E(x1041,f21(x1042,x1043)) % 5.94/6.01 [105]~P1(x1052)+~P3(x1053)+P1(x1051)+~E(x1051,f22(x1052,x1053)) % 5.94/6.01 [115]~P1(x1152)+P1(x1151)+~P2(x1153,a25)+~E(x1151,f24(x1152,x1153)) % 5.94/6.01 [130]~P2(x1301,x1302)+~P2(x1303,a25)+P2(x1301,a25)+~E(x1302,f20(x1303)) % 5.94/6.01 [147]~P2(x1471,x1473)+~P2(x1472,a25)+P8(f26(x1471),x1472)+~E(x1473,f20(x1472)) % 5.94/6.01 [127]~P1(x1272)+~P1(x1271)+~P6(x1272,x1271)+~P6(x1271,x1272)+E(x1271,x1272) % 5.94/6.01 [162]~P8(x1622,x1621)+~P8(x1621,x1622)+E(x1621,x1622)+~P2(x1622,a25)+~P2(x1621,a25) % 5.94/6.01 [109]~P4(x1091)+P2(x1092,x1091)+~E(x1092,f28(x1091))+~P6(x1091,a25)+E(x1091,a23) % 5.94/6.01 [135]~P1(x1352)+~P5(x1352)+~P2(x1351,a25)+E(x1351,a19)+P5(f24(x1352,x1351)) % 5.94/6.01 [169]~P2(x1692,x1691)+P2(f15(x1691,x1692),x1691)+~P6(x1691,a25)+E(x1691,a23)+E(x1692,f27(x1691)) % 5.94/6.01 [179]~P1(x1791)+~P4(x1791)+~P2(x1792,a25)+~P8(x1792,f2(x1791))+P6(f16(x1791,x1792),x1791) % 5.94/6.01 [180]~P1(x1801)+P2(f18(x1802,x1801),x1801)+~P2(x1802,a25)+E(x1801,f20(x1802))+P2(f18(x1802,x1801),a25) % 5.94/6.01 [181]~P2(x1812,x1811)+~P6(x1811,a25)+~P8(x1812,f15(x1811,x1812))+E(x1811,a23)+E(x1812,f27(x1811)) % 5.94/6.01 [151]P2(x1512,x1511)+~P1(x1511)+~P3(x1512)+~P4(x1511)+E(f2(f21(x1511,x1512)),f26(f2(x1511))) % 5.94/6.01 [176]~P1(x1761)+~P4(x1761)+~P2(x1762,a25)+~P8(x1762,f2(x1761))+E(f2(f16(x1761,x1762)),x1762) % 5.94/6.01 [182]E(x1821,x1822)+P2(x1821,f20(x1822))+~P2(x1822,a25)+~P2(x1821,a25)+~P2(x1821,f20(f26(x1822))) % 5.94/6.01 [186]~P1(x1861)+P2(f18(x1862,x1861),x1861)+~P2(x1862,a25)+E(x1861,f20(x1862))+P8(f26(f18(x1862,x1861)),x1862) % 5.94/6.01 [140]~P2(x1403,x1401)+P8(x1402,x1403)+~E(x1402,f27(x1401))+~P6(x1401,a25)+E(x1401,a23) % 5.94/6.01 [171]P2(x1711,x1712)+~P2(x1713,a25)+~P2(x1711,a25)+~P8(f26(x1711),x1713)+~E(x1712,f20(x1713)) % 5.94/6.01 [131]~P1(x1314)+~P3(x1312)+~P2(x1311,x1313)+~E(x1311,x1312)+~E(x1313,f22(x1314,x1312)) % 5.94/6.01 [133]~P1(x1333)+~P3(x1334)+~P2(x1331,x1332)+P3(x1331)+~E(x1332,f21(x1333,x1334)) % 5.94/6.01 [134]~P1(x1343)+~P3(x1344)+~P2(x1341,x1342)+P3(x1341)+~E(x1342,f22(x1343,x1344)) % 5.94/6.01 [149]~P1(x1492)+~P3(x1494)+~P2(x1491,x1493)+P2(x1491,x1492)+~E(x1493,f22(x1492,x1494)) % 5.94/6.01 [157]~P1(x1574)+~P2(x1571,x1573)+~P2(x1572,a25)+E(f2(x1571),x1572)+~E(x1573,f24(x1574,x1572)) % 5.94/6.01 [163]~P1(x1632)+~P2(x1631,x1633)+P6(x1631,x1632)+~P2(x1634,a25)+~E(x1633,f24(x1632,x1634)) % 5.94/6.01 [175]~P4(x1751)+~P2(x1752,x1751)+P2(f17(x1751,x1752),x1751)+~P6(x1751,a25)+E(x1751,a23)+E(x1752,f28(x1751)) % 5.94/6.01 [184]~P4(x1841)+~P2(x1842,x1841)+~P6(x1841,a25)+~P8(f17(x1841,x1842),x1842)+E(x1841,a23)+E(x1842,f28(x1841)) % 5.94/6.01 [190]~P1(x1901)+~P2(x1902,a25)+~P2(f18(x1902,x1901),x1901)+E(x1901,f20(x1902))+~P2(f18(x1902,x1901),a25)+~P8(f26(f18(x1902,x1901)),x1902) % 5.94/6.01 [158]~P1(x1582)+~P1(x1581)+~P6(x1583,x1582)+~P6(x1581,x1583)+P6(x1581,x1582)+~P1(x1583) % 5.94/6.01 [185]~P8(x1851,x1853)+P8(x1851,x1852)+~P8(x1853,x1852)+~P2(x1852,a25)+~P2(x1853,a25)+~P2(x1851,a25) % 5.94/6.01 [148]~P4(x1481)+~P2(x1482,x1481)+P8(x1482,x1483)+~E(x1483,f28(x1481))+~P6(x1481,a25)+E(x1481,a23) % 5.94/6.01 [187]~P1(x1871)+~P1(x1872)+~P3(x1873)+P2(f13(x1872,x1873,x1871),x1871)+~E(f13(x1872,x1873,x1871),x1873)+E(x1871,f22(x1872,x1873)) % 5.94/6.01 [188]~P1(x1881)+~P1(x1882)+~P3(x1883)+P2(f14(x1882,x1883,x1881),x1881)+E(x1881,f21(x1882,x1883))+P3(f14(x1882,x1883,x1881)) % 5.94/6.01 [189]~P1(x1891)+~P1(x1892)+~P3(x1893)+P2(f13(x1892,x1893,x1891),x1891)+E(x1891,f22(x1892,x1893))+P3(f13(x1892,x1893,x1891)) % 5.94/6.01 [191]~P1(x1911)+~P1(x1912)+~P3(x1913)+P2(f13(x1912,x1913,x1911),x1911)+P2(f13(x1912,x1913,x1911),x1912)+E(x1911,f22(x1912,x1913)) % 5.94/6.01 [193]~P1(x1931)+~P1(x1932)+P2(f7(x1932,x1933,x1931),x1931)+P6(f7(x1932,x1933,x1931),x1932)+~P2(x1933,a25)+E(x1931,f24(x1932,x1933)) % 5.94/6.01 [192]~P1(x1921)+~P1(x1922)+P2(f7(x1922,x1923,x1921),x1921)+~P2(x1923,a25)+E(x1921,f24(x1922,x1923))+E(f2(f7(x1922,x1923,x1921)),x1923) % 5.94/6.01 [128]~P1(x1284)+~P3(x1283)+~P3(x1281)+P2(x1281,x1282)+~E(x1281,x1283)+~E(x1282,f21(x1284,x1283)) % 5.94/6.01 [153]~P1(x1533)+~P3(x1532)+~P2(x1531,x1534)+E(x1531,x1532)+P2(x1531,x1533)+~E(x1534,f21(x1533,x1532)) % 5.94/6.01 [159]~P1(x1593)+~P3(x1594)+~P3(x1591)+~P2(x1591,x1593)+P2(x1591,x1592)+~E(x1592,f21(x1593,x1594)) % 5.94/6.01 [174]~P1(x1744)+~P6(x1741,x1744)+P2(x1741,x1742)+~P2(x1743,a25)+~E(x1742,f24(x1744,x1743))+~E(f2(x1741),x1743) % 5.94/6.01 [183]E(f27(x1832),f27(x1831))+~P6(x1831,a25)+~P6(x1832,a25)+~P2(f27(x1831),x1832)+~P2(f27(x1832),x1831)+E(x1831,a23)+E(x1832,a23) % 5.94/6.01 [194]~P1(x1941)+~P1(x1942)+~P3(x1943)+E(f14(x1942,x1943,x1941),x1943)+P2(f14(x1942,x1943,x1941),x1941)+P2(f14(x1942,x1943,x1941),x1942)+E(x1941,f21(x1942,x1943)) % 5.94/6.01 [195]~P1(x1951)+~P1(x1952)+~P3(x1953)+~E(f14(x1952,x1953,x1951),x1953)+~P2(f14(x1952,x1953,x1951),x1951)+E(x1951,f21(x1952,x1953))+~P3(f14(x1952,x1953,x1951)) % 5.94/6.01 [196]~P1(x1961)+~P1(x1962)+~P3(x1963)+~P2(f14(x1962,x1963,x1961),x1961)+~P2(f14(x1962,x1963,x1961),x1962)+E(x1961,f21(x1962,x1963))+~P3(f14(x1962,x1963,x1961)) % 5.94/6.01 [197]~P1(x1971)+~P1(x1972)+~P2(x1973,a25)+~P2(f7(x1972,x1973,x1971),x1971)+~P6(f7(x1972,x1973,x1971),x1972)+E(x1971,f24(x1972,x1973))+~E(f2(f7(x1972,x1973,x1971)),x1973) % 5.94/6.01 [160]~P1(x1604)+~P3(x1602)+~P3(x1601)+~P2(x1601,x1604)+E(x1601,x1602)+P2(x1601,x1603)+~E(x1603,f22(x1604,x1602)) % 5.94/6.01 [198]~P1(x1981)+~P1(x1982)+~P3(x1983)+E(f13(x1982,x1983,x1981),x1983)+~P2(f13(x1982,x1983,x1981),x1981)+~P2(f13(x1982,x1983,x1981),x1982)+E(x1981,f22(x1982,x1983))+~P3(f13(x1982,x1983,x1981)) % 5.94/6.01 %EqnAxiom % 5.94/6.01 [1]E(x11,x11) % 5.94/6.01 [2]E(x22,x21)+~E(x21,x22) % 5.94/6.01 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 5.94/6.01 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 5.94/6.01 [5]~E(x51,x52)+E(f13(x51,x53,x54),f13(x52,x53,x54)) % 5.94/6.01 [6]~E(x61,x62)+E(f13(x63,x61,x64),f13(x63,x62,x64)) % 5.94/6.01 [7]~E(x71,x72)+E(f13(x73,x74,x71),f13(x73,x74,x72)) % 5.94/6.01 [8]~E(x81,x82)+E(f20(x81),f20(x82)) % 5.94/6.01 [9]~E(x91,x92)+E(f24(x91,x93),f24(x92,x93)) % 5.94/6.01 [10]~E(x101,x102)+E(f24(x103,x101),f24(x103,x102)) % 5.94/6.01 [11]~E(x111,x112)+E(f27(x111),f27(x112)) % 5.94/6.01 [12]~E(x121,x122)+E(f18(x121,x123),f18(x122,x123)) % 5.94/6.01 [13]~E(x131,x132)+E(f18(x133,x131),f18(x133,x132)) % 5.94/6.01 [14]~E(x141,x142)+E(f9(x141),f9(x142)) % 5.94/6.01 [15]~E(x151,x152)+E(f15(x151,x153),f15(x152,x153)) % 5.94/6.01 [16]~E(x161,x162)+E(f15(x163,x161),f15(x163,x162)) % 5.94/6.01 [17]~E(x171,x172)+E(f22(x171,x173),f22(x172,x173)) % 5.94/6.01 [18]~E(x181,x182)+E(f22(x183,x181),f22(x183,x182)) % 5.94/6.01 [19]~E(x191,x192)+E(f16(x191,x193),f16(x192,x193)) % 5.94/6.01 [20]~E(x201,x202)+E(f16(x203,x201),f16(x203,x202)) % 5.94/6.01 [21]~E(x211,x212)+E(f26(x211),f26(x212)) % 5.94/6.01 [22]~E(x221,x222)+E(f7(x221,x223,x224),f7(x222,x223,x224)) % 5.94/6.01 [23]~E(x231,x232)+E(f7(x233,x231,x234),f7(x233,x232,x234)) % 5.94/6.01 [24]~E(x241,x242)+E(f7(x243,x244,x241),f7(x243,x244,x242)) % 5.94/6.01 [25]~E(x251,x252)+E(f14(x251,x253,x254),f14(x252,x253,x254)) % 5.94/6.01 [26]~E(x261,x262)+E(f14(x263,x261,x264),f14(x263,x262,x264)) % 5.94/6.01 [27]~E(x271,x272)+E(f14(x273,x274,x271),f14(x273,x274,x272)) % 5.94/6.01 [28]~E(x281,x282)+E(f21(x281,x283),f21(x282,x283)) % 5.94/6.01 [29]~E(x291,x292)+E(f21(x293,x291),f21(x293,x292)) % 5.94/6.01 [30]~E(x301,x302)+E(f28(x301),f28(x302)) % 5.94/6.01 [31]~E(x311,x312)+E(f10(x311),f10(x312)) % 5.94/6.01 [32]~E(x321,x322)+E(f17(x321,x323),f17(x322,x323)) % 5.94/6.01 [33]~E(x331,x332)+E(f17(x333,x331),f17(x333,x332)) % 5.94/6.01 [34]~E(x341,x342)+E(f6(x341),f6(x342)) % 5.94/6.01 [35]~E(x351,x352)+E(f12(x351,x353),f12(x352,x353)) % 5.94/6.01 [36]~E(x361,x362)+E(f12(x363,x361),f12(x363,x362)) % 5.94/6.01 [37]~E(x371,x372)+E(f11(x371),f11(x372)) % 5.94/6.01 [38]~E(x381,x382)+E(f8(x381),f8(x382)) % 5.94/6.01 [39]~E(x391,x392)+E(f5(x391),f5(x392)) % 5.94/6.01 [40]~P1(x401)+P1(x402)+~E(x401,x402) % 5.94/6.01 [41]P2(x412,x413)+~E(x411,x412)+~P2(x411,x413) % 5.94/6.01 [42]P2(x423,x422)+~E(x421,x422)+~P2(x423,x421) % 5.94/6.01 [43]~P4(x431)+P4(x432)+~E(x431,x432) % 5.94/6.01 [44]~P3(x441)+P3(x442)+~E(x441,x442) % 5.94/6.01 [45]~P5(x451)+P5(x452)+~E(x451,x452) % 5.94/6.01 [46]P6(x462,x463)+~E(x461,x462)+~P6(x461,x463) % 5.94/6.01 [47]P6(x473,x472)+~E(x471,x472)+~P6(x473,x471) % 5.94/6.01 [48]P8(x482,x483)+~E(x481,x482)+~P8(x481,x483) % 5.94/6.01 [49]P8(x493,x492)+~E(x491,x492)+~P8(x493,x491) % 5.94/6.01 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503) % 5.94/6.01 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511) % 5.94/6.01 % 5.94/6.01 %------------------------------------------- % 5.94/6.01 cnf(226,plain, % 5.94/6.01 (~P3(a3)), % 5.94/6.01 inference(scs_inference,[],[66,85])). % 5.94/6.01 cnf(996,plain, % 5.94/6.01 ($false), % 5.94/6.01 inference(scs_inference,[],[226,66,59,96]), % 5.94/6.01 ['proof']). % 5.94/6.01 % SZS output end Proof % 5.94/6.01 % Total time :5.300000s %------------------------------------------------------------------------------