%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM548+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 : 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 12:24:58 EDT 2024 % Result : Theorem 0.12s 0.56s % Output : CNFRefutation 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : NUM548+3 : 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 % 0.08/0.27 % Computer : n032.cluster.edu % 0.08/0.27 % Model : x86_64 x86_64 % 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.27 % Memory : 8042.1875MB % 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.27 % CPULimit : 300 % 0.08/0.27 % WCLimit : 300 % 0.08/0.27 % DateTime : Sun Jun 23 01:02:08 EDT 2024 % 0.08/0.28 % CPUTime : % 0.12/0.47 start to proof:theBenchmark % 0.12/0.54 %------------------------------------------- % 0.12/0.54 % File :CSE---1.7 % 0.12/0.54 % Problem :theBenchmark % 0.12/0.54 % Transform :cnf % 0.12/0.54 % Format :tptp:raw % 0.12/0.54 % Command :java -jar mcs_scs.jar %d %s % 0.12/0.54 % 0.12/0.54 % Result :Theorem 0.010000s % 0.12/0.54 % Output :CNFRefutation 0.010000s % 0.12/0.54 %------------------------------------------- % 0.12/0.55 %------------------------------------------------------------------------------ % 0.12/0.55 % File : NUM548+3 : TPTP v8.2.0. Released v4.0.0. % 0.12/0.55 % Domain : Number Theory % 0.12/0.55 % Problem : Ramsey's Infinite Theorem 12_02, 02 expansion % 0.12/0.55 % Version : Especial. % 0.12/0.55 % English : % 0.12/0.55 % 0.12/0.55 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.12/0.55 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.12/0.55 % Source : [Pas08] % 0.12/0.55 % Names : ramsey_12_02.02 [Pas08] % 0.12/0.55 % 0.12/0.55 % Status : Theorem % 0.12/0.55 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.23 v6.0.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.10 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.74 v4.0.0 % 0.12/0.55 % Syntax : Number of formulae : 66 ( 6 unt; 8 def) % 0.12/0.55 % Number of atoms : 283 ( 45 equ) % 0.12/0.55 % Maximal formula atoms : 43 ( 4 avg) % 0.12/0.55 % Number of connectives : 236 ( 19 ~; 8 |; 93 &) % 0.12/0.55 % ( 17 <=>; 99 =>; 0 <=; 0 <~>) % 0.12/0.55 % Maximal formula depth : 17 ( 5 avg) % 0.12/0.55 % Maximal term depth : 4 ( 1 avg) % 0.12/0.55 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty) % 0.12/0.55 % Number of functors : 16 ( 16 usr; 8 con; 0-2 aty) % 0.12/0.55 % Number of variables : 118 ( 113 !; 5 ?) % 0.12/0.55 % SPC : FOF_THM_RFO_SEQ % 0.12/0.55 % 0.12/0.55 % Comments : Problem generated by the SAD system [VLP07] % 0.12/0.55 %------------------------------------------------------------------------------ % 0.12/0.55 fof(mSetSort,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => $true ) ). % 0.12/0.55 % 0.12/0.55 fof(mElmSort,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElement0(W0) % 0.12/0.55 => $true ) ). % 0.12/0.55 % 0.12/0.55 fof(mEOfElem,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( aElementOf0(W1,W0) % 0.12/0.55 => aElement0(W1) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mFinRel,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ( isFinite0(W0) % 0.12/0.55 => $true ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mDefEmp,definition, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( W0 = slcrc0 % 0.12/0.55 <=> ( aSet0(W0) % 0.12/0.55 & ~ ? [W1] : aElementOf0(W1,W0) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mEmpFin,axiom, % 0.12/0.55 isFinite0(slcrc0) ). % 0.12/0.55 % 0.12/0.55 fof(mCntRel,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ( isCountable0(W0) % 0.12/0.55 => $true ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCountNFin,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & isCountable0(W0) ) % 0.12/0.55 => ~ isFinite0(W0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCountNFin_01,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & isCountable0(W0) ) % 0.12/0.55 => W0 != slcrc0 ) ). % 0.12/0.55 % 0.12/0.55 fof(mDefSub,definition, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( aSubsetOf0(W1,W0) % 0.12/0.55 <=> ( aSet0(W1) % 0.12/0.55 & ! [W2] : % 0.12/0.55 ( aElementOf0(W2,W1) % 0.12/0.55 => aElementOf0(W2,W0) ) ) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSubFSet,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & isFinite0(W0) ) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( aSubsetOf0(W1,W0) % 0.12/0.55 => isFinite0(W1) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSubRefl,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => aSubsetOf0(W0,W0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSubASymm,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & aSet0(W1) ) % 0.12/0.55 => ( ( aSubsetOf0(W0,W1) % 0.12/0.55 & aSubsetOf0(W1,W0) ) % 0.12/0.55 => W0 = W1 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSubTrans,axiom, % 0.12/0.55 ! [W0,W1,W2] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & aSet0(W1) % 0.12/0.55 & aSet0(W2) ) % 0.12/0.55 => ( ( aSubsetOf0(W0,W1) % 0.12/0.55 & aSubsetOf0(W1,W2) ) % 0.12/0.55 => aSubsetOf0(W0,W2) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mDefCons,definition, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & aElement0(W1) ) % 0.12/0.55 => ! [W2] : % 0.12/0.55 ( W2 = sdtpldt0(W0,W1) % 0.12/0.55 <=> ( aSet0(W2) % 0.12/0.55 & ! [W3] : % 0.12/0.55 ( aElementOf0(W3,W2) % 0.12/0.55 <=> ( aElement0(W3) % 0.12/0.55 & ( aElementOf0(W3,W0) % 0.12/0.55 | W3 = W1 ) ) ) ) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mDefDiff,definition, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & aElement0(W1) ) % 0.12/0.55 => ! [W2] : % 0.12/0.55 ( W2 = sdtmndt0(W0,W1) % 0.12/0.55 <=> ( aSet0(W2) % 0.12/0.55 & ! [W3] : % 0.12/0.55 ( aElementOf0(W3,W2) % 0.12/0.55 <=> ( aElement0(W3) % 0.12/0.55 & aElementOf0(W3,W0) % 0.12/0.55 & W3 != W1 ) ) ) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mConsDiff,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( aElementOf0(W1,W0) % 0.12/0.55 => sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mDiffCons,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElement0(W0) % 0.12/0.55 & aSet0(W1) ) % 0.12/0.55 => ( ~ aElementOf0(W0,W1) % 0.12/0.55 => sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCConsSet,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElement0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( ( aSet0(W1) % 0.12/0.55 & isCountable0(W1) ) % 0.12/0.55 => isCountable0(sdtpldt0(W1,W0)) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCDiffSet,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElement0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( ( aSet0(W1) % 0.12/0.55 & isCountable0(W1) ) % 0.12/0.55 => isCountable0(sdtmndt0(W1,W0)) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mFConsSet,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElement0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( ( aSet0(W1) % 0.12/0.55 & isFinite0(W1) ) % 0.12/0.55 => isFinite0(sdtpldt0(W1,W0)) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mFDiffSet,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElement0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( ( aSet0(W1) % 0.12/0.55 & isFinite0(W1) ) % 0.12/0.55 => isFinite0(sdtmndt0(W1,W0)) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mNATSet,axiom, % 0.12/0.55 ( aSet0(szNzAzT0) % 0.12/0.55 & isCountable0(szNzAzT0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mZeroNum,axiom, % 0.12/0.55 aElementOf0(sz00,szNzAzT0) ). % 0.12/0.55 % 0.12/0.55 fof(mSuccNum,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0) % 0.12/0.55 & szszuzczcdt0(W0) != sz00 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSuccEquSucc,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( szszuzczcdt0(W0) = szszuzczcdt0(W1) % 0.12/0.55 => W0 = W1 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mNatExtra,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => ( W0 = sz00 % 0.12/0.55 | ? [W1] : % 0.12/0.55 ( aElementOf0(W1,szNzAzT0) % 0.12/0.55 & W0 = szszuzczcdt0(W1) ) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mNatNSucc,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => W0 != szszuzczcdt0(W0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessRel,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( sdtlseqdt0(W0,W1) % 0.12/0.55 => $true ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mZeroLess,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => sdtlseqdt0(sz00,W0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mNoScLessZr,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ). % 0.12/0.55 % 0.12/0.55 fof(mSuccLess,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( sdtlseqdt0(W0,W1) % 0.12/0.55 <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessSucc,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessRefl,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => sdtlseqdt0(W0,W0) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessASymm,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( ( sdtlseqdt0(W0,W1) % 0.12/0.55 & sdtlseqdt0(W1,W0) ) % 0.12/0.55 => W0 = W1 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessTrans,axiom, % 0.12/0.55 ! [W0,W1,W2] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) % 0.12/0.55 & aElementOf0(W2,szNzAzT0) ) % 0.12/0.55 => ( ( sdtlseqdt0(W0,W1) % 0.12/0.55 & sdtlseqdt0(W1,W2) ) % 0.12/0.55 => sdtlseqdt0(W0,W2) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mLessTotal,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( sdtlseqdt0(W0,W1) % 0.12/0.55 | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mIHSort,axiom, % 0.12/0.55 ! [W0,W1] : % 0.12/0.55 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.55 => ( iLess0(W0,W1) % 0.12/0.55 => $true ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mIH,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aElementOf0(W0,szNzAzT0) % 0.12/0.55 => iLess0(W0,szszuzczcdt0(W0)) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCardS,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => aElement0(sbrdtbr0(W0)) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCardNum,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ( aElementOf0(sbrdtbr0(W0),szNzAzT0) % 0.12/0.55 <=> isFinite0(W0) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCardEmpty,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ( sbrdtbr0(W0) = sz00 % 0.12/0.55 <=> W0 = slcrc0 ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCardCons,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( ( aSet0(W0) % 0.12/0.55 & isFinite0(W0) ) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( aElement0(W1) % 0.12/0.55 => ( ~ aElementOf0(W1,W0) % 0.12/0.55 => sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ). % 0.12/0.55 % 0.12/0.55 fof(mCardDiff,axiom, % 0.12/0.55 ! [W0] : % 0.12/0.55 ( aSet0(W0) % 0.12/0.55 => ! [W1] : % 0.12/0.55 ( ( isFinite0(W0) % 0.12/0.55 & aElementOf0(W1,W0) ) % 0.12/0.55 => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ). % 0.12/0.55 % 0.12/0.56 fof(mCardSub,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( aSet0(W0) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( ( isFinite0(W0) % 0.12/0.56 & aSubsetOf0(W1,W0) ) % 0.12/0.56 => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mCardSubEx,axiom, % 0.12/0.56 ! [W0,W1] : % 0.12/0.56 ( ( aSet0(W0) % 0.12/0.56 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.56 => ( ( isFinite0(W0) % 0.12/0.56 & sdtlseqdt0(W1,sbrdtbr0(W0)) ) % 0.12/0.56 => ? [W2] : % 0.12/0.56 ( aSubsetOf0(W2,W0) % 0.12/0.56 & sbrdtbr0(W2) = W1 ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mDefMin,definition, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSubsetOf0(W0,szNzAzT0) % 0.12/0.56 & W0 != slcrc0 ) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( W1 = szmzizndt0(W0) % 0.12/0.56 <=> ( aElementOf0(W1,W0) % 0.12/0.56 & ! [W2] : % 0.12/0.56 ( aElementOf0(W2,W0) % 0.12/0.56 => sdtlseqdt0(W1,W2) ) ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mDefMax,definition, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSubsetOf0(W0,szNzAzT0) % 0.12/0.56 & isFinite0(W0) % 0.12/0.56 & W0 != slcrc0 ) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( W1 = szmzazxdt0(W0) % 0.12/0.56 <=> ( aElementOf0(W1,W0) % 0.12/0.56 & ! [W2] : % 0.12/0.56 ( aElementOf0(W2,W0) % 0.12/0.56 => sdtlseqdt0(W2,W1) ) ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mMinMin,axiom, % 0.12/0.56 ! [W0,W1] : % 0.12/0.56 ( ( aSubsetOf0(W0,szNzAzT0) % 0.12/0.56 & aSubsetOf0(W1,szNzAzT0) % 0.12/0.56 & W0 != slcrc0 % 0.12/0.56 & W1 != slcrc0 ) % 0.12/0.56 => ( ( aElementOf0(szmzizndt0(W0),W1) % 0.12/0.56 & aElementOf0(szmzizndt0(W1),W0) ) % 0.12/0.56 => szmzizndt0(W0) = szmzizndt0(W1) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mDefSeg,definition, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( aElementOf0(W0,szNzAzT0) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( W1 = slbdtrb0(W0) % 0.12/0.56 <=> ( aSet0(W1) % 0.12/0.56 & ! [W2] : % 0.12/0.56 ( aElementOf0(W2,W1) % 0.12/0.56 <=> ( aElementOf0(W2,szNzAzT0) % 0.12/0.56 & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSegFin,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( aElementOf0(W0,szNzAzT0) % 0.12/0.56 => isFinite0(slbdtrb0(W0)) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSegZero,axiom, % 0.12/0.56 slbdtrb0(sz00) = slcrc0 ). % 0.12/0.56 % 0.12/0.56 fof(mSegSucc,axiom, % 0.12/0.56 ! [W0,W1] : % 0.12/0.56 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.56 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.56 => ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) % 0.12/0.56 <=> ( aElementOf0(W0,slbdtrb0(W1)) % 0.12/0.56 | W0 = W1 ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSegLess,axiom, % 0.12/0.56 ! [W0,W1] : % 0.12/0.56 ( ( aElementOf0(W0,szNzAzT0) % 0.12/0.56 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.56 => ( sdtlseqdt0(W0,W1) % 0.12/0.56 <=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mFinSubSeg,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSubsetOf0(W0,szNzAzT0) % 0.12/0.56 & isFinite0(W0) ) % 0.12/0.56 => ? [W1] : % 0.12/0.56 ( aElementOf0(W1,szNzAzT0) % 0.12/0.56 & aSubsetOf0(W0,slbdtrb0(W1)) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mCardSeg,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( aElementOf0(W0,szNzAzT0) % 0.12/0.56 => sbrdtbr0(slbdtrb0(W0)) = W0 ) ). % 0.12/0.56 % 0.12/0.56 fof(mDefSel,definition, % 0.12/0.56 ! [W0,W1] : % 0.12/0.56 ( ( aSet0(W0) % 0.12/0.56 & aElementOf0(W1,szNzAzT0) ) % 0.12/0.56 => ! [W2] : % 0.12/0.56 ( W2 = slbdtsldtrb0(W0,W1) % 0.12/0.56 <=> ( aSet0(W2) % 0.12/0.56 & ! [W3] : % 0.12/0.56 ( aElementOf0(W3,W2) % 0.12/0.56 <=> ( aSubsetOf0(W3,W0) % 0.12/0.56 & sbrdtbr0(W3) = W1 ) ) ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSelFSet,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSet0(W0) % 0.12/0.56 & isFinite0(W0) ) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( aElementOf0(W1,szNzAzT0) % 0.12/0.56 => isFinite0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSelNSet,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSet0(W0) % 0.12/0.56 & ~ isFinite0(W0) ) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( aElementOf0(W1,szNzAzT0) % 0.12/0.56 => slbdtsldtrb0(W0,W1) != slcrc0 ) ) ). % 0.12/0.56 % 0.12/0.56 fof(mSelCSet,axiom, % 0.12/0.56 ! [W0] : % 0.12/0.56 ( ( aSet0(W0) % 0.12/0.56 & isCountable0(W0) ) % 0.12/0.56 => ! [W1] : % 0.12/0.56 ( ( aElementOf0(W1,szNzAzT0) % 0.12/0.56 & W1 != sz00 ) % 0.12/0.56 => isCountable0(slbdtsldtrb0(W0,W1)) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(m__2202,hypothesis, % 0.12/0.56 aElementOf0(xk,szNzAzT0) ). % 0.12/0.56 % 0.12/0.56 fof(m__2202_02,hypothesis, % 0.12/0.56 ( aSet0(xS) % 0.12/0.56 & aSet0(xT) % 0.12/0.56 & xk != sz00 ) ). % 0.12/0.56 % 0.12/0.56 fof(m__2227,hypothesis, % 0.12/0.56 ( aSet0(slbdtsldtrb0(xS,xk)) % 0.12/0.56 & ! [W0] : % 0.12/0.56 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.12/0.56 => ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xS) ) % 0.12/0.56 & aSubsetOf0(W0,xS) % 0.12/0.56 & sbrdtbr0(W0) = xk ) ) % 0.12/0.56 & ( ( ( ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xS) ) ) % 0.12/0.56 | aSubsetOf0(W0,xS) ) % 0.12/0.56 & sbrdtbr0(W0) = xk ) % 0.12/0.56 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.12/0.56 & aSet0(slbdtsldtrb0(xT,xk)) % 0.12/0.56 & ! [W0] : % 0.12/0.56 ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk)) % 0.12/0.56 => ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xT) ) % 0.12/0.56 & aSubsetOf0(W0,xT) % 0.12/0.56 & sbrdtbr0(W0) = xk ) ) % 0.12/0.56 & ( ( ( ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xT) ) ) % 0.12/0.56 | aSubsetOf0(W0,xT) ) % 0.12/0.56 & sbrdtbr0(W0) = xk ) % 0.12/0.56 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) % 0.12/0.56 & ! [W0] : % 0.12/0.56 ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.12/0.56 => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) % 0.12/0.56 & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) % 0.12/0.56 & ~ ( ! [W0] : % 0.12/0.56 ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.12/0.56 => ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xS) ) % 0.12/0.56 & aSubsetOf0(W0,xS) % 0.12/0.56 & sbrdtbr0(W0) = xk ) ) % 0.12/0.56 & ( ( ( ( aSet0(W0) % 0.12/0.56 & ! [W1] : % 0.12/0.56 ( aElementOf0(W1,W0) % 0.12/0.56 => aElementOf0(W1,xS) ) ) % 0.12/0.56 | aSubsetOf0(W0,xS) ) % 0.12/0.56 & sbrdtbr0(W0) = xk ) % 0.12/0.56 => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ) % 0.12/0.56 => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) % 0.12/0.56 | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ). % 0.12/0.56 % 0.12/0.56 fof(m__2256,hypothesis, % 0.12/0.56 aElementOf0(xx,xS) ). % 0.12/0.56 % 0.12/0.56 fof(m__2270,hypothesis, % 0.12/0.56 ( aSet0(xQ) % 0.12/0.56 & ! [W0] : % 0.12/0.56 ( aElementOf0(W0,xQ) % 0.12/0.56 => aElementOf0(W0,xS) ) % 0.12/0.56 & aSubsetOf0(xQ,xS) % 0.12/0.56 & sbrdtbr0(xQ) = xk % 0.12/0.56 & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ). % 0.12/0.56 % 0.12/0.56 fof(m__,conjecture, % 0.12/0.56 isFinite0(xQ) ). % 0.12/0.56 % 0.12/0.56 %------------------------------------------------------------------------------ % 0.12/0.56 %------------------------------------------- % 0.12/0.56 % Proof found % 0.12/0.56 % SZS status Theorem for theBenchmark % 0.12/0.56 % SZS output start Proof % 0.12/0.56 %ClaNum:193(EqnAxiom:51) % 0.12/0.56 %VarNum:771(SingletonVarNum:238) % 0.12/0.56 %MaxLitNum:8 % 0.12/0.56 %MaxfuncDepth:3 % 0.12/0.56 %SharedTerms:33 % 0.12/0.56 %goalClause: 70 % 0.12/0.56 %singleGoalClaCount:1 % 0.12/0.56 [54]P1(a24) % 0.12/0.56 [55]P1(a29) % 0.12/0.56 [56]P1(a30) % 0.12/0.56 [57]P1(a1) % 0.12/0.56 [58]P4(a22) % 0.12/0.56 [59]P5(a24) % 0.12/0.56 [60]P2(a18,a24) % 0.12/0.56 [61]P2(a28,a24) % 0.12/0.56 [62]P2(a31,a29) % 0.12/0.56 [63]P6(a1,a29) % 0.12/0.56 [69]~E(a18,a28) % 0.12/0.56 [70]~P4(a1) % 0.12/0.56 [52]E(f2(a1),a28) % 0.12/0.56 [53]E(f19(a18),a22) % 0.12/0.56 [64]P1(f23(a29,a28)) % 0.12/0.56 [65]P1(f23(a30,a28)) % 0.12/0.56 [66]P2(a1,f23(a29,a28)) % 0.12/0.56 [67]P2(a3,f23(a29,a28)) % 0.12/0.56 [68]P6(f23(a29,a28),f23(a30,a28)) % 0.12/0.56 [71]~E(f23(a29,a28),a22) % 0.12/0.56 [72]P1(x721)+~E(x721,a22) % 0.12/0.56 [78]~P1(x781)+P6(x781,x781) % 0.12/0.56 [85]~P2(x851,a1)+P2(x851,a29) % 0.12/0.56 [86]~P2(x861,a24)+P8(a18,x861) % 0.12/0.56 [92]P8(x921,x921)+~P2(x921,a24) % 0.12/0.56 [76]~P1(x761)+P3(f2(x761)) % 0.12/0.56 [80]~P2(x801,a24)+~E(f25(x801),a18) % 0.12/0.56 [81]~P2(x811,a24)+~E(f25(x811),x811) % 0.12/0.56 [83]~P2(x831,a24)+P4(f19(x831)) % 0.12/0.56 [93]~P2(x931,a24)+P2(f25(x931),a24) % 0.12/0.56 [94]~P2(x941,a24)+P8(x941,f25(x941)) % 0.12/0.56 [95]~P2(x951,a24)+P7(x951,f25(x951)) % 0.12/0.56 [103]~P2(x1031,a24)+~P8(f25(x1031),a18) % 0.12/0.56 [113]~P2(x1131,f23(a29,a28))+E(f2(x1131),a28) % 0.12/0.56 [114]~P2(x1141,f23(a30,a28))+E(f2(x1141),a28) % 0.12/0.56 [116]P1(x1161)+~P2(x1161,f23(a29,a28)) % 0.12/0.56 [117]P1(x1171)+~P2(x1171,f23(a30,a28)) % 0.12/0.56 [132]P6(x1321,a29)+~P2(x1321,f23(a29,a28)) % 0.12/0.56 [133]P6(x1331,a30)+~P2(x1331,f23(a30,a28)) % 0.12/0.56 [156]~P2(x1561,f23(a29,a28))+P2(x1561,f23(a30,a28)) % 0.12/0.56 [84]~P2(x841,a24)+E(f2(f19(x841)),x841) % 0.12/0.56 [79]~P2(x792,x791)+~E(x791,a22) % 0.12/0.56 [75]~P1(x751)+~P5(x751)+~E(x751,a22) % 0.12/0.56 [77]~P4(x771)+~P5(x771)+~P1(x771) % 0.12/0.56 [73]~P1(x731)+~E(x731,a22)+E(f2(x731),a18) % 0.12/0.56 [74]~P1(x741)+E(x741,a22)+~E(f2(x741),a18) % 0.12/0.56 [82]~P1(x821)+P2(f9(x821),x821)+E(x821,a22) % 0.12/0.56 [89]~P1(x891)+~P4(x891)+P2(f2(x891),a24) % 0.12/0.56 [96]~P2(x961,a24)+E(x961,a18)+P2(f10(x961),a24) % 0.12/0.56 [97]~P1(x971)+P4(x971)+~P2(f2(x971),a24) % 0.12/0.56 [102]~P4(x1021)+~P6(x1021,a24)+P2(f4(x1021),a24) % 0.12/0.56 [120]~P6(x1201,a29)+P2(x1201,f23(a29,a28))+~E(f2(x1201),a28) % 0.12/0.56 [121]~P6(x1211,a30)+P2(x1211,f23(a30,a28))+~E(f2(x1211),a28) % 0.12/0.56 [87]~P2(x871,a24)+E(x871,a18)+E(f25(f10(x871)),x871) % 0.12/0.56 [118]~P4(x1181)+~P6(x1181,a24)+P6(x1181,f19(f4(x1181))) % 0.12/0.56 [90]~P6(x901,x902)+P1(x901)+~P1(x902) % 0.12/0.56 [91]~P2(x911,x912)+P3(x911)+~P1(x912) % 0.12/0.56 [88]P1(x881)+~P2(x882,a24)+~E(x881,f19(x882)) % 0.12/0.56 [160]~P2(x1601,x1602)+P2(x1601,a29)+~P2(x1602,f23(a29,a28)) % 0.12/0.56 [161]~P2(x1611,x1612)+P2(x1611,a30)+~P2(x1612,f23(a30,a28)) % 0.12/0.56 [141]~P1(x1411)+~P2(x1412,x1411)+E(f20(f21(x1411,x1412),x1412),x1411) % 0.12/0.56 [137]~P1(x1371)+P2(f5(x1371),x1371)+P2(x1371,f23(a29,a28))+~E(f2(x1371),a28) % 0.12/0.56 [138]~P1(x1381)+P2(f7(x1381),x1381)+P2(x1381,f23(a30,a28))+~E(f2(x1381),a28) % 0.12/0.56 [139]~P1(x1391)+P2(f8(x1391),x1391)+P2(x1391,f23(a29,a28))+~E(f2(x1391),a28) % 0.12/0.56 [149]~P1(x1491)+P2(x1491,f23(a29,a28))+~E(f2(x1491),a28)+~P2(f5(x1491),a29) % 0.12/0.56 [150]~P1(x1501)+P2(x1501,f23(a29,a28))+~E(f2(x1501),a28)+~P2(f8(x1501),a29) % 0.12/0.56 [151]~P1(x1511)+P2(x1511,f23(a30,a28))+~E(f2(x1511),a28)+~P2(f7(x1511),a30) % 0.12/0.56 [98]~P4(x982)+~P6(x981,x982)+P4(x981)+~P1(x982) % 0.12/0.56 [101]P2(x1012,x1011)+~E(x1012,f26(x1011))+~P6(x1011,a24)+E(x1011,a22) % 0.12/0.56 [105]~P1(x1051)+~P3(x1052)+~P4(x1051)+P4(f20(x1051,x1052)) % 0.12/0.56 [106]~P1(x1061)+~P3(x1062)+~P4(x1061)+P4(f21(x1061,x1062)) % 0.12/0.56 [107]~P1(x1071)+~P3(x1072)+~P5(x1071)+P5(f20(x1071,x1072)) % 0.12/0.56 [108]~P1(x1081)+~P3(x1082)+~P5(x1081)+P5(f21(x1081,x1082)) % 0.12/0.56 [109]~P1(x1091)+P4(x1091)+~P2(x1092,a24)+~E(f23(x1091,x1092),a22) % 0.12/0.56 [111]E(x1111,x1112)+~E(f25(x1111),f25(x1112))+~P2(x1112,a24)+~P2(x1111,a24) % 0.12/0.56 [124]~P1(x1242)+~P4(x1242)+~P6(x1241,x1242)+P8(f2(x1241),f2(x1242)) % 0.12/0.56 [127]~P1(x1271)+~P4(x1271)+~P2(x1272,a24)+P4(f23(x1271,x1272)) % 0.12/0.56 [136]~P1(x1361)+~P1(x1362)+P6(x1361,x1362)+P2(f11(x1362,x1361),x1361) % 0.12/0.56 [145]P8(x1451,x1452)+P8(f25(x1452),x1451)+~P2(x1452,a24)+~P2(x1451,a24) % 0.12/0.56 [162]~P8(x1621,x1622)+~P2(x1622,a24)+~P2(x1621,a24)+P6(f19(x1621),f19(x1622)) % 0.12/0.56 [163]~P8(x1631,x1632)+~P2(x1632,a24)+~P2(x1631,a24)+P8(f25(x1631),f25(x1632)) % 0.12/0.56 [165]~P1(x1651)+~P1(x1652)+P6(x1651,x1652)+~P2(f11(x1652,x1651),x1652) % 0.12/0.56 [167]P8(x1671,x1672)+~P2(x1672,a24)+~P2(x1671,a24)+~P6(f19(x1671),f19(x1672)) % 0.12/0.56 [168]P8(x1681,x1682)+~P2(x1682,a24)+~P2(x1681,a24)+~P8(f25(x1681),f25(x1682)) % 0.12/0.56 [140]P2(x1402,x1401)+~P1(x1401)+~P3(x1402)+E(f21(f20(x1401,x1402),x1402),x1401) % 0.12/0.56 [147]~E(x1471,x1472)+~P2(x1472,a24)+~P2(x1471,a24)+P2(x1471,f19(f25(x1472))) % 0.12/0.56 [173]~P2(x1732,a24)+~P2(x1731,a24)+~P2(x1731,f19(x1732))+P2(x1731,f19(f25(x1732))) % 0.12/0.56 [172]~P1(x1721)+~P4(x1721)+~P2(x1722,x1721)+E(f25(f2(f21(x1721,x1722))),f2(x1721)) % 0.12/0.56 [134]~P1(x1342)+~P6(x1343,x1342)+P2(x1341,x1342)+~P2(x1341,x1343) % 0.12/0.56 [99]~P1(x992)+~P3(x993)+P1(x991)+~E(x991,f20(x992,x993)) % 0.12/0.56 [100]~P1(x1002)+~P3(x1003)+P1(x1001)+~E(x1001,f21(x1002,x1003)) % 0.12/0.56 [110]~P1(x1102)+P1(x1101)+~P2(x1103,a24)+~E(x1101,f23(x1102,x1103)) % 0.12/0.56 [125]~P2(x1251,x1252)+~P2(x1253,a24)+P2(x1251,a24)+~E(x1252,f19(x1253)) % 0.12/0.56 [142]~P2(x1421,x1423)+~P2(x1422,a24)+P8(f25(x1421),x1422)+~E(x1423,f19(x1422)) % 0.12/0.56 [122]~P1(x1222)+~P1(x1221)+~P6(x1222,x1221)+~P6(x1221,x1222)+E(x1221,x1222) % 0.12/0.56 [157]~P8(x1572,x1571)+~P8(x1571,x1572)+E(x1571,x1572)+~P2(x1572,a24)+~P2(x1571,a24) % 0.12/0.56 [104]~P4(x1041)+P2(x1042,x1041)+~E(x1042,f27(x1041))+~P6(x1041,a24)+E(x1041,a22) % 0.12/0.56 [130]~P1(x1302)+~P5(x1302)+~P2(x1301,a24)+E(x1301,a18)+P5(f23(x1302,x1301)) % 0.12/0.56 [164]~P2(x1642,x1641)+P2(f14(x1641,x1642),x1641)+~P6(x1641,a24)+E(x1641,a22)+E(x1642,f26(x1641)) % 0.12/0.56 [174]~P1(x1741)+~P4(x1741)+~P2(x1742,a24)+~P8(x1742,f2(x1741))+P6(f15(x1741,x1742),x1741) % 0.12/0.56 [175]~P1(x1751)+P2(f17(x1752,x1751),x1751)+~P2(x1752,a24)+E(x1751,f19(x1752))+P2(f17(x1752,x1751),a24) % 0.12/0.56 [176]~P2(x1762,x1761)+~P6(x1761,a24)+~P8(x1762,f14(x1761,x1762))+E(x1761,a22)+E(x1762,f26(x1761)) % 0.12/0.56 [146]P2(x1462,x1461)+~P1(x1461)+~P3(x1462)+~P4(x1461)+E(f2(f20(x1461,x1462)),f25(f2(x1461))) % 0.12/0.56 [171]~P1(x1711)+~P4(x1711)+~P2(x1712,a24)+~P8(x1712,f2(x1711))+E(f2(f15(x1711,x1712)),x1712) % 0.12/0.56 [177]E(x1771,x1772)+P2(x1771,f19(x1772))+~P2(x1772,a24)+~P2(x1771,a24)+~P2(x1771,f19(f25(x1772))) % 0.12/0.56 [181]~P1(x1811)+P2(f17(x1812,x1811),x1811)+~P2(x1812,a24)+E(x1811,f19(x1812))+P8(f25(f17(x1812,x1811)),x1812) % 0.12/0.56 [135]~P2(x1353,x1351)+P8(x1352,x1353)+~E(x1352,f26(x1351))+~P6(x1351,a24)+E(x1351,a22) % 0.12/0.56 [166]P2(x1661,x1662)+~P2(x1663,a24)+~P2(x1661,a24)+~P8(f25(x1661),x1663)+~E(x1662,f19(x1663)) % 0.12/0.56 [126]~P1(x1264)+~P3(x1262)+~P2(x1261,x1263)+~E(x1261,x1262)+~E(x1263,f21(x1264,x1262)) % 0.12/0.56 [128]~P1(x1283)+~P3(x1284)+~P2(x1281,x1282)+P3(x1281)+~E(x1282,f20(x1283,x1284)) % 0.12/0.56 [129]~P1(x1293)+~P3(x1294)+~P2(x1291,x1292)+P3(x1291)+~E(x1292,f21(x1293,x1294)) % 0.12/0.56 [144]~P1(x1442)+~P3(x1444)+~P2(x1441,x1443)+P2(x1441,x1442)+~E(x1443,f21(x1442,x1444)) % 0.12/0.56 [152]~P1(x1524)+~P2(x1521,x1523)+~P2(x1522,a24)+E(f2(x1521),x1522)+~E(x1523,f23(x1524,x1522)) % 0.12/0.56 [158]~P1(x1582)+~P2(x1581,x1583)+P6(x1581,x1582)+~P2(x1584,a24)+~E(x1583,f23(x1582,x1584)) % 0.12/0.56 [170]~P4(x1701)+~P2(x1702,x1701)+P2(f16(x1701,x1702),x1701)+~P6(x1701,a24)+E(x1701,a22)+E(x1702,f27(x1701)) % 0.12/0.56 [179]~P4(x1791)+~P2(x1792,x1791)+~P6(x1791,a24)+~P8(f16(x1791,x1792),x1792)+E(x1791,a22)+E(x1792,f27(x1791)) % 0.12/0.56 [185]~P1(x1851)+~P2(x1852,a24)+~P2(f17(x1852,x1851),x1851)+E(x1851,f19(x1852))+~P2(f17(x1852,x1851),a24)+~P8(f25(f17(x1852,x1851)),x1852) % 0.12/0.56 [153]~P1(x1532)+~P1(x1531)+~P6(x1533,x1532)+~P6(x1531,x1533)+P6(x1531,x1532)+~P1(x1533) % 0.12/0.56 [180]~P8(x1801,x1803)+P8(x1801,x1802)+~P8(x1803,x1802)+~P2(x1802,a24)+~P2(x1803,a24)+~P2(x1801,a24) % 0.12/0.56 [143]~P4(x1431)+~P2(x1432,x1431)+P8(x1432,x1433)+~E(x1433,f27(x1431))+~P6(x1431,a24)+E(x1431,a22) % 0.12/0.56 [182]~P1(x1821)+~P1(x1822)+~P3(x1823)+P2(f12(x1822,x1823,x1821),x1821)+~E(f12(x1822,x1823,x1821),x1823)+E(x1821,f21(x1822,x1823)) % 0.12/0.56 [183]~P1(x1831)+~P1(x1832)+~P3(x1833)+P2(f13(x1832,x1833,x1831),x1831)+E(x1831,f20(x1832,x1833))+P3(f13(x1832,x1833,x1831)) % 0.12/0.56 [184]~P1(x1841)+~P1(x1842)+~P3(x1843)+P2(f12(x1842,x1843,x1841),x1841)+E(x1841,f21(x1842,x1843))+P3(f12(x1842,x1843,x1841)) % 0.12/0.56 [186]~P1(x1861)+~P1(x1862)+~P3(x1863)+P2(f12(x1862,x1863,x1861),x1861)+P2(f12(x1862,x1863,x1861),x1862)+E(x1861,f21(x1862,x1863)) % 0.12/0.56 [188]~P1(x1881)+~P1(x1882)+P2(f6(x1882,x1883,x1881),x1881)+P6(f6(x1882,x1883,x1881),x1882)+~P2(x1883,a24)+E(x1881,f23(x1882,x1883)) % 0.12/0.56 [187]~P1(x1871)+~P1(x1872)+P2(f6(x1872,x1873,x1871),x1871)+~P2(x1873,a24)+E(x1871,f23(x1872,x1873))+E(f2(f6(x1872,x1873,x1871)),x1873) % 0.12/0.56 [123]~P1(x1234)+~P3(x1233)+~P3(x1231)+P2(x1231,x1232)+~E(x1231,x1233)+~E(x1232,f20(x1234,x1233)) % 0.12/0.56 [148]~P1(x1483)+~P3(x1482)+~P2(x1481,x1484)+E(x1481,x1482)+P2(x1481,x1483)+~E(x1484,f20(x1483,x1482)) % 0.12/0.56 [154]~P1(x1543)+~P3(x1544)+~P3(x1541)+~P2(x1541,x1543)+P2(x1541,x1542)+~E(x1542,f20(x1543,x1544)) % 0.12/0.56 [169]~P1(x1694)+~P6(x1691,x1694)+P2(x1691,x1692)+~P2(x1693,a24)+~E(x1692,f23(x1694,x1693))+~E(f2(x1691),x1693) % 0.12/0.56 [178]E(f26(x1782),f26(x1781))+~P6(x1781,a24)+~P6(x1782,a24)+~P2(f26(x1781),x1782)+~P2(f26(x1782),x1781)+E(x1781,a22)+E(x1782,a22) % 0.12/0.56 [189]~P1(x1891)+~P1(x1892)+~P3(x1893)+E(f13(x1892,x1893,x1891),x1893)+P2(f13(x1892,x1893,x1891),x1891)+P2(f13(x1892,x1893,x1891),x1892)+E(x1891,f20(x1892,x1893)) % 0.12/0.56 [190]~P1(x1901)+~P1(x1902)+~P3(x1903)+~E(f13(x1902,x1903,x1901),x1903)+~P2(f13(x1902,x1903,x1901),x1901)+E(x1901,f20(x1902,x1903))+~P3(f13(x1902,x1903,x1901)) % 0.12/0.56 [191]~P1(x1911)+~P1(x1912)+~P3(x1913)+~P2(f13(x1912,x1913,x1911),x1911)+~P2(f13(x1912,x1913,x1911),x1912)+E(x1911,f20(x1912,x1913))+~P3(f13(x1912,x1913,x1911)) % 0.12/0.56 [192]~P1(x1921)+~P1(x1922)+~P2(x1923,a24)+~P2(f6(x1922,x1923,x1921),x1921)+~P6(f6(x1922,x1923,x1921),x1922)+E(x1921,f23(x1922,x1923))+~E(f2(f6(x1922,x1923,x1921)),x1923) % 0.12/0.56 [155]~P1(x1554)+~P3(x1552)+~P3(x1551)+~P2(x1551,x1554)+E(x1551,x1552)+P2(x1551,x1553)+~E(x1553,f21(x1554,x1552)) % 0.12/0.56 [193]~P1(x1931)+~P1(x1932)+~P3(x1933)+E(f12(x1932,x1933,x1931),x1933)+~P2(f12(x1932,x1933,x1931),x1931)+~P2(f12(x1932,x1933,x1931),x1932)+E(x1931,f21(x1932,x1933))+~P3(f12(x1932,x1933,x1931)) % 0.12/0.56 %EqnAxiom % 0.12/0.56 [1]E(x11,x11) % 0.12/0.56 [2]E(x22,x21)+~E(x21,x22) % 0.12/0.56 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.12/0.56 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.12/0.56 [5]~E(x51,x52)+E(f19(x51),f19(x52)) % 0.12/0.56 [6]~E(x61,x62)+E(f23(x61,x63),f23(x62,x63)) % 0.12/0.56 [7]~E(x71,x72)+E(f23(x73,x71),f23(x73,x72)) % 0.12/0.56 [8]~E(x81,x82)+E(f16(x81,x83),f16(x82,x83)) % 0.12/0.56 [9]~E(x91,x92)+E(f16(x93,x91),f16(x93,x92)) % 0.12/0.56 [10]~E(x101,x102)+E(f27(x101),f27(x102)) % 0.12/0.56 [11]~E(x111,x112)+E(f26(x111),f26(x112)) % 0.12/0.56 [12]~E(x121,x122)+E(f14(x121,x123),f14(x122,x123)) % 0.12/0.56 [13]~E(x131,x132)+E(f14(x133,x131),f14(x133,x132)) % 0.12/0.56 [14]~E(x141,x142)+E(f11(x141,x143),f11(x142,x143)) % 0.12/0.56 [15]~E(x151,x152)+E(f11(x153,x151),f11(x153,x152)) % 0.12/0.56 [16]~E(x161,x162)+E(f13(x161,x163,x164),f13(x162,x163,x164)) % 0.12/0.56 [17]~E(x171,x172)+E(f13(x173,x171,x174),f13(x173,x172,x174)) % 0.12/0.56 [18]~E(x181,x182)+E(f13(x183,x184,x181),f13(x183,x184,x182)) % 0.12/0.56 [19]~E(x191,x192)+E(f12(x191,x193,x194),f12(x192,x193,x194)) % 0.12/0.56 [20]~E(x201,x202)+E(f12(x203,x201,x204),f12(x203,x202,x204)) % 0.12/0.56 [21]~E(x211,x212)+E(f12(x213,x214,x211),f12(x213,x214,x212)) % 0.12/0.56 [22]~E(x221,x222)+E(f20(x221,x223),f20(x222,x223)) % 0.12/0.56 [23]~E(x231,x232)+E(f20(x233,x231),f20(x233,x232)) % 0.12/0.56 [24]~E(x241,x242)+E(f25(x241),f25(x242)) % 0.12/0.56 [25]~E(x251,x252)+E(f8(x251),f8(x252)) % 0.12/0.56 [26]~E(x261,x262)+E(f6(x261,x263,x264),f6(x262,x263,x264)) % 0.12/0.56 [27]~E(x271,x272)+E(f6(x273,x271,x274),f6(x273,x272,x274)) % 0.12/0.56 [28]~E(x281,x282)+E(f6(x283,x284,x281),f6(x283,x284,x282)) % 0.12/0.56 [29]~E(x291,x292)+E(f9(x291),f9(x292)) % 0.12/0.56 [30]~E(x301,x302)+E(f21(x301,x303),f21(x302,x303)) % 0.12/0.56 [31]~E(x311,x312)+E(f21(x313,x311),f21(x313,x312)) % 0.12/0.56 [32]~E(x321,x322)+E(f5(x321),f5(x322)) % 0.12/0.56 [33]~E(x331,x332)+E(f17(x331,x333),f17(x332,x333)) % 0.12/0.56 [34]~E(x341,x342)+E(f17(x343,x341),f17(x343,x342)) % 0.12/0.56 [35]~E(x351,x352)+E(f10(x351),f10(x352)) % 0.12/0.56 [36]~E(x361,x362)+E(f4(x361),f4(x362)) % 0.12/0.56 [37]~E(x371,x372)+E(f15(x371,x373),f15(x372,x373)) % 0.12/0.56 [38]~E(x381,x382)+E(f15(x383,x381),f15(x383,x382)) % 0.12/0.56 [39]~E(x391,x392)+E(f7(x391),f7(x392)) % 0.12/0.56 [40]~P1(x401)+P1(x402)+~E(x401,x402) % 0.12/0.56 [41]P2(x412,x413)+~E(x411,x412)+~P2(x411,x413) % 0.12/0.56 [42]P2(x423,x422)+~E(x421,x422)+~P2(x423,x421) % 0.12/0.56 [43]~P4(x431)+P4(x432)+~E(x431,x432) % 0.12/0.56 [44]~P3(x441)+P3(x442)+~E(x441,x442) % 0.12/0.56 [45]P8(x452,x453)+~E(x451,x452)+~P8(x451,x453) % 0.12/0.56 [46]P8(x463,x462)+~E(x461,x462)+~P8(x463,x461) % 0.12/0.56 [47]~P5(x471)+P5(x472)+~E(x471,x472) % 0.12/0.56 [48]P6(x482,x483)+~E(x481,x482)+~P6(x481,x483) % 0.12/0.56 [49]P6(x493,x492)+~E(x491,x492)+~P6(x493,x491) % 0.12/0.56 [50]P7(x502,x503)+~E(x501,x502)+~P7(x501,x503) % 0.12/0.56 [51]P7(x513,x512)+~E(x511,x512)+~P7(x513,x511) % 0.12/0.56 % 0.12/0.56 %------------------------------------------- % 0.12/0.56 cnf(194,plain, % 0.12/0.56 (P1(a22)), % 0.12/0.56 inference(equality_inference,[],[72])). % 0.12/0.56 cnf(197,plain, % 0.12/0.56 (~P2(x1971,a22)), % 0.12/0.56 inference(equality_inference,[],[79])). % 0.12/0.56 cnf(198,plain, % 0.12/0.56 (P1(f19(x1981))+~P2(x1981,a24)), % 0.12/0.56 inference(equality_inference,[],[88])). % 0.12/0.56 cnf(203,plain, % 0.12/0.56 (~P1(x2031)+P1(f23(x2031,x2032))+~P2(x2032,a24)), % 0.12/0.56 inference(equality_inference,[],[110])). % 0.12/0.56 cnf(212,plain, % 0.12/0.56 (~P2(x2121,a24)+~P2(x2121,a24)+P2(x2121,f19(f25(x2121)))), % 0.12/0.56 inference(equality_inference,[],[147])). % 0.12/0.56 cnf(218,plain, % 0.12/0.56 (P2(x2181,f19(x2182))+~P2(x2181,a24)+~P8(f25(x2181),x2182)+~P2(x2182,a24)), % 0.12/0.56 inference(equality_inference,[],[166])). % 0.12/0.56 cnf(245,plain, % 0.12/0.56 (~P2(x2451,a22)), % 0.12/0.56 inference(rename_variables,[],[197])). % 0.12/0.56 cnf(259,plain, % 0.12/0.56 ($false), % 0.12/0.56 inference(scs_inference,[],[70,54,57,194,197,245,59,60,61,69,67,52,53,72,116,198,79,92,132,2,77,203,75,212,3,41,42,218,136,142,162,163,122,97]), % 0.12/0.56 ['proof']). % 0.12/0.56 % SZS output end Proof % 0.12/0.56 % Total time :0.010000s %------------------------------------------------------------------------------