TSTP Solution File: NUM449+6 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n014.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 : Thu Aug 31 10:22:11 EDT 2023
% Result : Theorem 0.67s 0.86s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 17:50:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.67/0.84 %-------------------------------------------
% 0.67/0.84 % File :CSE---1.6
% 0.67/0.84 % Problem :theBenchmark
% 0.67/0.84 % Transform :cnf
% 0.67/0.84 % Format :tptp:raw
% 0.67/0.84 % Command :java -jar mcs_scs.jar %d %s
% 0.67/0.84
% 0.67/0.84 % Result :Theorem 0.150000s
% 0.67/0.84 % Output :CNFRefutation 0.150000s
% 0.67/0.84 %-------------------------------------------
% 0.67/0.85 %------------------------------------------------------------------------------
% 0.67/0.85 % File : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% 0.67/0.85 % Domain : Number Theory
% 0.67/0.85 % Problem : Fuerstenberg's infinitude of primes 11_02, 05 expansion
% 0.67/0.85 % Version : Especial.
% 0.67/0.85 % English :
% 0.67/0.85
% 0.67/0.85 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.67/0.85 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.67/0.85 % Source : [Pas08]
% 0.67/0.85 % Names : fuerst_11_02.05 [Pas08]
% 0.67/0.85
% 0.67/0.85 % Status : Theorem
% 0.67/0.85 % Rating : 0.39 v8.1.0, 0.33 v7.5.0, 0.44 v7.4.0, 0.27 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.30 v7.0.0, 0.37 v6.4.0, 0.38 v6.3.0, 0.33 v6.2.0, 0.40 v6.1.0, 0.50 v6.0.0, 0.43 v5.5.0, 0.63 v5.4.0, 0.68 v5.3.0, 0.70 v5.2.0, 0.65 v5.1.0, 0.76 v5.0.0, 0.79 v4.1.0, 0.83 v4.0.1, 0.87 v4.0.0
% 0.67/0.85 % Syntax : Number of formulae : 45 ( 3 unt; 10 def)
% 0.67/0.85 % Number of atoms : 267 ( 53 equ)
% 0.67/0.85 % Maximal formula atoms : 38 ( 5 avg)
% 0.67/0.85 % Number of connectives : 241 ( 19 ~; 12 |; 124 &)
% 0.67/0.85 % ( 21 <=>; 65 =>; 0 <=; 0 <~>)
% 0.67/0.85 % Maximal formula depth : 19 ( 7 avg)
% 0.67/0.85 % Maximal term depth : 3 ( 1 avg)
% 0.67/0.85 % Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% 0.67/0.85 % Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% 0.67/0.85 % Number of variables : 111 ( 96 !; 15 ?)
% 0.67/0.85 % SPC : FOF_THM_RFO_SEQ
% 0.67/0.85
% 0.67/0.85 % Comments : Problem generated by the SAD system [VLP07]
% 0.67/0.85 %------------------------------------------------------------------------------
% 0.67/0.85 fof(mIntegers,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => $true ) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntZero,axiom,
% 0.67/0.85 aInteger0(sz00) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntOne,axiom,
% 0.67/0.85 aInteger0(sz10) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntNeg,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => aInteger0(smndt0(W0)) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntPlus,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1) )
% 0.67/0.85 => aInteger0(sdtpldt0(W0,W1)) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntMult,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1) )
% 0.67/0.85 => aInteger0(sdtasdt0(W0,W1)) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mAddAsso,axiom,
% 0.67/0.85 ! [W0,W1,W2] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2) )
% 0.67/0.85 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mAddComm,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1) )
% 0.67/0.85 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mAddZero,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( sdtpldt0(W0,sz00) = W0
% 0.67/0.85 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mAddNeg,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.67/0.85 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mMulAsso,axiom,
% 0.67/0.85 ! [W0,W1,W2] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2) )
% 0.67/0.85 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mMulComm,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1) )
% 0.67/0.85 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mMulOne,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( sdtasdt0(W0,sz10) = W0
% 0.67/0.85 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mDistrib,axiom,
% 0.67/0.85 ! [W0,W1,W2] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2) )
% 0.67/0.85 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.67/0.85 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mMulZero,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( sdtasdt0(W0,sz00) = sz00
% 0.67/0.85 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mMulMinOne,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.67/0.85 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mZeroDiv,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1) )
% 0.67/0.85 => ( sdtasdt0(W0,W1) = sz00
% 0.67/0.85 => ( W0 = sz00
% 0.67/0.85 | W1 = sz00 ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mDivisor,definition,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ! [W1] :
% 0.67/0.85 ( aDivisorOf0(W1,W0)
% 0.67/0.85 <=> ( aInteger0(W1)
% 0.67/0.85 & W1 != sz00
% 0.67/0.85 & ? [W2] :
% 0.67/0.85 ( aInteger0(W2)
% 0.67/0.85 & sdtasdt0(W1,W2) = W0 ) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mEquMod,definition,
% 0.67/0.85 ! [W0,W1,W2] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2)
% 0.67/0.85 & W2 != sz00 )
% 0.67/0.85 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.67/0.85 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mEquModRef,axiom,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & W1 != sz00 )
% 0.67/0.85 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mEquModSym,axiom,
% 0.67/0.85 ! [W0,W1,W2] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2)
% 0.67/0.85 & W2 != sz00 )
% 0.67/0.85 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.67/0.85 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mEquModTrn,axiom,
% 0.67/0.85 ! [W0,W1,W2,W3] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2)
% 0.67/0.85 & W2 != sz00
% 0.67/0.85 & aInteger0(W3) )
% 0.67/0.85 => ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.67/0.85 & sdteqdtlpzmzozddtrp0(W1,W3,W2) )
% 0.67/0.85 => sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mEquModMul,axiom,
% 0.67/0.85 ! [W0,W1,W2,W3] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & aInteger0(W1)
% 0.67/0.85 & aInteger0(W2)
% 0.67/0.85 & W2 != sz00
% 0.67/0.85 & aInteger0(W3)
% 0.67/0.85 & W3 != sz00 )
% 0.67/0.85 => ( sdteqdtlpzmzozddtrp0(W0,W1,sdtasdt0(W2,W3))
% 0.67/0.85 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.67/0.85 & sdteqdtlpzmzozddtrp0(W0,W1,W3) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mPrime,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( ( aInteger0(W0)
% 0.67/0.85 & W0 != sz00 )
% 0.67/0.85 => ( isPrime0(W0)
% 0.67/0.85 => $true ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mPrimeDivisor,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aInteger0(W0)
% 0.67/0.85 => ( ? [W1] :
% 0.67/0.85 ( aDivisorOf0(W1,W0)
% 0.67/0.85 & isPrime0(W1) )
% 0.67/0.85 <=> ( W0 != sz10
% 0.67/0.85 & W0 != smndt0(sz10) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mSets,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aSet0(W0)
% 0.67/0.85 => $true ) ).
% 0.67/0.85
% 0.67/0.85 fof(mElements,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aSet0(W0)
% 0.67/0.85 => ! [W1] :
% 0.67/0.85 ( aElementOf0(W1,W0)
% 0.67/0.85 => $true ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mSubset,definition,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aSet0(W0)
% 0.67/0.85 => ! [W1] :
% 0.67/0.85 ( aSubsetOf0(W1,W0)
% 0.67/0.85 <=> ( aSet0(W1)
% 0.67/0.85 & ! [W2] :
% 0.67/0.85 ( aElementOf0(W2,W1)
% 0.67/0.85 => aElementOf0(W2,W0) ) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mFinSet,axiom,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( aSet0(W0)
% 0.67/0.85 => ( isFinite0(W0)
% 0.67/0.85 => $true ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mUnion,definition,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aSubsetOf0(W0,cS1395)
% 0.67/0.85 & aSubsetOf0(W1,cS1395) )
% 0.67/0.85 => ! [W2] :
% 0.67/0.85 ( W2 = sdtbsmnsldt0(W0,W1)
% 0.67/0.85 <=> ( aSet0(W2)
% 0.67/0.85 & ! [W3] :
% 0.67/0.85 ( aElementOf0(W3,W2)
% 0.67/0.85 <=> ( aInteger0(W3)
% 0.67/0.85 & ( aElementOf0(W3,W0)
% 0.67/0.85 | aElementOf0(W3,W1) ) ) ) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mIntersection,definition,
% 0.67/0.85 ! [W0,W1] :
% 0.67/0.85 ( ( aSubsetOf0(W0,cS1395)
% 0.67/0.85 & aSubsetOf0(W1,cS1395) )
% 0.67/0.85 => ! [W2] :
% 0.67/0.85 ( W2 = sdtslmnbsdt0(W0,W1)
% 0.67/0.85 <=> ( aSet0(W2)
% 0.67/0.85 & ! [W3] :
% 0.67/0.85 ( aElementOf0(W3,W2)
% 0.67/0.85 <=> ( aInteger0(W3)
% 0.67/0.85 & aElementOf0(W3,W0)
% 0.67/0.85 & aElementOf0(W3,W1) ) ) ) ) ) ).
% 0.67/0.85
% 0.67/0.85 fof(mUnionSet,definition,
% 0.67/0.85 ! [W0] :
% 0.67/0.85 ( ( aSet0(W0)
% 0.67/0.85 & ! [W1] :
% 0.67/0.85 ( aElementOf0(W1,W0)
% 0.67/0.85 => aSubsetOf0(W1,cS1395) ) )
% 0.67/0.85 => ! [W1] :
% 0.67/0.85 ( W1 = sbsmnsldt0(W0)
% 0.67/0.85 <=> ( aSet0(W1)
% 0.67/0.85 & ! [W2] :
% 0.67/0.85 ( aElementOf0(W2,W1)
% 0.67/0.86 <=> ( aInteger0(W2)
% 0.67/0.86 & ? [W3] :
% 0.67/0.86 ( aElementOf0(W3,W0)
% 0.67/0.86 & aElementOf0(W2,W3) ) ) ) ) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mComplement,definition,
% 0.67/0.86 ! [W0] :
% 0.67/0.86 ( aSubsetOf0(W0,cS1395)
% 0.67/0.86 => ! [W1] :
% 0.67/0.86 ( W1 = stldt0(W0)
% 0.67/0.86 <=> ( aSet0(W1)
% 0.67/0.86 & ! [W2] :
% 0.67/0.86 ( aElementOf0(W2,W1)
% 0.67/0.86 <=> ( aInteger0(W2)
% 0.67/0.86 & ~ aElementOf0(W2,W0) ) ) ) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mArSeq,definition,
% 0.67/0.86 ! [W0,W1] :
% 0.67/0.86 ( ( aInteger0(W0)
% 0.67/0.86 & aInteger0(W1)
% 0.67/0.86 & W1 != sz00 )
% 0.67/0.86 => ! [W2] :
% 0.67/0.86 ( W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1)
% 0.67/0.86 <=> ( aSet0(W2)
% 0.67/0.86 & ! [W3] :
% 0.67/0.86 ( aElementOf0(W3,W2)
% 0.67/0.86 <=> ( aInteger0(W3)
% 0.67/0.86 & sdteqdtlpzmzozddtrp0(W3,W0,W1) ) ) ) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mOpen,definition,
% 0.67/0.86 ! [W0] :
% 0.67/0.86 ( aSubsetOf0(W0,cS1395)
% 0.67/0.86 => ( isOpen0(W0)
% 0.67/0.86 <=> ! [W1] :
% 0.67/0.86 ( aElementOf0(W1,W0)
% 0.67/0.86 => ? [W2] :
% 0.67/0.86 ( aInteger0(W2)
% 0.67/0.86 & W2 != sz00
% 0.67/0.86 & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0) ) ) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mClosed,definition,
% 0.67/0.86 ! [W0] :
% 0.67/0.86 ( aSubsetOf0(W0,cS1395)
% 0.67/0.86 => ( isClosed0(W0)
% 0.67/0.86 <=> isOpen0(stldt0(W0)) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mUnionOpen,axiom,
% 0.67/0.86 ! [W0] :
% 0.67/0.86 ( ( aSet0(W0)
% 0.67/0.86 & ! [W1] :
% 0.67/0.86 ( aElementOf0(W1,W0)
% 0.67/0.86 => ( aSubsetOf0(W1,cS1395)
% 0.67/0.86 & isOpen0(W1) ) ) )
% 0.67/0.86 => isOpen0(sbsmnsldt0(W0)) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mInterOpen,axiom,
% 0.67/0.86 ! [W0,W1] :
% 0.67/0.86 ( ( aSubsetOf0(W0,cS1395)
% 0.67/0.86 & aSubsetOf0(W1,cS1395)
% 0.67/0.86 & isOpen0(W0)
% 0.67/0.86 & isOpen0(W1) )
% 0.67/0.86 => isOpen0(sdtslmnbsdt0(W0,W1)) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mUnionClosed,axiom,
% 0.67/0.86 ! [W0,W1] :
% 0.67/0.86 ( ( aSubsetOf0(W0,cS1395)
% 0.67/0.86 & aSubsetOf0(W1,cS1395)
% 0.67/0.86 & isClosed0(W0)
% 0.67/0.86 & isClosed0(W1) )
% 0.67/0.86 => isClosed0(sdtbsmnsldt0(W0,W1)) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mUnionSClosed,axiom,
% 0.67/0.86 ! [W0] :
% 0.67/0.86 ( ( aSet0(W0)
% 0.67/0.86 & isFinite0(W0)
% 0.67/0.86 & ! [W1] :
% 0.67/0.86 ( aElementOf0(W1,W0)
% 0.67/0.86 => ( aSubsetOf0(W1,cS1395)
% 0.67/0.86 & isClosed0(W1) ) ) )
% 0.67/0.86 => isClosed0(sbsmnsldt0(W0)) ) ).
% 0.67/0.86
% 0.67/0.86 fof(mArSeqClosed,axiom,
% 0.67/0.86 ! [W0,W1] :
% 0.67/0.86 ( ( aInteger0(W0)
% 0.67/0.86 & aInteger0(W1)
% 0.67/0.86 & W1 != sz00 )
% 0.67/0.86 => ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),cS1395)
% 0.67/0.86 & isClosed0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) ).
% 0.67/0.86
% 0.67/0.86 fof(m__2046,hypothesis,
% 0.67/0.86 ( aSet0(xS)
% 0.67/0.86 & ! [W0] :
% 0.67/0.86 ( ( aElementOf0(W0,xS)
% 0.67/0.86 => ? [W1] :
% 0.67/0.86 ( aInteger0(W1)
% 0.67/0.86 & W1 != sz00
% 0.67/0.86 & isPrime0(W1)
% 0.67/0.86 & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
% 0.67/0.86 & ! [W2] :
% 0.67/0.86 ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
% 0.67/0.86 => ( aInteger0(W2)
% 0.67/0.86 & ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) )
% 0.67/0.86 & aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
% 0.67/0.86 & sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
% 0.67/0.86 & ( ( aInteger0(W2)
% 0.67/0.86 & ( ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) )
% 0.67/0.86 | aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
% 0.67/0.86 | sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
% 0.67/0.86 => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
% 0.67/0.86 & szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 ) )
% 0.67/0.86 & ( ? [W1] :
% 0.67/0.86 ( aInteger0(W1)
% 0.67/0.86 & W1 != sz00
% 0.67/0.86 & isPrime0(W1)
% 0.67/0.86 & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
% 0.67/0.86 & ! [W2] :
% 0.67/0.86 ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
% 0.67/0.86 => ( aInteger0(W2)
% 0.67/0.86 & ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) )
% 0.67/0.86 & aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
% 0.67/0.86 & sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
% 0.67/0.86 & ( ( aInteger0(W2)
% 0.67/0.86 & ( ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) )
% 0.67/0.86 | aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
% 0.67/0.86 | sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
% 0.67/0.86 => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) ) )
% 0.67/0.86 => szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 ) )
% 0.67/0.86 => aElementOf0(W0,xS) ) )
% 0.67/0.86 & xS = cS2043 ) ).
% 0.67/0.86
% 0.67/0.86 fof(m__2079,hypothesis,
% 0.67/0.86 ( aSet0(sbsmnsldt0(xS))
% 0.67/0.86 & ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,sbsmnsldt0(xS))
% 0.67/0.86 <=> ( aInteger0(W0)
% 0.67/0.86 & ? [W1] :
% 0.67/0.86 ( aElementOf0(W1,xS)
% 0.67/0.86 & aElementOf0(W0,W1) ) ) )
% 0.67/0.86 & aSet0(stldt0(sbsmnsldt0(xS)))
% 0.67/0.86 & ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
% 0.67/0.86 <=> ( aInteger0(W0)
% 0.67/0.86 & ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
% 0.67/0.86 & ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
% 0.67/0.86 <=> ( W0 = sz10
% 0.67/0.86 | W0 = smndt0(sz10) ) )
% 0.67/0.86 & stldt0(sbsmnsldt0(xS)) = cS2076 ) ).
% 0.67/0.86
% 0.67/0.86 fof(m__2117,hypothesis,
% 0.67/0.86 isFinite0(xS) ).
% 0.67/0.86
% 0.67/0.86 fof(m__,conjecture,
% 0.67/0.86 ( ( aSet0(sbsmnsldt0(xS))
% 0.67/0.86 & ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,sbsmnsldt0(xS))
% 0.67/0.86 <=> ( aInteger0(W0)
% 0.67/0.86 & ? [W1] :
% 0.67/0.86 ( aElementOf0(W1,xS)
% 0.67/0.86 & aElementOf0(W0,W1) ) ) ) )
% 0.67/0.86 => ( ( ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
% 0.67/0.86 <=> ( aInteger0(W0)
% 0.67/0.86 & ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
% 0.67/0.86 => ( ! [W0] :
% 0.67/0.86 ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
% 0.67/0.86 => ? [W1] :
% 0.67/0.86 ( aInteger0(W1)
% 0.67/0.86 & W1 != sz00
% 0.67/0.86 & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
% 0.67/0.86 & ! [W2] :
% 0.67/0.86 ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
% 0.67/0.86 => ( aInteger0(W2)
% 0.67/0.86 & ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
% 0.67/0.86 & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
% 0.67/0.86 & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
% 0.67/0.86 & ( ( aInteger0(W2)
% 0.67/0.86 & ( ? [W3] :
% 0.67/0.86 ( aInteger0(W3)
% 0.67/0.86 & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
% 0.67/0.86 | aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
% 0.67/0.86 | sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
% 0.67/0.86 => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
% 0.67/0.86 => ( ! [W2] :
% 0.67/0.86 ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
% 0.67/0.86 => aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
% 0.67/0.86 | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS))) ) ) ) )
% 0.67/0.86 | isOpen0(stldt0(sbsmnsldt0(xS))) ) )
% 0.67/0.86 | isClosed0(sbsmnsldt0(xS)) ) ) ).
% 0.67/0.86
% 0.67/0.86 %------------------------------------------------------------------------------
% 0.67/0.86 %-------------------------------------------
% 0.67/0.86 % Proof found
% 0.67/0.86 % SZS status Theorem for theBenchmark
% 0.67/0.86 % SZS output start Proof
% 0.67/0.86 %ClaNum:240(EqnAxiom:71)
% 0.67/0.86 %VarNum:1109(SingletonVarNum:341)
% 0.67/0.86 %MaxLitNum:8
% 0.67/0.86 %MaxfuncDepth:2
% 0.67/0.86 %SharedTerms:23
% 0.67/0.86 %goalClause: 79 81 82 83 101 108 126 128 131 135 136 141 150 155 159 166 171 181 184 189 191 192 201
% 0.67/0.86 %singleGoalClaCount:4
% 0.67/0.86 [72]E(a1,a2)
% 0.67/0.86 [73]P1(a4)
% 0.67/0.86 [74]P1(a36)
% 0.67/0.86 [75]P4(a1)
% 0.67/0.86 [76]P5(a1)
% 0.67/0.86 [79]P4(f5(a1))
% 0.67/0.86 [82]~P6(f5(a1))
% 0.67/0.86 [77]E(f30(f5(a1)),a6)
% 0.67/0.86 [80]P4(f30(f5(a1)))
% 0.67/0.86 [81]P2(a7,f30(f5(a1)))
% 0.67/0.86 [83]~P8(f30(f5(a1)))
% 0.67/0.86 [84]~P1(x841)+P1(f31(x841))
% 0.67/0.86 [85]~P1(x851)+E(f32(a4,x851),a4)
% 0.67/0.86 [86]~P1(x861)+E(f32(x861,a4),a4)
% 0.67/0.86 [87]~P1(x871)+E(f33(a4,x871),x871)
% 0.67/0.86 [88]~P1(x881)+E(f32(a36,x881),x881)
% 0.67/0.86 [89]~P1(x891)+E(f33(x891,a4),x891)
% 0.67/0.86 [90]~P1(x901)+E(f32(x901,a36),x901)
% 0.67/0.86 [92]~P2(x921,a1)+~E(f8(x921),a4)
% 0.67/0.86 [98]~P2(x981,a1)+P1(f8(x981))
% 0.67/0.86 [99]~P2(x991,a1)+P9(f8(x991))
% 0.67/0.86 [101]P1(x1011)+~P2(x1011,f5(a1))
% 0.67/0.86 [127]~P2(x1271,f5(a1))+P2(f15(x1271),a1)
% 0.67/0.86 [128]~P2(x1281,f5(a1))+P2(f18(x1281),a1)
% 0.67/0.86 [130]P2(x1301,f15(x1301))+~P2(x1301,f5(a1))
% 0.67/0.86 [131]P2(x1311,f18(x1311))+~P2(x1311,f5(a1))
% 0.67/0.86 [93]~P1(x931)+E(f33(f31(x931),x931),a4)
% 0.67/0.86 [94]~P1(x941)+E(f33(x941,f31(x941)),a4)
% 0.67/0.86 [95]~P1(x951)+E(f32(x951,f31(a36)),f31(x951))
% 0.67/0.86 [96]~P1(x961)+E(f32(f31(a36),x961),f31(x961))
% 0.67/0.86 [97]~E(x971,a36)+P2(x971,f30(f5(a1)))
% 0.67/0.86 [103]~E(x1031,f31(a36))+P2(x1031,f30(f5(a1)))
% 0.67/0.86 [112]~P2(x1121,a1)+E(f37(a4,f8(x1121)),x1121)
% 0.67/0.86 [126]P1(x1261)+~P2(x1261,f30(f5(a1)))
% 0.67/0.86 [140]~P2(x1401,a1)+P4(f37(a4,f8(x1401)))
% 0.67/0.86 [155]~P2(x1551,f5(a1))+~P2(x1551,f30(f5(a1)))
% 0.67/0.86 [108]~P1(x1081)+E(x1081,a4)+P4(f37(a7,x1081))
% 0.67/0.86 [109]~P6(x1091)+~P7(x1091,a3)+P8(f30(x1091))
% 0.67/0.86 [110]~P4(x1101)+P2(f9(x1101),x1101)+P8(f5(x1101))
% 0.67/0.86 [115]P6(x1151)+~P7(x1151,a3)+~P8(f30(x1151))
% 0.67/0.86 [122]P8(x1221)+P2(f10(x1221),x1221)+~P7(x1221,a3)
% 0.67/0.86 [136]~P1(x1361)+E(x1361,a4)+P2(f21(x1361),f37(a7,x1361))
% 0.67/0.86 [129]E(x1291,a36)+E(x1291,f31(a36))+~P2(x1291,f30(f5(a1)))
% 0.67/0.86 [135]~P1(x1351)+P2(x1351,f5(a1))+P2(x1351,f30(f5(a1)))
% 0.67/0.86 [141]~P1(x1411)+E(x1411,a4)+~P2(f21(x1411),f30(f5(a1)))
% 0.67/0.86 [166]~P1(x1661)+E(x1661,a4)+~P7(f37(a7,x1661),f30(f5(a1)))
% 0.67/0.86 [102]~P3(x1021,x1022)+~P1(x1022)+~E(x1021,a4)
% 0.67/0.86 [106]~P3(x1061,x1062)+P1(x1061)+~P1(x1062)
% 0.67/0.86 [107]~P7(x1071,x1072)+P4(x1071)+~P4(x1072)
% 0.67/0.86 [105]P4(x1051)+~P7(x1052,a3)+~E(x1051,f30(x1052))
% 0.67/0.86 [116]~P1(x1162)+~P1(x1161)+E(f33(x1161,x1162),f33(x1162,x1161))
% 0.67/0.86 [117]~P1(x1172)+~P1(x1171)+E(f32(x1171,x1172),f32(x1172,x1171))
% 0.67/0.86 [120]~P1(x1202)+~P1(x1201)+P1(f33(x1201,x1202))
% 0.67/0.86 [121]~P1(x1212)+~P1(x1211)+P1(f32(x1211,x1212))
% 0.67/0.86 [142]~P1(x1421)+~P3(x1422,x1421)+P1(f19(x1421,x1422))
% 0.67/0.86 [157]~P1(x1572)+~P3(x1571,x1572)+E(f32(x1571,f19(x1572,x1571)),x1572)
% 0.67/0.86 [176]P1(x1761)+~P2(x1762,a1)+~P2(x1761,f37(a4,f8(x1762)))
% 0.67/0.86 [195]~P2(x1951,a1)+P1(f16(x1951,x1952))+~P2(x1952,f37(a4,f8(x1951)))
% 0.67/0.86 [208]~P2(x2081,a1)+P3(f8(x2081),f33(x2082,f31(a4)))+~P2(x2082,f37(a4,f8(x2081)))
% 0.67/0.86 [211]~P2(x2112,a1)+P10(x2111,a4,f8(x2112))+~P2(x2111,f37(a4,f8(x2112)))
% 0.67/0.86 [214]~P2(x2141,a1)+E(f32(f8(x2141),f16(x2141,x2142)),f33(x2142,f31(a4)))+~P2(x2142,f37(a4,f8(x2141)))
% 0.67/0.86 [91]~P1(x911)+E(x911,a36)+E(x911,f31(a36))+P9(f20(x911))
% 0.67/0.86 [104]~P1(x1041)+P3(f20(x1041),x1041)+E(x1041,a36)+E(x1041,f31(a36))
% 0.67/0.86 [123]~P4(x1231)+~P5(x1231)+P2(f14(x1231),x1231)+P6(f5(x1231))
% 0.67/0.86 [145]~P4(x1451)+~P8(f9(x1451))+~P7(f9(x1451),a3)+P8(f5(x1451))
% 0.67/0.86 [111]~P1(x1111)+~P3(x1112,x1111)+~P9(x1112)+~E(x1111,a36)
% 0.67/0.86 [156]~P1(x1561)+~P1(x1562)+P10(x1562,x1562,x1561)+E(x1561,a4)
% 0.67/0.86 [114]~P4(x1142)+P4(x1141)+~E(x1141,f5(x1142))+P2(f23(x1142),x1142)
% 0.67/0.86 [118]~P1(x1181)+~P3(x1182,x1181)+~P9(x1182)+~E(x1181,f31(a36))
% 0.67/0.86 [124]~P1(x1241)+~P1(x1242)+E(x1241,a4)+P6(f37(x1242,x1241))
% 0.67/0.86 [132]~P4(x1322)+P4(x1321)+~E(x1321,f5(x1322))+~P7(f23(x1322),a3)
% 0.67/0.86 [137]~P1(x1371)+~P1(x1372)+E(x1371,a4)+P7(f37(x1372,x1371),a3)
% 0.67/0.86 [150]~P1(x1501)+~P2(x1501,x1502)+~P2(x1502,a1)+P2(x1501,f5(a1))
% 0.67/0.86 [151]~P4(x1511)+~P4(x1512)+P7(x1511,x1512)+P2(f24(x1512,x1511),x1511)
% 0.67/0.86 [159]~P1(x1591)+P1(x1592)+E(x1591,a4)+~P2(x1592,f37(a7,x1591))
% 0.67/0.86 [161]~P8(x1611)+~P2(x1612,x1611)+~P7(x1611,a3)+~E(f11(x1611,x1612),a4)
% 0.67/0.86 [163]~P8(x1631)+~P2(x1632,x1631)+~P7(x1631,a3)+P1(f11(x1631,x1632))
% 0.67/0.86 [170]~P4(x1701)+~P4(x1702)+P7(x1701,x1702)+~P2(f24(x1702,x1701),x1702)
% 0.67/0.86 [171]~P1(x1711)+E(x1711,a4)+~P2(x1712,f37(a7,x1711))+P1(f22(x1711,x1712))
% 0.67/0.86 [189]~P1(x1891)+P10(x1892,a7,x1891)+E(x1891,a4)+~P2(x1892,f37(a7,x1891))
% 0.67/0.86 [184]~P1(x1841)+E(x1841,a4)+~P2(x1842,f37(a7,x1841))+P3(x1841,f33(x1842,f31(a7)))
% 0.67/0.86 [191]~P1(x1911)+E(x1911,a4)+~P2(x1912,f37(a7,x1911))+E(f32(x1911,f22(x1911,x1912)),f33(x1912,f31(a7)))
% 0.67/0.86 [203]~P8(x2032)+~P2(x2031,x2032)+~P7(x2032,a3)+P7(f37(x2031,f11(x2032,x2031)),x2032)
% 0.67/0.86 [212]~P1(x2121)+~P2(x2122,a1)+~P3(f8(x2122),f33(x2121,f31(a4)))+P2(x2121,f37(a4,f8(x2122)))
% 0.67/0.86 [217]~P1(x2171)+~P2(x2172,a1)+~P10(x2171,a4,f8(x2172))+P2(x2171,f37(a4,f8(x2172)))
% 0.67/0.86 [147]~P4(x1472)+~P7(x1473,x1472)+P2(x1471,x1472)+~P2(x1471,x1473)
% 0.67/0.86 [138]~P2(x1381,x1382)+P1(x1381)+~P7(x1383,a3)+~E(x1382,f30(x1383))
% 0.67/0.86 [152]P4(x1521)+~P7(x1523,a3)+~P7(x1522,a3)+~E(x1521,f34(x1522,x1523))
% 0.67/0.86 [153]P4(x1531)+~P7(x1533,a3)+~P7(x1532,a3)+~E(x1531,f35(x1532,x1533))
% 0.67/0.86 [162]~P2(x1623,x1622)+~P2(x1623,x1621)+~P7(x1622,a3)+~E(x1621,f30(x1622))
% 0.67/0.86 [172]~P1(x1723)+~P1(x1722)+~P1(x1721)+E(f33(f33(x1721,x1722),x1723),f33(x1721,f33(x1722,x1723)))
% 0.67/0.86 [173]~P1(x1733)+~P1(x1732)+~P1(x1731)+E(f32(f32(x1731,x1732),x1733),f32(x1731,f32(x1732,x1733)))
% 0.67/0.86 [193]~P1(x1933)+~P1(x1932)+~P1(x1931)+E(f33(f32(x1931,x1932),f32(x1931,x1933)),f32(x1931,f33(x1932,x1933)))
% 0.67/0.86 [194]~P1(x1942)+~P1(x1943)+~P1(x1941)+E(f33(f32(x1941,x1942),f32(x1943,x1942)),f32(f33(x1941,x1943),x1942))
% 0.67/0.86 [158]~P4(x1581)+~P5(x1581)+~P6(f14(x1581))+~P7(f14(x1581),a3)+P6(f5(x1581))
% 0.67/0.86 [113]~P1(x1131)+~P1(x1132)+E(x1131,a4)+E(x1132,a4)+~E(f32(x1132,x1131),a4)
% 0.67/0.86 [133]~P1(x1331)+~P9(x1331)+E(x1331,a4)+P2(x1332,a1)+~E(f37(a4,x1331),x1332)
% 0.67/0.86 [139]~P1(x1391)+~P9(x1391)+E(x1391,a4)+P2(x1392,a1)+P4(f37(a4,x1391))
% 0.67/0.86 [164]~P8(x1642)+~P8(x1641)+~P7(x1642,a3)+~P7(x1641,a3)+P8(f35(x1641,x1642))
% 0.67/0.86 [165]~P6(x1652)+~P6(x1651)+~P7(x1652,a3)+~P7(x1651,a3)+P6(f34(x1651,x1652))
% 0.67/0.86 [178]~P4(x1781)+P2(f12(x1782,x1781),x1781)+~P7(x1782,a3)+E(x1781,f30(x1782))+P1(f12(x1782,x1781))
% 0.67/0.86 [200]~P4(x2001)+P2(f12(x2002,x2001),x2001)+~P7(x2002,a3)+~P2(f12(x2002,x2001),x2002)+E(x2001,f30(x2002))
% 0.67/0.86 [201]~P1(x2011)+~P1(x2012)+~P10(x2012,a7,x2011)+E(x2011,a4)+P2(x2012,f37(a7,x2011))
% 0.67/0.86 [185]~P1(x1851)+P8(x1852)+~P7(x1852,a3)+E(x1851,a4)+~P7(f37(f10(x1852),x1851),x1852)
% 0.67/0.86 [192]~P1(x1922)+~P1(x1921)+E(x1921,a4)+P2(x1922,f37(a7,x1921))+~P3(x1921,f33(x1922,f31(a7)))
% 0.67/0.86 [119]~P1(x1191)+~P1(x1193)+P4(x1192)+E(x1191,a4)+~E(x1192,f37(x1193,x1191))
% 0.67/0.86 [144]~P4(x1442)+~P2(x1441,x1443)+P1(x1441)+P2(f23(x1442),x1442)+~E(x1443,f5(x1442))
% 0.67/0.86 [146]~P1(x1461)+P2(x1461,x1462)+P2(x1461,x1463)+~E(x1462,f30(x1463))+~P7(x1463,a3)
% 0.67/0.86 [160]~P4(x1603)+~P2(x1601,x1602)+P1(x1601)+~E(x1602,f5(x1603))+~P7(f23(x1603),a3)
% 0.67/0.86 [218]~P4(x2181)+~P2(x2182,x2183)+~E(x2183,f5(x2181))+P2(f23(x2181),x2181)+P2(x2182,f28(x2181,x2183,x2182))
% 0.67/0.86 [219]~P4(x2191)+~P2(x2193,x2192)+~E(x2192,f5(x2191))+P2(f23(x2191),x2191)+P2(f28(x2191,x2192,x2193),x2191)
% 0.67/0.86 [221]~P4(x2212)+~P2(x2211,x2213)+~E(x2213,f5(x2212))+P2(x2211,f28(x2212,x2213,x2211))+~P7(f23(x2212),a3)
% 0.67/0.86 [222]~P4(x2221)+~P2(x2223,x2222)+~E(x2222,f5(x2221))+P2(f28(x2221,x2222,x2223),x2221)+~P7(f23(x2221),a3)
% 0.67/0.86 [204]~P1(x2041)+~P1(x2043)+~P2(x2042,a1)+~E(f32(f8(x2042),x2043),f33(x2041,f31(a4)))+P2(x2041,f37(a4,f8(x2042)))
% 0.67/0.86 [167]~P2(x1671,x1672)+P1(x1671)+~P7(x1674,a3)+~P7(x1673,a3)+~E(x1672,f34(x1673,x1674))
% 0.67/0.86 [168]~P2(x1681,x1682)+P1(x1681)+~P7(x1684,a3)+~P7(x1683,a3)+~E(x1682,f35(x1683,x1684))
% 0.67/0.86 [174]~P2(x1741,x1743)+P2(x1741,x1742)+~P7(x1744,a3)+~P7(x1742,a3)+~E(x1743,f35(x1744,x1742))
% 0.67/0.86 [175]~P2(x1751,x1753)+P2(x1751,x1752)+~P7(x1754,a3)+~P7(x1752,a3)+~E(x1753,f35(x1752,x1754))
% 0.67/0.86 [182]~P4(x1821)+~P4(x1822)+P2(f23(x1822),x1822)+P2(f27(x1822,x1821),x1821)+E(x1821,f5(x1822))+P1(f27(x1822,x1821))
% 0.67/0.86 [188]~P4(x1881)+~P4(x1882)+P2(f27(x1882,x1881),x1881)+E(x1881,f5(x1882))+P1(f27(x1882,x1881))+~P7(f23(x1882),a3)
% 0.67/0.86 [190]~P4(x1901)+~P4(x1902)+P2(f23(x1902),x1902)+P2(f27(x1902,x1901),x1901)+P2(f29(x1902,x1901),x1902)+E(x1901,f5(x1902))
% 0.67/0.86 [197]~P4(x1971)+~P4(x1972)+P2(f27(x1972,x1971),x1971)+P2(f29(x1972,x1971),x1972)+E(x1971,f5(x1972))+~P7(f23(x1972),a3)
% 0.67/0.86 [206]~P4(x2061)+~P4(x2062)+P2(f23(x2062),x2062)+P2(f27(x2062,x2061),x2061)+P2(f27(x2062,x2061),f29(x2062,x2061))+E(x2061,f5(x2062))
% 0.67/0.86 [209]~P4(x2091)+~P4(x2092)+P2(f27(x2092,x2091),x2091)+P2(f27(x2092,x2091),f29(x2092,x2091))+E(x2091,f5(x2092))+~P7(f23(x2092),a3)
% 0.67/0.86 [220]~P4(x2201)+P2(f12(x2202,x2201),x2202)+~P7(x2202,a3)+~P2(f12(x2202,x2201),x2201)+E(x2201,f30(x2202))+~P1(f12(x2202,x2201))
% 0.67/0.86 [216]~P1(x2161)+~P1(x2162)+~P1(x2163)+~P10(x2163,x2162,x2161)+P10(x2162,x2163,x2161)+E(x2161,a4)
% 0.67/0.86 [143]~P1(x1432)+~P1(x1433)+~P1(x1431)+P3(x1431,x1432)+E(x1431,a4)+~E(f32(x1431,x1433),x1432)
% 0.67/0.86 [169]~P1(x1691)+~P9(x1691)+P1(x1692)+E(x1691,a4)+P2(x1693,a1)+~P2(x1692,f37(a4,x1691))
% 0.67/0.86 [202]~P1(x2021)+~P9(x2021)+P10(x2023,a4,x2021)+E(x2021,a4)+P2(x2022,a1)+~P2(x2023,f37(a4,x2021))
% 0.67/0.86 [223]~P1(x2231)+~P9(x2231)+E(x2231,a4)+P2(x2232,a1)+~P2(x2233,f37(a4,x2231))+P1(f17(x2232,x2231,x2233))
% 0.67/0.86 [231]~P4(x2311)+P2(f25(x2312,x2313,x2311),x2311)+~P7(x2313,a3)+~P7(x2312,a3)+E(x2311,f34(x2312,x2313))+P1(f25(x2312,x2313,x2311))
% 0.67/0.86 [232]~P4(x2321)+P2(f26(x2322,x2323,x2321),x2321)+~P7(x2323,a3)+~P7(x2322,a3)+E(x2321,f35(x2322,x2323))+P1(f26(x2322,x2323,x2321))
% 0.67/0.86 [233]~P4(x2331)+P2(f26(x2332,x2333,x2331),x2331)+P2(f26(x2332,x2333,x2331),x2333)+~P7(x2333,a3)+~P7(x2332,a3)+E(x2331,f35(x2332,x2333))
% 0.67/0.86 [234]~P4(x2341)+P2(f26(x2342,x2343,x2341),x2341)+P2(f26(x2342,x2343,x2341),x2342)+~P7(x2343,a3)+~P7(x2342,a3)+E(x2341,f35(x2342,x2343))
% 0.67/0.86 [181]~P1(x1812)+~P1(x1811)+~P1(x1813)+E(x1811,a4)+P2(x1812,f37(a7,x1811))+~E(f32(x1811,x1813),f33(x1812,f31(a7)))
% 0.67/0.86 [199]~P1(x1991)+~P9(x1991)+E(x1991,a4)+P2(x1992,a1)+~P2(x1993,f37(a4,x1991))+P3(x1991,f33(x1993,f31(a4)))
% 0.67/0.86 [213]~P1(x2133)+~P1(x2132)+~P1(x2131)+P10(x2132,x2133,x2131)+E(x2131,a4)+~P3(x2131,f33(x2132,f31(x2133)))
% 0.67/0.86 [215]~P1(x2151)+~P1(x2153)+~P1(x2152)+~P10(x2152,x2153,x2151)+E(x2151,a4)+P3(x2151,f33(x2152,f31(x2153)))
% 0.67/0.86 [226]~P1(x2261)+~P9(x2261)+P2(x2262,a1)+E(x2261,a4)+~P2(x2263,f37(a4,x2261))+E(f32(x2261,f17(x2262,x2261,x2263)),f33(x2263,f31(a4)))
% 0.67/0.86 [148]~P1(x1481)+~P1(x1484)+~P2(x1482,x1483)+P1(x1482)+E(x1481,a4)+~E(x1483,f37(x1484,x1481))
% 0.67/0.86 [179]~P1(x1791)+~P2(x1791,x1794)+P2(x1791,x1792)+~P7(x1793,a3)+~P7(x1794,a3)+~E(x1792,f34(x1793,x1794))
% 0.67/0.86 [180]~P1(x1801)+~P2(x1801,x1803)+P2(x1801,x1802)+~P7(x1804,a3)+~P7(x1803,a3)+~E(x1802,f34(x1803,x1804))
% 0.67/0.86 [186]~P2(x1861,x1864)+P2(x1861,x1862)+P2(x1861,x1863)+~P7(x1862,a3)+~P7(x1863,a3)+~E(x1864,f34(x1863,x1862))
% 0.67/0.86 [187]~P1(x1871)+~P1(x1873)+~P2(x1872,x1874)+P10(x1872,x1873,x1871)+E(x1871,a4)+~E(x1874,f37(x1873,x1871))
% 0.67/0.86 [210]~P1(x2101)+~P1(x2103)+~P9(x2101)+~P10(x2103,a4,x2101)+E(x2101,a4)+P2(x2102,a1)+P2(x2103,f37(a4,x2101))
% 0.67/0.86 [230]~P1(x2301)+~P1(x2303)+~P4(x2302)+P2(f13(x2303,x2301,x2302),x2302)+E(x2301,a4)+E(x2302,f37(x2303,x2301))+P1(f13(x2303,x2301,x2302))
% 0.67/0.86 [235]~P1(x2351)+~P1(x2353)+~P4(x2352)+P10(f13(x2353,x2351,x2352),x2353,x2351)+P2(f13(x2353,x2351,x2352),x2352)+E(x2351,a4)+E(x2352,f37(x2353,x2351))
% 0.67/0.86 [236]~P4(x2361)+P2(f25(x2362,x2363,x2361),x2361)+P2(f25(x2362,x2363,x2361),x2363)+P2(f25(x2362,x2363,x2361),x2362)+~P7(x2363,a3)+~P7(x2362,a3)+E(x2361,f34(x2362,x2363))
% 0.67/0.86 [237]~P4(x2371)+~P7(x2373,a3)+~P7(x2372,a3)+~P2(f25(x2372,x2373,x2371),x2371)+~P2(f25(x2372,x2373,x2371),x2373)+E(x2371,f34(x2372,x2373))+~P1(f25(x2372,x2373,x2371))
% 0.67/0.86 [238]~P4(x2381)+~P7(x2383,a3)+~P7(x2382,a3)+~P2(f25(x2382,x2383,x2381),x2381)+~P2(f25(x2382,x2383,x2381),x2382)+E(x2381,f34(x2382,x2383))+~P1(f25(x2382,x2383,x2381))
% 0.67/0.86 [205]~P1(x2053)+~P1(x2051)+~P9(x2051)+E(x2051,a4)+P2(x2052,a1)+P2(x2053,f37(a4,x2051))+~P3(x2051,f33(x2053,f31(a4)))
% 0.67/0.86 [177]~P1(x1771)+~P4(x1773)+~P2(x1771,x1774)+P2(x1771,x1772)+~P2(x1774,x1773)+~E(x1772,f5(x1773))+P2(f23(x1773),x1773)
% 0.67/0.86 [183]~P1(x1831)+~P4(x1833)+~P2(x1831,x1834)+P2(x1831,x1832)+~P2(x1834,x1833)+~E(x1832,f5(x1833))+~P7(f23(x1833),a3)
% 0.67/0.86 [198]~P1(x1981)+~P2(x1981,x1984)+~P2(x1981,x1983)+P2(x1981,x1982)+~P7(x1984,a3)+~P7(x1983,a3)+~E(x1982,f35(x1983,x1984))
% 0.67/0.86 [207]~P1(x2071)+~P1(x2074)+~P1(x2072)+~P10(x2072,x2074,x2071)+P2(x2072,x2073)+E(x2071,a4)+~E(x2073,f37(x2074,x2071))
% 0.67/0.86 [227]~P4(x2271)+~P4(x2272)+~P2(x2273,x2272)+P2(f23(x2272),x2272)+~P2(f27(x2272,x2271),x2273)+~P2(f27(x2272,x2271),x2271)+E(x2271,f5(x2272))+~P1(f27(x2272,x2271))
% 0.67/0.86 [228]~P4(x2281)+~P4(x2282)+~P2(x2283,x2282)+~P2(f27(x2282,x2281),x2283)+~P2(f27(x2282,x2281),x2281)+E(x2281,f5(x2282))+~P1(f27(x2282,x2281))+~P7(f23(x2282),a3)
% 0.67/0.86 [239]~P1(x2391)+~P1(x2393)+~P4(x2392)+~P10(f13(x2393,x2391,x2392),x2393,x2391)+~P2(f13(x2393,x2391,x2392),x2392)+E(x2391,a4)+E(x2392,f37(x2393,x2391))+~P1(f13(x2393,x2391,x2392))
% 0.67/0.86 [240]~P4(x2401)+~P7(x2403,a3)+~P7(x2402,a3)+~P2(f26(x2402,x2403,x2401),x2401)+~P2(f26(x2402,x2403,x2401),x2403)+~P2(f26(x2402,x2403,x2401),x2402)+E(x2401,f35(x2402,x2403))+~P1(f26(x2402,x2403,x2401))
% 0.67/0.86 [229]~P1(x2293)+~P1(x2291)+~P1(x2292)+~P10(x2294,x2293,x2291)+~P10(x2292,x2294,x2291)+P10(x2292,x2293,x2291)+~P1(x2294)+E(x2291,a4)
% 0.67/0.86 [224]~P1(x2241)+~P1(x2242)+~P1(x2244)+~P1(x2243)+P10(x2243,x2244,x2242)+~P10(x2243,x2244,f32(x2241,x2242))+E(x2241,a4)+E(x2242,a4)
% 0.67/0.86 [225]~P1(x2251)+~P1(x2252)+~P1(x2254)+~P1(x2253)+P10(x2253,x2254,x2252)+~P10(x2253,x2254,f32(x2252,x2251))+E(x2251,a4)+E(x2252,a4)
% 0.67/0.86 [196]~P1(x1963)+~P1(x1961)+~P1(x1964)+~P9(x1961)+E(x1961,a4)+P2(x1962,a1)+P2(x1963,f37(a4,x1961))+~E(f32(x1961,x1964),f33(x1963,f31(a4)))
% 0.67/0.86 %EqnAxiom
% 0.67/0.86 [1]E(x11,x11)
% 0.67/0.86 [2]E(x22,x21)+~E(x21,x22)
% 0.67/0.86 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.67/0.86 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.67/0.86 [5]~E(x51,x52)+E(f30(x51),f30(x52))
% 0.67/0.86 [6]~E(x61,x62)+E(f26(x61,x63,x64),f26(x62,x63,x64))
% 0.67/0.86 [7]~E(x71,x72)+E(f26(x73,x71,x74),f26(x73,x72,x74))
% 0.67/0.86 [8]~E(x81,x82)+E(f26(x83,x84,x81),f26(x83,x84,x82))
% 0.67/0.86 [9]~E(x91,x92)+E(f8(x91),f8(x92))
% 0.67/0.86 [10]~E(x101,x102)+E(f37(x101,x103),f37(x102,x103))
% 0.67/0.86 [11]~E(x111,x112)+E(f37(x113,x111),f37(x113,x112))
% 0.67/0.86 [12]~E(x121,x122)+E(f31(x121),f31(x122))
% 0.67/0.86 [13]~E(x131,x132)+E(f32(x131,x133),f32(x132,x133))
% 0.67/0.86 [14]~E(x141,x142)+E(f32(x143,x141),f32(x143,x142))
% 0.67/0.86 [15]~E(x151,x152)+E(f23(x151),f23(x152))
% 0.67/0.86 [16]~E(x161,x162)+E(f35(x161,x163),f35(x162,x163))
% 0.67/0.86 [17]~E(x171,x172)+E(f35(x173,x171),f35(x173,x172))
% 0.67/0.86 [18]~E(x181,x182)+E(f13(x181,x183,x184),f13(x182,x183,x184))
% 0.67/0.86 [19]~E(x191,x192)+E(f13(x193,x191,x194),f13(x193,x192,x194))
% 0.67/0.86 [20]~E(x201,x202)+E(f13(x203,x204,x201),f13(x203,x204,x202))
% 0.67/0.86 [21]~E(x211,x212)+E(f17(x211,x213,x214),f17(x212,x213,x214))
% 0.67/0.86 [22]~E(x221,x222)+E(f17(x223,x221,x224),f17(x223,x222,x224))
% 0.67/0.86 [23]~E(x231,x232)+E(f17(x233,x234,x231),f17(x233,x234,x232))
% 0.67/0.86 [24]~E(x241,x242)+E(f27(x241,x243),f27(x242,x243))
% 0.67/0.86 [25]~E(x251,x252)+E(f27(x253,x251),f27(x253,x252))
% 0.67/0.86 [26]~E(x261,x262)+E(f28(x261,x263,x264),f28(x262,x263,x264))
% 0.67/0.86 [27]~E(x271,x272)+E(f28(x273,x271,x274),f28(x273,x272,x274))
% 0.67/0.86 [28]~E(x281,x282)+E(f28(x283,x284,x281),f28(x283,x284,x282))
% 0.67/0.86 [29]~E(x291,x292)+E(f25(x291,x293,x294),f25(x292,x293,x294))
% 0.67/0.86 [30]~E(x301,x302)+E(f25(x303,x301,x304),f25(x303,x302,x304))
% 0.67/0.86 [31]~E(x311,x312)+E(f25(x313,x314,x311),f25(x313,x314,x312))
% 0.67/0.86 [32]~E(x321,x322)+E(f33(x321,x323),f33(x322,x323))
% 0.67/0.86 [33]~E(x331,x332)+E(f33(x333,x331),f33(x333,x332))
% 0.67/0.86 [34]~E(x341,x342)+E(f11(x341,x343),f11(x342,x343))
% 0.67/0.86 [35]~E(x351,x352)+E(f11(x353,x351),f11(x353,x352))
% 0.67/0.86 [36]~E(x361,x362)+E(f9(x361),f9(x362))
% 0.67/0.86 [37]~E(x371,x372)+E(f34(x371,x373),f34(x372,x373))
% 0.67/0.86 [38]~E(x381,x382)+E(f34(x383,x381),f34(x383,x382))
% 0.67/0.86 [39]~E(x391,x392)+E(f16(x391,x393),f16(x392,x393))
% 0.67/0.86 [40]~E(x401,x402)+E(f16(x403,x401),f16(x403,x402))
% 0.67/0.86 [41]~E(x411,x412)+E(f20(x411),f20(x412))
% 0.67/0.86 [42]~E(x421,x422)+E(f10(x421),f10(x422))
% 0.67/0.86 [43]~E(x431,x432)+E(f29(x431,x433),f29(x432,x433))
% 0.67/0.86 [44]~E(x441,x442)+E(f29(x443,x441),f29(x443,x442))
% 0.67/0.86 [45]~E(x451,x452)+E(f21(x451),f21(x452))
% 0.67/0.86 [46]~E(x461,x462)+E(f22(x461,x463),f22(x462,x463))
% 0.67/0.86 [47]~E(x471,x472)+E(f22(x473,x471),f22(x473,x472))
% 0.67/0.86 [48]~E(x481,x482)+E(f12(x481,x483),f12(x482,x483))
% 0.67/0.86 [49]~E(x491,x492)+E(f12(x493,x491),f12(x493,x492))
% 0.67/0.86 [50]~E(x501,x502)+E(f14(x501),f14(x502))
% 0.67/0.86 [51]~E(x511,x512)+E(f15(x511),f15(x512))
% 0.67/0.86 [52]~E(x521,x522)+E(f24(x521,x523),f24(x522,x523))
% 0.67/0.86 [53]~E(x531,x532)+E(f24(x533,x531),f24(x533,x532))
% 0.67/0.86 [54]~E(x541,x542)+E(f19(x541,x543),f19(x542,x543))
% 0.67/0.86 [55]~E(x551,x552)+E(f19(x553,x551),f19(x553,x552))
% 0.67/0.86 [56]~E(x561,x562)+E(f18(x561),f18(x562))
% 0.67/0.86 [57]~P1(x571)+P1(x572)+~E(x571,x572)
% 0.67/0.86 [58]P2(x582,x583)+~E(x581,x582)+~P2(x581,x583)
% 0.67/0.86 [59]P2(x593,x592)+~E(x591,x592)+~P2(x593,x591)
% 0.67/0.86 [60]~P4(x601)+P4(x602)+~E(x601,x602)
% 0.67/0.86 [61]~P5(x611)+P5(x612)+~E(x611,x612)
% 0.67/0.86 [62]~P6(x621)+P6(x622)+~E(x621,x622)
% 0.67/0.86 [63]P7(x632,x633)+~E(x631,x632)+~P7(x631,x633)
% 0.67/0.86 [64]P7(x643,x642)+~E(x641,x642)+~P7(x643,x641)
% 0.67/0.86 [65]P3(x652,x653)+~E(x651,x652)+~P3(x651,x653)
% 0.67/0.86 [66]P3(x663,x662)+~E(x661,x662)+~P3(x663,x661)
% 0.67/0.86 [67]P10(x672,x673,x674)+~E(x671,x672)+~P10(x671,x673,x674)
% 0.67/0.86 [68]P10(x683,x682,x684)+~E(x681,x682)+~P10(x683,x681,x684)
% 0.67/0.86 [69]P10(x693,x694,x692)+~E(x691,x692)+~P10(x693,x694,x691)
% 0.67/0.86 [70]~P9(x701)+P9(x702)+~E(x701,x702)
% 0.67/0.86 [71]~P8(x711)+P8(x712)+~E(x711,x712)
% 0.67/0.86
% 0.67/0.86 %-------------------------------------------
% 0.67/0.87 cnf(241,plain,
% 0.67/0.87 (E(a2,a1)),
% 0.67/0.87 inference(scs_inference,[],[72,2])).
% 0.67/0.87 cnf(242,plain,
% 0.67/0.87 (P1(a7)),
% 0.67/0.87 inference(scs_inference,[],[72,81,2,126])).
% 0.67/0.87 cnf(248,plain,
% 0.67/0.87 (~E(f30(f5(a1)),f5(a1))),
% 0.67/0.87 inference(scs_inference,[],[72,75,76,81,2,126,155,61,60,59])).
% 0.67/0.87 cnf(251,plain,
% 0.67/0.87 (~P2(f30(f5(a1)),a1)),
% 0.67/0.87 inference(scs_inference,[],[79,72,75,76,81,2,126,155,61,60,59,147,150])).
% 0.67/0.87 cnf(257,plain,
% 0.67/0.87 (E(f37(a4,f8(f14(a1))),f14(a1))),
% 0.67/0.87 inference(scs_inference,[],[79,72,75,76,82,81,2,126,155,61,60,59,147,150,123,140,112])).
% 0.67/0.87 cnf(261,plain,
% 0.67/0.87 (P1(f8(f14(a1)))),
% 0.67/0.87 inference(scs_inference,[],[79,72,75,76,82,81,2,126,155,61,60,59,147,150,123,140,112,99,98])).
% 0.67/0.87 cnf(263,plain,
% 0.67/0.87 (~E(f8(f14(a1)),a4)),
% 0.67/0.87 inference(scs_inference,[],[79,72,75,76,82,81,2,126,155,61,60,59,147,150,123,140,112,99,98,92])).
% 0.67/0.87 cnf(271,plain,
% 0.67/0.87 (E(f33(a4,a36),a36)),
% 0.67/0.87 inference(scs_inference,[],[79,72,73,74,75,76,82,81,2,126,155,61,60,59,147,150,123,140,112,99,98,92,90,89,88,87])).
% 0.67/0.87 cnf(331,plain,
% 0.67/0.87 (E(f5(a1),f5(a2))),
% 0.67/0.87 inference(scs_inference,[],[79,72,73,74,75,76,82,81,2,126,155,61,60,59,147,150,123,140,112,99,98,92,90,89,88,87,86,85,84,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4])).
% 0.67/0.87 cnf(351,plain,
% 0.67/0.87 (P7(f37(a4,f8(f14(a1))),a3)),
% 0.67/0.87 inference(scs_inference,[],[79,72,73,74,75,76,82,81,77,2,126,155,61,60,59,147,150,123,140,112,99,98,92,90,89,88,87,86,85,84,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,96,95,94,93,70,58,3,102,121,120,108,137])).
% 0.67/0.87 cnf(353,plain,
% 0.67/0.87 (P6(f37(a4,f8(f14(a1))))),
% 0.67/0.87 inference(scs_inference,[],[79,72,73,74,75,76,82,81,77,2,126,155,61,60,59,147,150,123,140,112,99,98,92,90,89,88,87,86,85,84,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,96,95,94,93,70,58,3,102,121,120,108,137,124])).
% 0.67/0.87 cnf(413,plain,
% 0.67/0.87 (P7(f14(a1),a3)),
% 0.67/0.87 inference(scs_inference,[],[79,74,261,257,248,331,351,251,263,271,241,97,156,121,120,173,172,2,60,59,194,193,63])).
% 0.67/0.87 cnf(414,plain,
% 0.67/0.87 (P6(f14(a1))),
% 0.67/0.87 inference(scs_inference,[],[79,74,353,261,257,248,331,351,251,263,271,241,97,156,121,120,173,172,2,60,59,194,193,63,62])).
% 0.67/0.87 cnf(457,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(scs_inference,[],[75,76,82,74,414,413,242,263,261,156,173,172,158]),
% 0.67/0.87 ['proof']).
% 0.67/0.87 % SZS output end Proof
% 0.67/0.87 % Total time :0.150000s
%------------------------------------------------------------------------------