TSTP Solution File: RNG102+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG102+2 : 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 : n031.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 13:48:10 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG102+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Sun Aug 27 02:58:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 start to proof:theBenchmark
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % File :CSE---1.6
% 0.20/0.67 % Problem :theBenchmark
% 0.20/0.67 % Transform :cnf
% 0.20/0.67 % Format :tptp:raw
% 0.20/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.67
% 0.20/0.67 % Result :Theorem 0.000000s
% 0.20/0.67 % Output :CNFRefutation 0.000000s
% 0.20/0.67 %-------------------------------------------
% 0.20/0.68 %------------------------------------------------------------------------------
% 0.20/0.68 % File : RNG102+2 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.68 % Domain : Ring Theory
% 0.20/0.68 % Problem : Chinese remainder theorem in a ring 06_02, 01 expansion
% 0.20/0.68 % Version : Especial.
% 0.20/0.68 % English :
% 0.20/0.68
% 0.20/0.68 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.68 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.68 % Source : [Pas08]
% 0.20/0.68 % Names : chines_06_02.01 [Pas08]
% 0.20/0.68
% 0.20/0.68 % Status : Theorem
% 0.20/0.68 % Rating : 0.06 v8.1.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.10 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.35 v4.0.1, 0.70 v4.0.0
% 0.20/0.68 % Syntax : Number of formulae : 41 ( 4 unt; 9 def)
% 0.20/0.68 % Number of atoms : 162 ( 35 equ)
% 0.20/0.68 % Maximal formula atoms : 9 ( 3 avg)
% 0.20/0.68 % Number of connectives : 125 ( 4 ~; 1 |; 61 &)
% 0.20/0.68 % ( 12 <=>; 47 =>; 0 <=; 0 <~>)
% 0.20/0.68 % Maximal formula depth : 13 ( 6 avg)
% 0.20/0.68 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.68 % Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% 0.20/0.68 % Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% 0.20/0.68 % Number of variables : 86 ( 76 !; 10 ?)
% 0.20/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.68
% 0.20/0.68 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.68 %------------------------------------------------------------------------------
% 0.20/0.68 fof(mElmSort,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aElement0(W0)
% 0.20/0.68 => $true ) ).
% 0.20/0.68
% 0.20/0.68 fof(mSortsC,axiom,
% 0.20/0.68 aElement0(sz00) ).
% 0.20/0.68
% 0.20/0.68 fof(mSortsC_01,axiom,
% 0.20/0.68 aElement0(sz10) ).
% 0.20/0.68
% 0.20/0.68 fof(mSortsU,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aElement0(W0)
% 0.20/0.68 => aElement0(smndt0(W0)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mSortsB,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1) )
% 0.20/0.68 => aElement0(sdtpldt0(W0,W1)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mSortsB_02,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1) )
% 0.20/0.68 => aElement0(sdtasdt0(W0,W1)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAddComm,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1) )
% 0.20/0.68 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAddAsso,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1)
% 0.20/0.68 & aElement0(W2) )
% 0.20/0.68 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAddZero,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aElement0(W0)
% 0.20/0.68 => ( sdtpldt0(W0,sz00) = W0
% 0.20/0.68 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mAddInvr,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.68 ( aElement0(W0)
% 0.20/0.68 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.20/0.68 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMulComm,axiom,
% 0.20/0.68 ! [W0,W1] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1) )
% 0.20/0.68 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMulAsso,axiom,
% 0.20/0.68 ! [W0,W1,W2] :
% 0.20/0.68 ( ( aElement0(W0)
% 0.20/0.68 & aElement0(W1)
% 0.20/0.68 & aElement0(W2) )
% 0.20/0.68 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.20/0.68
% 0.20/0.68 fof(mMulUnit,axiom,
% 0.20/0.68 ! [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 => ( sdtasdt0(W0,sz10) = W0
% 0.20/0.69 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mAMDistr,axiom,
% 0.20/0.69 ! [W0,W1,W2] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1)
% 0.20/0.69 & aElement0(W2) )
% 0.20/0.69 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.69 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mMulMnOne,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.20/0.69 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mMulZero,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 => ( sdtasdt0(W0,sz00) = sz00
% 0.20/0.69 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mCancel,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1) )
% 0.20/0.69 => ( sdtasdt0(W0,W1) = sz00
% 0.20/0.69 => ( W0 = sz00
% 0.20/0.69 | W1 = sz00 ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mUnNeZr,axiom,
% 0.20/0.69 sz10 != sz00 ).
% 0.20/0.69
% 0.20/0.69 fof(mSetSort,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aSet0(W0)
% 0.20/0.69 => $true ) ).
% 0.20/0.69
% 0.20/0.69 fof(mEOfElem,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aSet0(W0)
% 0.20/0.69 => ! [W1] :
% 0.20/0.69 ( aElementOf0(W1,W0)
% 0.20/0.69 => aElement0(W1) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mSetEq,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aSet0(W0)
% 0.20/0.69 & aSet0(W1) )
% 0.20/0.69 => ( ( ! [W2] :
% 0.20/0.69 ( aElementOf0(W2,W0)
% 0.20/0.69 => aElementOf0(W2,W1) )
% 0.20/0.69 & ! [W2] :
% 0.20/0.69 ( aElementOf0(W2,W1)
% 0.20/0.69 => aElementOf0(W2,W0) ) )
% 0.20/0.69 => W0 = W1 ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefSSum,definition,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aSet0(W0)
% 0.20/0.69 & aSet0(W1) )
% 0.20/0.69 => ! [W2] :
% 0.20/0.69 ( W2 = sdtpldt1(W0,W1)
% 0.20/0.69 <=> ( aSet0(W2)
% 0.20/0.69 & ! [W3] :
% 0.20/0.69 ( aElementOf0(W3,W2)
% 0.20/0.69 <=> ? [W4,W5] :
% 0.20/0.69 ( aElementOf0(W4,W0)
% 0.20/0.69 & aElementOf0(W5,W1)
% 0.20/0.69 & sdtpldt0(W4,W5) = W3 ) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefSInt,definition,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aSet0(W0)
% 0.20/0.69 & aSet0(W1) )
% 0.20/0.69 => ! [W2] :
% 0.20/0.69 ( W2 = sdtasasdt0(W0,W1)
% 0.20/0.69 <=> ( aSet0(W2)
% 0.20/0.69 & ! [W3] :
% 0.20/0.69 ( aElementOf0(W3,W2)
% 0.20/0.69 <=> ( aElementOf0(W3,W0)
% 0.20/0.69 & aElementOf0(W3,W1) ) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefIdeal,definition,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aIdeal0(W0)
% 0.20/0.69 <=> ( aSet0(W0)
% 0.20/0.69 & ! [W1] :
% 0.20/0.69 ( aElementOf0(W1,W0)
% 0.20/0.69 => ( ! [W2] :
% 0.20/0.69 ( aElementOf0(W2,W0)
% 0.20/0.69 => aElementOf0(sdtpldt0(W1,W2),W0) )
% 0.20/0.69 & ! [W2] :
% 0.20/0.69 ( aElement0(W2)
% 0.20/0.69 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mIdeSum,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aIdeal0(W0)
% 0.20/0.69 & aIdeal0(W1) )
% 0.20/0.69 => aIdeal0(sdtpldt1(W0,W1)) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mIdeInt,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aIdeal0(W0)
% 0.20/0.69 & aIdeal0(W1) )
% 0.20/0.69 => aIdeal0(sdtasasdt0(W0,W1)) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefMod,definition,
% 0.20/0.69 ! [W0,W1,W2] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1)
% 0.20/0.69 & aIdeal0(W2) )
% 0.20/0.69 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.20/0.69 <=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mChineseRemainder,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aIdeal0(W0)
% 0.20/0.69 & aIdeal0(W1) )
% 0.20/0.69 => ( ! [W2] :
% 0.20/0.69 ( aElement0(W2)
% 0.20/0.69 => aElementOf0(W2,sdtpldt1(W0,W1)) )
% 0.20/0.69 => ! [W2,W3] :
% 0.20/0.69 ( ( aElement0(W2)
% 0.20/0.69 & aElement0(W3) )
% 0.20/0.69 => ? [W4] :
% 0.20/0.69 ( aElement0(W4)
% 0.20/0.69 & sdteqdtlpzmzozddtrp0(W4,W2,W0)
% 0.20/0.69 & sdteqdtlpzmzozddtrp0(W4,W3,W1) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mNatSort,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aNaturalNumber0(W0)
% 0.20/0.69 => $true ) ).
% 0.20/0.69
% 0.20/0.69 fof(mEucSort,axiom,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & W0 != sz00 )
% 0.20/0.69 => aNaturalNumber0(sbrdtbr0(W0)) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mNatLess,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aNaturalNumber0(W0)
% 0.20/0.69 & aNaturalNumber0(W1) )
% 0.20/0.69 => ( iLess0(W0,W1)
% 0.20/0.69 => $true ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDivision,axiom,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1)
% 0.20/0.69 & W1 != sz00 )
% 0.20/0.69 => ? [W2,W3] :
% 0.20/0.69 ( aElement0(W2)
% 0.20/0.69 & aElement0(W3)
% 0.20/0.69 & W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
% 0.20/0.69 & ( W3 != sz00
% 0.20/0.69 => iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefDiv,definition,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1) )
% 0.20/0.69 => ( doDivides0(W0,W1)
% 0.20/0.69 <=> ? [W2] :
% 0.20/0.69 ( aElement0(W2)
% 0.20/0.69 & sdtasdt0(W0,W2) = W1 ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefDvs,definition,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 => ! [W1] :
% 0.20/0.69 ( aDivisorOf0(W1,W0)
% 0.20/0.69 <=> ( aElement0(W1)
% 0.20/0.69 & doDivides0(W1,W0) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefGCD,definition,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1) )
% 0.20/0.69 => ! [W2] :
% 0.20/0.69 ( aGcdOfAnd0(W2,W0,W1)
% 0.20/0.69 <=> ( aDivisorOf0(W2,W0)
% 0.20/0.69 & aDivisorOf0(W2,W1)
% 0.20/0.69 & ! [W3] :
% 0.20/0.69 ( ( aDivisorOf0(W3,W0)
% 0.20/0.69 & aDivisorOf0(W3,W1) )
% 0.20/0.69 => doDivides0(W3,W2) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefRel,definition,
% 0.20/0.69 ! [W0,W1] :
% 0.20/0.69 ( ( aElement0(W0)
% 0.20/0.69 & aElement0(W1) )
% 0.20/0.69 => ( misRelativelyPrime0(W0,W1)
% 0.20/0.69 <=> aGcdOfAnd0(sz10,W0,W1) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(mDefPrIdeal,definition,
% 0.20/0.69 ! [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 => ! [W1] :
% 0.20/0.69 ( W1 = slsdtgt0(W0)
% 0.20/0.69 <=> ( aSet0(W1)
% 0.20/0.69 & ! [W2] :
% 0.20/0.69 ( aElementOf0(W2,W1)
% 0.20/0.69 <=> ? [W3] :
% 0.20/0.69 ( aElement0(W3)
% 0.20/0.69 & sdtasdt0(W0,W3) = W2 ) ) ) ) ) ).
% 0.20/0.69
% 0.20/0.69 fof(m__1905,hypothesis,
% 0.20/0.69 aElement0(xc) ).
% 0.20/0.69
% 0.20/0.69 fof(m__1933,hypothesis,
% 0.20/0.69 ( ? [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 & sdtasdt0(xc,W0) = xx )
% 0.20/0.69 & aElementOf0(xx,slsdtgt0(xc))
% 0.20/0.69 & ? [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 & sdtasdt0(xc,W0) = xy )
% 0.20/0.69 & aElementOf0(xy,slsdtgt0(xc))
% 0.20/0.69 & aElement0(xz) ) ).
% 0.20/0.69
% 0.20/0.69 fof(m__1956,hypothesis,
% 0.20/0.69 ( aElement0(xu)
% 0.20/0.69 & sdtasdt0(xc,xu) = xx ) ).
% 0.20/0.69
% 0.20/0.69 fof(m__,conjecture,
% 0.20/0.69 ? [W0] :
% 0.20/0.69 ( aElement0(W0)
% 0.20/0.69 & sdtasdt0(xc,W0) = xy ) ).
% 0.20/0.69
% 0.20/0.69 %------------------------------------------------------------------------------
% 0.20/0.69 %-------------------------------------------
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark
% 0.20/0.69 % SZS output start Proof
% 0.20/0.69 %ClaNum:182(EqnAxiom:83)
% 0.20/0.69 %VarNum:701(SingletonVarNum:213)
% 0.20/0.69 %MaxLitNum:8
% 0.20/0.69 %MaxfuncDepth:2
% 0.20/0.69 %SharedTerms:27
% 0.20/0.69 %goalClause: 107
% 0.20/0.69 [84]P1(a1)
% 0.20/0.69 [85]P1(a31)
% 0.20/0.69 [86]P1(a32)
% 0.20/0.69 [87]P1(a33)
% 0.20/0.69 [88]P1(a34)
% 0.20/0.69 [89]P1(a2)
% 0.20/0.69 [90]P1(a15)
% 0.20/0.69 [96]~E(a1,a31)
% 0.20/0.69 [91]E(f16(a32,a34),a35)
% 0.20/0.69 [92]E(f16(a32,a2),a35)
% 0.20/0.69 [93]E(f16(a32,a15),a36)
% 0.20/0.69 [94]P3(a35,f27(a32))
% 0.20/0.69 [95]P3(a36,f27(a32))
% 0.20/0.69 [97]~P5(x971)+P4(x971)
% 0.20/0.69 [98]~P1(x981)+P1(f30(x981))
% 0.20/0.69 [100]~P1(x1001)+E(f16(a1,x1001),a1)
% 0.20/0.69 [101]~P1(x1011)+E(f16(x1011,a1),a1)
% 0.20/0.69 [103]~P1(x1031)+E(f28(a1,x1031),x1031)
% 0.20/0.69 [104]~P1(x1041)+E(f16(a31,x1041),x1041)
% 0.20/0.69 [105]~P1(x1051)+E(f28(x1051,a1),x1051)
% 0.20/0.69 [106]~P1(x1061)+E(f16(x1061,a31),x1061)
% 0.20/0.69 [107]~P1(x1071)+~E(f16(a32,x1071),a36)
% 0.20/0.69 [108]~P1(x1081)+E(f28(f30(x1081),x1081),a1)
% 0.20/0.69 [109]~P1(x1091)+E(f28(x1091,f30(x1091)),a1)
% 0.20/0.69 [110]~P1(x1101)+E(f16(x1101,f30(a31)),f30(x1101))
% 0.20/0.69 [111]~P1(x1111)+E(f16(f30(a31),x1111),f30(x1111))
% 0.20/0.69 [99]~P1(x991)+E(x991,a1)+P7(f17(x991))
% 0.20/0.69 [112]~P4(x1121)+P5(x1121)+P3(f18(x1121),x1121)
% 0.20/0.69 [113]~P3(x1131,x1132)+P1(x1131)+~P4(x1132)
% 0.20/0.69 [114]~P2(x1141,x1142)+P1(x1141)+~P1(x1142)
% 0.20/0.69 [121]~P1(x1212)+~P2(x1211,x1212)+P8(x1211,x1212)
% 0.20/0.70 [102]~P1(x1022)+P4(x1021)+~E(x1021,f27(x1022))
% 0.20/0.70 [116]~P1(x1162)+~P1(x1161)+E(f28(x1161,x1162),f28(x1162,x1161))
% 0.20/0.70 [117]~P1(x1172)+~P1(x1171)+E(f16(x1171,x1172),f16(x1172,x1171))
% 0.20/0.70 [122]~P1(x1222)+~P1(x1221)+P1(f28(x1221,x1222))
% 0.20/0.70 [123]~P1(x1232)+~P1(x1231)+P1(f16(x1231,x1232))
% 0.20/0.70 [124]~P5(x1242)+~P5(x1241)+P5(f29(x1241,x1242))
% 0.20/0.70 [125]~P5(x1252)+~P5(x1251)+P5(f26(x1251,x1252))
% 0.20/0.70 [120]~P4(x1201)+P5(x1201)+P3(f4(x1201),x1201)+P1(f3(x1201))
% 0.20/0.70 [151]~P4(x1511)+P5(x1511)+P1(f3(x1511))+~P3(f28(f18(x1511),f4(x1511)),x1511)
% 0.20/0.70 [154]~P4(x1541)+P5(x1541)+P3(f4(x1541),x1541)+~P3(f16(f3(x1541),f18(x1541)),x1541)
% 0.20/0.70 [163]~P4(x1631)+P5(x1631)+~P3(f28(f18(x1631),f4(x1631)),x1631)+~P3(f16(f3(x1631),f18(x1631)),x1631)
% 0.20/0.70 [128]~P1(x1282)+~P1(x1281)+~P8(x1281,x1282)+P2(x1281,x1282)
% 0.20/0.70 [136]~P1(x1362)+~P1(x1361)+~P9(x1361,x1362)+P6(a31,x1361,x1362)
% 0.20/0.70 [144]~P1(x1442)+~P1(x1441)+P9(x1441,x1442)+~P6(a31,x1441,x1442)
% 0.20/0.70 [126]~P1(x1261)+~P1(x1262)+E(x1261,a1)+P1(f5(x1262,x1261))
% 0.20/0.70 [127]~P1(x1271)+~P1(x1272)+E(x1271,a1)+P1(f8(x1272,x1271))
% 0.20/0.70 [131]~P1(x1312)+~P1(x1311)+~P8(x1311,x1312)+P1(f9(x1311,x1312))
% 0.20/0.70 [135]~P1(x1352)+~P1(x1351)+~P8(x1351,x1352)+E(f16(x1351,f9(x1351,x1352)),x1352)
% 0.20/0.70 [156]~P1(x1561)+~P1(x1562)+E(x1561,a1)+E(f28(f16(f5(x1562,x1561),x1561),f8(x1562,x1561)),x1562)
% 0.20/0.70 [146]~P1(x1462)+~P6(x1461,x1463,x1462)+P2(x1461,x1462)+~P1(x1463)
% 0.20/0.70 [147]~P1(x1472)+~P6(x1471,x1472,x1473)+P2(x1471,x1472)+~P1(x1473)
% 0.20/0.70 [118]~P4(x1183)+~P4(x1182)+P4(x1181)+~E(x1181,f29(x1182,x1183))
% 0.20/0.70 [119]~P4(x1193)+~P4(x1192)+P4(x1191)+~E(x1191,f26(x1192,x1193))
% 0.20/0.70 [134]~P1(x1341)+~P5(x1343)+~P3(x1342,x1343)+P3(f16(x1341,x1342),x1343)
% 0.20/0.70 [138]~P5(x1383)+~P3(x1381,x1383)+~P3(x1382,x1383)+P3(f28(x1381,x1382),x1383)
% 0.20/0.70 [158]~P1(x1581)+~P3(x1583,x1582)+~E(x1582,f27(x1581))+P1(f12(x1581,x1582,x1583))
% 0.20/0.70 [141]~P1(x1413)+~P1(x1412)+~P1(x1411)+E(f28(f28(x1411,x1412),x1413),f28(x1411,f28(x1412,x1413)))
% 0.20/0.70 [142]~P1(x1423)+~P1(x1422)+~P1(x1421)+E(f16(f16(x1421,x1422),x1423),f16(x1421,f16(x1422,x1423)))
% 0.20/0.70 [152]~P1(x1523)+~P1(x1522)+~P1(x1521)+E(f28(f16(x1521,x1522),f16(x1521,x1523)),f16(x1521,f28(x1522,x1523)))
% 0.20/0.70 [153]~P1(x1532)+~P1(x1533)+~P1(x1531)+E(f28(f16(x1531,x1532),f16(x1533,x1532)),f16(f28(x1531,x1533),x1532))
% 0.20/0.70 [160]~P1(x1601)+~P3(x1603,x1602)+~E(x1602,f27(x1601))+E(f16(x1601,f12(x1601,x1602,x1603)),x1603)
% 0.20/0.70 [115]~P1(x1151)+~P1(x1152)+E(x1151,a1)+E(x1152,a1)+~E(f16(x1152,x1151),a1)
% 0.20/0.70 [137]~P1(x1372)+~P4(x1371)+P3(f11(x1372,x1371),x1371)+E(x1371,f27(x1372))+P1(f10(x1372,x1371))
% 0.20/0.70 [139]~P4(x1392)+~P4(x1391)+E(x1391,x1392)+P3(f14(x1391,x1392),x1391)+P3(f19(x1391,x1392),x1392)
% 0.20/0.70 [148]~P4(x1482)+~P4(x1481)+E(x1481,x1482)+P3(f14(x1481,x1482),x1481)+~P3(f19(x1481,x1482),x1481)
% 0.20/0.70 [149]~P4(x1492)+~P4(x1491)+E(x1491,x1492)+P3(f19(x1491,x1492),x1492)+~P3(f14(x1491,x1492),x1492)
% 0.20/0.70 [157]~P4(x1572)+~P4(x1571)+E(x1571,x1572)+~P3(f14(x1571,x1572),x1572)+~P3(f19(x1571,x1572),x1571)
% 0.20/0.70 [143]~P1(x1431)+~P1(x1432)+E(x1431,a1)+P10(f17(f8(x1432,x1431)),f17(x1431))+E(f8(x1432,x1431),a1)
% 0.20/0.70 [145]~P1(x1452)+~P4(x1451)+P3(f11(x1452,x1451),x1451)+E(x1451,f27(x1452))+E(f16(x1452,f10(x1452,x1451)),f11(x1452,x1451))
% 0.20/0.70 [129]~P1(x1292)+~P1(x1291)+~P1(x1293)+P8(x1291,x1292)+~E(f16(x1291,x1293),x1292)
% 0.20/0.70 [159]~P1(x1592)+~P1(x1591)+~P5(x1593)+P11(x1591,x1592,x1593)+~P3(f28(x1591,f30(x1592)),x1593)
% 0.20/0.70 [161]~P1(x1612)+~P1(x1611)+~P5(x1613)+~P11(x1611,x1612,x1613)+P3(f28(x1611,f30(x1612)),x1613)
% 0.20/0.70 [130]~P1(x1303)+~P1(x1304)+P3(x1301,x1302)+~E(f16(x1303,x1304),x1301)+~E(x1302,f27(x1303))
% 0.20/0.70 [132]~P4(x1324)+~P4(x1322)+~P3(x1321,x1323)+P3(x1321,x1322)+~E(x1323,f26(x1324,x1322))
% 0.20/0.70 [133]~P4(x1334)+~P4(x1332)+~P3(x1331,x1333)+P3(x1331,x1332)+~E(x1333,f26(x1332,x1334))
% 0.20/0.70 [174]~P4(x1742)+~P4(x1741)+~P3(x1744,x1743)+~E(x1743,f29(x1741,x1742))+P3(f21(x1741,x1742,x1743,x1744),x1741)
% 0.20/0.70 [175]~P4(x1752)+~P4(x1751)+~P3(x1754,x1753)+~E(x1753,f29(x1751,x1752))+P3(f22(x1751,x1752,x1753,x1754),x1752)
% 0.20/0.70 [182]~P4(x1822)+~P4(x1821)+~P3(x1824,x1823)+~E(x1823,f29(x1821,x1822))+E(f28(f21(x1821,x1822,x1823,x1824),f22(x1821,x1822,x1823,x1824)),x1824)
% 0.20/0.70 [155]~P1(x1553)+~P1(x1552)+~P4(x1551)+~P3(f11(x1552,x1551),x1551)+~E(f11(x1552,x1551),f16(x1552,x1553))+E(x1551,f27(x1552))
% 0.20/0.70 [164]~P1(x1643)+~P1(x1642)+~P2(x1641,x1643)+~P2(x1641,x1642)+P6(x1641,x1642,x1643)+P2(f13(x1642,x1643,x1641),x1643)
% 0.20/0.70 [165]~P1(x1653)+~P1(x1652)+~P2(x1651,x1653)+~P2(x1651,x1652)+P6(x1651,x1652,x1653)+P2(f13(x1652,x1653,x1651),x1652)
% 0.20/0.70 [166]~P4(x1661)+~P4(x1663)+~P4(x1662)+P3(f20(x1662,x1663,x1661),x1661)+P3(f23(x1662,x1663,x1661),x1662)+E(x1661,f29(x1662,x1663))
% 0.20/0.70 [167]~P4(x1671)+~P4(x1673)+~P4(x1672)+P3(f20(x1672,x1673,x1671),x1671)+P3(f24(x1672,x1673,x1671),x1673)+E(x1671,f29(x1672,x1673))
% 0.20/0.70 [168]~P4(x1681)+~P4(x1683)+~P4(x1682)+P3(f25(x1682,x1683,x1681),x1681)+P3(f25(x1682,x1683,x1681),x1683)+E(x1681,f26(x1682,x1683))
% 0.20/0.70 [169]~P4(x1691)+~P4(x1693)+~P4(x1692)+P3(f25(x1692,x1693,x1691),x1691)+P3(f25(x1692,x1693,x1691),x1692)+E(x1691,f26(x1692,x1693))
% 0.20/0.70 [170]~P1(x1703)+~P1(x1702)+~P2(x1701,x1703)+~P2(x1701,x1702)+P6(x1701,x1702,x1703)+~P8(f13(x1702,x1703,x1701),x1701)
% 0.20/0.70 [172]~P4(x1721)+~P4(x1723)+~P4(x1722)+P3(f20(x1722,x1723,x1721),x1721)+E(x1721,f29(x1722,x1723))+E(f28(f23(x1722,x1723,x1721),f24(x1722,x1723,x1721)),f20(x1722,x1723,x1721))
% 0.20/0.70 [162]~P2(x1621,x1623)+~P2(x1621,x1624)+~P6(x1622,x1624,x1623)+P8(x1621,x1622)+~P1(x1623)+~P1(x1624)
% 0.20/0.70 [140]~P4(x1404)+~P4(x1403)+~P3(x1401,x1404)+~P3(x1401,x1403)+P3(x1401,x1402)+~E(x1402,f26(x1403,x1404))
% 0.20/0.70 [173]~P1(x1734)+~P1(x1733)+~P5(x1732)+~P5(x1731)+P1(f6(x1731,x1732))+P1(f7(x1731,x1732,x1733,x1734))
% 0.20/0.70 [176]~P1(x1764)+~P1(x1763)+~P5(x1762)+~P5(x1761)+P11(f7(x1761,x1762,x1763,x1764),x1764,x1762)+P1(f6(x1761,x1762))
% 0.20/0.70 [177]~P1(x1774)+~P1(x1773)+~P5(x1772)+~P5(x1771)+P11(f7(x1771,x1772,x1773,x1774),x1773,x1771)+P1(f6(x1771,x1772))
% 0.20/0.70 [179]~P1(x1794)+~P1(x1793)+~P5(x1792)+~P5(x1791)+~P3(f6(x1791,x1792),f29(x1791,x1792))+P1(f7(x1791,x1792,x1793,x1794))
% 0.20/0.70 [180]~P1(x1804)+~P1(x1803)+~P5(x1802)+~P5(x1801)+P11(f7(x1801,x1802,x1803,x1804),x1804,x1802)+~P3(f6(x1801,x1802),f29(x1801,x1802))
% 0.20/0.70 [181]~P1(x1814)+~P1(x1813)+~P5(x1812)+~P5(x1811)+P11(f7(x1811,x1812,x1813,x1814),x1813,x1811)+~P3(f6(x1811,x1812),f29(x1811,x1812))
% 0.20/0.70 [178]~P4(x1781)+~P4(x1783)+~P4(x1782)+~P3(f25(x1782,x1783,x1781),x1781)+~P3(f25(x1782,x1783,x1781),x1783)+~P3(f25(x1782,x1783,x1781),x1782)+E(x1781,f26(x1782,x1783))
% 0.20/0.70 [150]~P4(x1504)+~P4(x1503)+~P3(x1506,x1504)+~P3(x1505,x1503)+P3(x1501,x1502)+~E(x1502,f29(x1503,x1504))+~E(f28(x1505,x1506),x1501)
% 0.20/0.70 [171]~P4(x1711)+~P4(x1713)+~P4(x1712)+~P3(x1715,x1713)+~P3(x1714,x1712)+~P3(f20(x1712,x1713,x1711),x1711)+E(x1711,f29(x1712,x1713))+~E(f28(x1714,x1715),f20(x1712,x1713,x1711))
% 0.20/0.70 %EqnAxiom
% 0.20/0.70 [1]E(x11,x11)
% 0.20/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.70 [4]~E(x41,x42)+E(f16(x41,x43),f16(x42,x43))
% 0.20/0.70 [5]~E(x51,x52)+E(f16(x53,x51),f16(x53,x52))
% 0.20/0.70 [6]~E(x61,x62)+E(f29(x61,x63),f29(x62,x63))
% 0.20/0.70 [7]~E(x71,x72)+E(f29(x73,x71),f29(x73,x72))
% 0.20/0.70 [8]~E(x81,x82)+E(f28(x81,x83),f28(x82,x83))
% 0.20/0.70 [9]~E(x91,x92)+E(f28(x93,x91),f28(x93,x92))
% 0.20/0.70 [10]~E(x101,x102)+E(f27(x101),f27(x102))
% 0.20/0.70 [11]~E(x111,x112)+E(f14(x111,x113),f14(x112,x113))
% 0.20/0.70 [12]~E(x121,x122)+E(f14(x123,x121),f14(x123,x122))
% 0.20/0.70 [13]~E(x131,x132)+E(f30(x131),f30(x132))
% 0.20/0.70 [14]~E(x141,x142)+E(f17(x141),f17(x142))
% 0.20/0.70 [15]~E(x151,x152)+E(f22(x151,x153,x154,x155),f22(x152,x153,x154,x155))
% 0.20/0.70 [16]~E(x161,x162)+E(f22(x163,x161,x164,x165),f22(x163,x162,x164,x165))
% 0.20/0.70 [17]~E(x171,x172)+E(f22(x173,x174,x171,x175),f22(x173,x174,x172,x175))
% 0.20/0.70 [18]~E(x181,x182)+E(f22(x183,x184,x185,x181),f22(x183,x184,x185,x182))
% 0.20/0.70 [19]~E(x191,x192)+E(f21(x191,x193,x194,x195),f21(x192,x193,x194,x195))
% 0.20/0.70 [20]~E(x201,x202)+E(f21(x203,x201,x204,x205),f21(x203,x202,x204,x205))
% 0.20/0.70 [21]~E(x211,x212)+E(f21(x213,x214,x211,x215),f21(x213,x214,x212,x215))
% 0.20/0.70 [22]~E(x221,x222)+E(f21(x223,x224,x225,x221),f21(x223,x224,x225,x222))
% 0.20/0.70 [23]~E(x231,x232)+E(f8(x231,x233),f8(x232,x233))
% 0.20/0.70 [24]~E(x241,x242)+E(f8(x243,x241),f8(x243,x242))
% 0.20/0.70 [25]~E(x251,x252)+E(f20(x251,x253,x254),f20(x252,x253,x254))
% 0.20/0.70 [26]~E(x261,x262)+E(f20(x263,x261,x264),f20(x263,x262,x264))
% 0.20/0.70 [27]~E(x271,x272)+E(f20(x273,x274,x271),f20(x273,x274,x272))
% 0.20/0.70 [28]~E(x281,x282)+E(f19(x281,x283),f19(x282,x283))
% 0.20/0.70 [29]~E(x291,x292)+E(f19(x293,x291),f19(x293,x292))
% 0.20/0.70 [30]~E(x301,x302)+E(f24(x301,x303,x304),f24(x302,x303,x304))
% 0.20/0.70 [31]~E(x311,x312)+E(f24(x313,x311,x314),f24(x313,x312,x314))
% 0.20/0.70 [32]~E(x321,x322)+E(f24(x323,x324,x321),f24(x323,x324,x322))
% 0.20/0.70 [33]~E(x331,x332)+E(f6(x331,x333),f6(x332,x333))
% 0.20/0.70 [34]~E(x341,x342)+E(f6(x343,x341),f6(x343,x342))
% 0.20/0.70 [35]~E(x351,x352)+E(f7(x351,x353,x354,x355),f7(x352,x353,x354,x355))
% 0.20/0.70 [36]~E(x361,x362)+E(f7(x363,x361,x364,x365),f7(x363,x362,x364,x365))
% 0.20/0.70 [37]~E(x371,x372)+E(f7(x373,x374,x371,x375),f7(x373,x374,x372,x375))
% 0.20/0.70 [38]~E(x381,x382)+E(f7(x383,x384,x385,x381),f7(x383,x384,x385,x382))
% 0.20/0.70 [39]~E(x391,x392)+E(f4(x391),f4(x392))
% 0.20/0.70 [40]~E(x401,x402)+E(f23(x401,x403,x404),f23(x402,x403,x404))
% 0.20/0.70 [41]~E(x411,x412)+E(f23(x413,x411,x414),f23(x413,x412,x414))
% 0.20/0.70 [42]~E(x421,x422)+E(f23(x423,x424,x421),f23(x423,x424,x422))
% 0.20/0.70 [43]~E(x431,x432)+E(f26(x431,x433),f26(x432,x433))
% 0.20/0.70 [44]~E(x441,x442)+E(f26(x443,x441),f26(x443,x442))
% 0.20/0.70 [45]~E(x451,x452)+E(f3(x451),f3(x452))
% 0.20/0.70 [46]~E(x461,x462)+E(f12(x461,x463,x464),f12(x462,x463,x464))
% 0.20/0.70 [47]~E(x471,x472)+E(f12(x473,x471,x474),f12(x473,x472,x474))
% 0.20/0.70 [48]~E(x481,x482)+E(f12(x483,x484,x481),f12(x483,x484,x482))
% 0.20/0.70 [49]~E(x491,x492)+E(f18(x491),f18(x492))
% 0.20/0.70 [50]~E(x501,x502)+E(f11(x501,x503),f11(x502,x503))
% 0.20/0.70 [51]~E(x511,x512)+E(f11(x513,x511),f11(x513,x512))
% 0.20/0.70 [52]~E(x521,x522)+E(f10(x521,x523),f10(x522,x523))
% 0.20/0.70 [53]~E(x531,x532)+E(f10(x533,x531),f10(x533,x532))
% 0.20/0.70 [54]~E(x541,x542)+E(f25(x541,x543,x544),f25(x542,x543,x544))
% 0.20/0.70 [55]~E(x551,x552)+E(f25(x553,x551,x554),f25(x553,x552,x554))
% 0.20/0.70 [56]~E(x561,x562)+E(f25(x563,x564,x561),f25(x563,x564,x562))
% 0.20/0.70 [57]~E(x571,x572)+E(f9(x571,x573),f9(x572,x573))
% 0.20/0.70 [58]~E(x581,x582)+E(f9(x583,x581),f9(x583,x582))
% 0.20/0.70 [59]~E(x591,x592)+E(f13(x591,x593,x594),f13(x592,x593,x594))
% 0.20/0.70 [60]~E(x601,x602)+E(f13(x603,x601,x604),f13(x603,x602,x604))
% 0.20/0.70 [61]~E(x611,x612)+E(f13(x613,x614,x611),f13(x613,x614,x612))
% 0.20/0.70 [62]~E(x621,x622)+E(f5(x621,x623),f5(x622,x623))
% 0.20/0.70 [63]~E(x631,x632)+E(f5(x633,x631),f5(x633,x632))
% 0.20/0.70 [64]~P1(x641)+P1(x642)+~E(x641,x642)
% 0.20/0.70 [65]P3(x652,x653)+~E(x651,x652)+~P3(x651,x653)
% 0.20/0.70 [66]P3(x663,x662)+~E(x661,x662)+~P3(x663,x661)
% 0.20/0.70 [67]~P4(x671)+P4(x672)+~E(x671,x672)
% 0.20/0.70 [68]P10(x682,x683)+~E(x681,x682)+~P10(x681,x683)
% 0.20/0.70 [69]P10(x693,x692)+~E(x691,x692)+~P10(x693,x691)
% 0.20/0.70 [70]~P5(x701)+P5(x702)+~E(x701,x702)
% 0.20/0.70 [71]P2(x712,x713)+~E(x711,x712)+~P2(x711,x713)
% 0.20/0.70 [72]P2(x723,x722)+~E(x721,x722)+~P2(x723,x721)
% 0.20/0.70 [73]P6(x732,x733,x734)+~E(x731,x732)+~P6(x731,x733,x734)
% 0.20/0.70 [74]P6(x743,x742,x744)+~E(x741,x742)+~P6(x743,x741,x744)
% 0.20/0.70 [75]P6(x753,x754,x752)+~E(x751,x752)+~P6(x753,x754,x751)
% 0.20/0.70 [76]P11(x762,x763,x764)+~E(x761,x762)+~P11(x761,x763,x764)
% 0.20/0.70 [77]P11(x773,x772,x774)+~E(x771,x772)+~P11(x773,x771,x774)
% 0.20/0.70 [78]P11(x783,x784,x782)+~E(x781,x782)+~P11(x783,x784,x781)
% 0.20/0.70 [79]P8(x792,x793)+~E(x791,x792)+~P8(x791,x793)
% 0.20/0.70 [80]P8(x803,x802)+~E(x801,x802)+~P8(x803,x801)
% 0.20/0.70 [81]P9(x812,x813)+~E(x811,x812)+~P9(x811,x813)
% 0.20/0.70 [82]P9(x823,x822)+~E(x821,x822)+~P9(x823,x821)
% 0.20/0.70 [83]~P7(x831)+P7(x832)+~E(x831,x832)
% 0.20/0.70
% 0.20/0.70 %-------------------------------------------
% 0.20/0.70 cnf(184,plain,
% 0.20/0.70 ($false),
% 0.20/0.70 inference(scs_inference,[],[90,91,93,2,107]),
% 0.20/0.70 ['proof']).
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time :0.000000s
%------------------------------------------------------------------------------